Georgia State Standards for Mathematics:

GA.MKN. NUMBER AND OPERATIONS: Students will correctly represent the number and order of objects using numbers and understand them.

MKN1. Students will connect numerals to the quantities they represent.

MKN1.a. Count a number of objects up to 30.

MKN1.b. Produce models for number words through ten.

MKN1.c. Write numerals through 20 to label sets.

MKN1.d. Sequence and identify using ordinal numbers (1st-10th).

MKN1.e. Compare two or more sets of objects (1-10) and identify which set is equal to, more than, or less than the other.

MKN1.f. Estimate quantities using five and ten as a benchmark. (e.g. 9 is one five and four more. It is closer to 10, which can be represented as one ten or two fives, than it is to five.)

MKN1.g. Use informal strategies to share objects equally (divide) between two to three people or sets.

MKN1.h. Identify coins by name and value (penny, nickel, dime, and quarter).

MKN1.i. Count out pennies to buy items that together cost less than 30 cents.

MKN1.j. Make fair trades using combinations involving pennies and nickels and pennies and dimes.

MKN2. Students will use representations to model addition and subtraction.

MKN2.a. Use counting strategies to find out how many items are in two sets when they are combined, separated, or compared.

MKN2.b. Build number combinations up to 10 (e.g., 4 and 1, 2 and 3, 3 and 2, 4 and 1 for five) and for doubles to 10 (3 and 3 for six).

MKN2.c. Use objects, pictures, numbers, or words to create, solve and explain story problems (combining, separating, or comparing) for two numbers that are each less than 10.

GA.MKM. MEASUREMENT: Students will explore quantitative situations involving, length, capacity, weight, and height by direct comparison. Students will explore time through calendars and schedules.

MKM1. Students will group objects according to common properties such as longer/shorter, more/less, taller/shorter, and heavier/lighter.

MKM1.a. Compare and order objects on the basis of length.

MKM1.b. Compare and order objects on the basis of capacity.

MKM1.c. Compare and order objects on the basis of height.

MKM1.d. Compare and order objects on the basis of weight.

MKM2. Students will understand the measurement of calendar time.

MKM2.a. Know the names of the days of the week, as well as understand yesterday, today and tomorrow.

MKM2.b. Know the months of the year.

MKM2.c. Know the four seasons.

MKM3. Students will understand time as it relates to a daily schedule.

MKM3.a. Order daily events.

MKM3.b. Tell the time when daily events occur, such as morning, afternoon, and evening.

MKM3.c. Know the name of the day of the week when weekly events occur in class

GA.MKG. GEOMETRY: Students will recognize and name basic geometric shapes and spatial relationships.

MKG1. Students will correctly name simple two and three-dimensional figures, and recognize them in the environment.

MKG1.a. Recognize and name the following basic two-dimensional figures: triangles, quadrilaterals (rectangles, squares) and circles.

MKG1.b. Recognize and name the following three-dimensional figures: spheres and cubes.

MKG1.c. Observe concrete objects in the environment and represent the objects using basic shapes.

MKG1.d. Combine basic figures to form other basic and complex figures into basic figures; decompose basic and complex figures into basic figures.

MKG1.e. Compare geometric shapes and identify similarities and differences of the following two and three-dimensional shapes: triangles, rectangles, squares, circles, spheres, and cubes.

MKG2. Students will understand basic spatial relationships.

MKG2.a. Identify when an object is beside another object, above another object, or below another object.

MKG2.b. Identify when an object is in front of another object, behind another object, inside another object, or outside it.

MKG3. Students will identify, create, extend, and transfer patterns from one representation to another using actions, objects, and geometric shapes.

MKG3.a. Identify missing elements within a given pattern.

MKG3.b. Extend a given pattern and recognize similarities in different patterns.

MKG3.c. Create a pattern in a different context with attributes similar to a given pattern.

GA.MKD. DATA ANALYSIS AND PROBABILITY: Students will pose questions and gather data about themselves and their surroundings.

MKD1. Students will pose information questions, collect data, organize, and display results using objects, pictures, and picture graphs.

GA.MKP. PROCESS STANDARDS

MKP1. Students will solve problems (using appropriate technology).

MKP1.a. Build new mathematical knowledge through problem solving.

MKP1.b. Solve problems that arise in mathematics and in other contexts.

MKP1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MKP1.d. Monitor and reflect on the process of mathematical problem solving.

MKP2. Students will reason and evaluate mathematical arguments.

MKP2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MKP2.b. Make and investigate mathematical conjectures.

MKP2.c. Develop and evaluate mathematical arguments and proofs.

MKP2.d. Select and use various types of reasoning and methods of proof.

MKP3. Students will communicate mathematically.

MKP3.a. Organize and consolidate their mathematical thinking through communication.

MKP3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MKP3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MKP3.d. Use the language of mathematics to express mathematical ideas precisely.

MKP4. Students will make connections among mathematical ideas and to other disciplines.

MKP4.a. Recognize and use connections among mathematical ideas.

MKP4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MKP4.c. Recognize and apply mathematics in contexts outside of mathematics.

MKP5. Students will represent mathematics in multiple ways.

MKP5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MKP5.b. Select, apply, and translate among mathematical representations to solve problems.

MKP5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.M1N. NUMBER AND OPERATIONS: Students will understand how to represent numbers, and be able to add and subtract small numbers.

M1N1. Students will estimate, model, compare, order, and represent whole numbers up to 100.

M1N1.a. Represent numbers up to 100 using a variety of models, diagrams, and number sentences. Represent numbers larger than 10 in terms of tens and ones using manipulatives and pictures.

M1N1.b. Correctly count and represent the number of objects in set using numerals.

M1N1.c. Compare small sets using the terms greater than, less than, and equal to.

M1N1.d. Understand the magnitude and order of numbers up to 100 by making ordered sequences and representing them on a number line.

M1N1.e. Exchange equivalent quantities of coins by making fair trades involving combinations of pennies, nickels, dimes, and quarters up to one dollar; count out a combination of coins needed to purchase items up to one dollar.

M1N1.f. Identify bills ($1, $5, $10, $20) by name and value and exchange equivalent quantities by making fair trades involving combinations of bills; count out a combination of bills needed to purchase items that total up to twenty dollars.

M1N2. Students will understand place value notation for the numbers 1 to 99. (Discussions may allude to 3-digit numbers to assist in understanding place value.)

M1N2.a. Determine to which ten a given number is closest using tools such as a sequential number line or chart.

M1N2.b. Represent collections of less than 30 objects with 2-digit numbers and understand the meaning of place value.

M1N2.c. Decompose numbers from 10 to 99 as the appropriate number of tens and ones.

M1N3. Students will add and subtract numbers less than 100, as well as understand and use the inverse relationship between addition and subtraction.

M1N3.a. Identify one more than, one less than, 10 more than, and 10 less than a given number.

M1N3.b. Skip-count by 2s, 5s, and 10s, forward and backwards; to and from numbers up to 100.

M1N3.c. Compose/decompose numbers up to 10 (e. g. 3+5=8, 8=5+2+1).

M1N3.d. Understand a variety of situations to which subtraction may apply: taking away from a set, comparing two sets, and determining how many more or how many less.

M1N3.e. Understand addition and subtraction number combinations using strategies such as counting on, counting back, doubles and making tens.

M1N3.f. Know the single-digit addition facts to 18 and corresponding subtraction facts with understanding and fluency. (Use strategies such as relating to facts already known, applying the commutative property, and grouping facts into families.)

M1N3.g. Apply addition and subtraction to 2 digit numbers without regrouping (e.g.15 + 4, 80-60, 56 + 10, 100-30, 52 + 5).

M1N3.h. Solve and create word problems involving addition and subtraction to 100 without regrouping. Use words, pictures and concrete models to interpret story problems and reflect the combining of sets as addition and taking away or comparing elements of sets as subtraction.

M1N4. Students will count collections of up to 100 objects by dividing them into equal parts and represent the results using words, pictures, or diagrams.

M1N4.a. Use informal strategies to share objects equally between two to five people.

M1N4.b. Build number patterns, including concepts of even and odd, using various concrete representations. (Examples of concrete representations include a hundreds chart, ten grid frame, place value chart, number line, counters, or other objects.)

M1N4.c. Identify, label, and relate fractions (halves, fourths) as equal parts of a collection of objects or a whole using pictures and models.

M1N4.d. Understand halves and fourths as representations of equal parts of a whole.

GA.M1M. MEASUREMENT: Students will measure basic quantitative attributes of concrete objects.

M1M1. Students will compare and/or order the length, height, weight, or capacity of two or more objects by using direct comparison or a nonstandard unit.

M1M1.a. Directly compare and/or order length, height, weight, and capacity of concrete objects.

M1M1.b. Estimate and measure using a non-standard unit that is smaller than the object to be measured.

M1M1.c. Measure with a tool by creating a '''ruled'' stick, tape, or container by marking off ten segments of the repeated single unit.

M1M2. Students will develop an understanding of the measurement of time.

M1M2.a. Tell time to the nearest hour and half hour and understand the movement of the minute hand and how it relates to the hour hand.

M1M2.b. Begin to understand the relationship of calendar time by knowing the number of days in a week and months in a year.

M1M2.c. Compare and/or order the sequence or duration of events (e.g., shorter/longer and before/after).

GA.M1G. GEOMETRY: Students will understand the concepts of basic geometric shapes and spatial relationships of concrete objects.

M1G1. Students will study and create various two and three-dimensional figures and identify basic figures (squares, circles, triangles, and rectangles) within them.

M1G1.a. Build, draw, name, and describe triangles, rectangles, pentagons, and hexagons.

M1G1.b. Build, represent, name, and describe cylinders, cones, and rectangular prisms.

M1G1.c. Create pictures and designs using shapes, including overlapping shapes.

M1G2. Students will compare, contrast, and/or classify geometric shapes by the common attributes of position, shape, size, number of sides, and number of corners.

M1G3. Students will arrange and describe objects in space by proximity, position, and direction (near, far, below, above, up, down, behind, in front of, next to, and left or right of).

GA.M1D. DATA ANALYSIS AND PROBABILITY: Students will pose questions, collect, organize and interpret data about themselves and their surroundings.

M1D1. Students will create simple tables and graphs and interpret them.

M1D1.a. Interpret tally marks, picture graphs, and bar graphs.

M1D1.b. Pose questions, collect, sort, organize and record data using objects, pictures, tally marks, picture graphs, and bar graphs.

GA.M1P. PROCESS STANDARDS

M1P1. Students will solve problems (using appropriate technology).

M1P1.a. Build new mathematical knowledge through problem solving.

M1P1.b. Solve problems that arise in mathematics and in other contexts.

M1P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

M1P1.d. Monitor and reflect on the process of mathematical problem solving.

M1P2. Students will reason and evaluate mathematical arguments.

M1P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

M1P2.b. Make and investigate mathematical conjectures.

M1P2.c. Develop and evaluate mathematical arguments and proofs.

M1P2.d. Select and use various types of reasoning and methods of proof.

M1P3. Students will communicate mathematically.

M1P3.a. Organize and consolidate their mathematical thinking through communication.

M1P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

M1P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

M1P3.d. Use the language of mathematics to express mathematical ideas precisely.

M1P4. Students will make connections among mathematical ideas and to other disciplines.

M1P4.a. Recognize and use connections among mathematical ideas.

M1P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

M1P4.c. Recognize and apply mathematics in contexts outside of mathematics.

M1P5. Students will represent mathematics in multiple ways.

M1P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

M1P5.b. Select, apply, and translate among mathematical representations to solve problems.

M1P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.M2N. NUMBER AND OPERATIONS: Students will further develop their understanding of numbers (including fractions) and how to represent them. The students will understand and apply addition, subtraction and multiplication through concrete manipulation and perform basic calculations.

M2N1. Students will use multiple representations of numbers to connect symbols to quantities.

M2N1.a. Represent numbers using a variety of models, diagrams, and number sentences (e.g., 4703 represented as 4,000 + 700 + 3, and units, 47 hundreds + 3, or 4,500 + 203).

M2N1.b. Understand the relative magnitudes of numbers using 10 as a unit, 100 as a unit, or 1000 as a unit. Represent 2-digit numbers with drawings of tens and ones and 3-digit numbers with drawings of hundreds, tens, and ones.

M2N1.c. Use money as a medium of exchange. Make change and use decimal notation and the dollar and cent symbols to represent the collection of coins and currency.

M2N2. Students will build fluency with multi-digit addition and subtraction.

M2N2.a. Correctly add and subtract two whole numbers up to three digits each with regrouping.

M2N2.b. Understand and use the inverse relation between addition and subtraction to solve problems and check solutions.

M2N2.c. Use mental math strategies such as benchmark numbers to solve problems.

M2N2.d. Use basic properties of addition (commutative, associative, and identity) to simplify problems (e.g. 98 + 17 by taking two from 17 and adding it to the 98 to make 100 and replacing the original problem by the sum 100 + 15).

M2N2.e. Estimate to determine if solutions are reasonable for addition and subtraction.

M2N3. Students will understand multiplication, multiply numbers, and verify results.

M2N3.a. Understand multiplication as repeated addition.

M2N3.b. Use repeated addition, arrays, and counting by multiples (skip counting) to correctly multiply 1-digit numbers and construct the multiplication table.

M2N3.c. Use the multiplication table (grid) to determine a product of two numbers.

M2N3.d. Use repeated subtraction, equal sharing, and forming equal groups to divide large collections of objects and determine factors for multiplication.

M2N4. Students will understand and compare fractions.

M2N4.a. Model, identify, label, and compare fractions (thirds, sixths, eighths, tenths) as a representation of equal parts of a whole or of a set.

M2N4.b. Know that when all fractional parts are included, such as three thirds, the result is equal to the whole.

M2N5. Students will represent and interpret quantities and relationships using mathematical expressions including equality and inequality signs (=, >, <, not equal to).

M2N5.a. Include the use of boxes or ___ to represent a missing value.

M2N5.b. Represent problem solving situations where addition, subtraction or multiplication may be applied using mathematical expressions.

GA.M2M. MEASUREMENT: Students will understand length, time, and temperature and choose an appropriate tool to measure them.

M2M1. Students will know the standard units of inch, foot, yard, and metric units of centimeter and meter and measure length to the nearest inch or centimeter.

M2M1.a. Compare the relationship of one unit to another by measuring objects twice using different units each time.

M2M1.b. Estimate lengths, and then measure to determine if estimations were reasonable.

M2M1.c. Determine an appropriate tool and unit for measuring.

M2M2. Students will tell time to the nearest five minutes and know relationships of time such as the number of seconds in a minute, minutes in an hour and hours in a day.

M2M3. Students will explore temperature.

M2M3.a. Determine a reasonable temperature for a given situation.

M2M3.b. Read a thermometer.

GA.M2G. GEOMETRY: Students will understand basic and compound geometric shapes together with the elements from which they are composed.

M2G1. Students will describe and classify plane figures (triangles, square, rectangle, trapezoid, quadrilateral, pentagon, hexagon, and irregular polygonal shapes) according to the number of sides and vertices and the sizes of angles (right angle, obtuse, acute).

M2G2. Students will describe and classify solid geometric figures (prisms, pyramids, cylinders, cones, and spheres) according to such things as the number of edges and vertices and the number and shape of faces and angles.

M2G2.a. Recognize the (plane) shapes of the faces of a geometric solid and count the number of faces of each type.

M2G2.b. Recognize the shape of an angle as a right angle, an obtuse, or acute angle.

M2G3. Students will describe the change in attributes as two and three-dimensional shapes are cut and rearranged.

GA.M2D. DATA ANALYSIS AND PROBABILITY: Students will pose questions, collect, organize, and interpret data about themselves and their surroundings.

M2D1. Students will create simple tables and graphs and interpret their meaning.

M2D1.a. Create, organize and display data using pictographs, Venn diagrams, bar graphs, picture graphs, simple charts, and tables to record results with scales of 1, 2 and 5.

M2D1.b. Know how to interpret picture graphs, Venn diagrams, and bar graphs.

GA.M2P. PROCESS STANDARDS

M2P1. Students will solve problems (using appropriate technology).

M2P1.a. Build new mathematical knowledge through problem solving.

M2P1.b. Solve problems that arise in mathematics and in other contexts.

M2P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

M2P1.d. Monitor and reflect on the process of mathematical problem solving.

M2P2. Students will reason and evaluate mathematical arguments.

M2P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

M2P2.b. Make and investigate mathematical conjectures.

M2P2.c. Develop and evaluate mathematical arguments and proofs.

M2P2.d. Select and use various types of reasoning and methods of proof.

M2P3. Students will communicate mathematically.

M2P3.a. Organize and consolidate their mathematical thinking through communication.

M2P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

M2P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

M2P3.d. Use the language of mathematics to express mathematical ideas precisely.

M2P4. Students will make connections among mathematical ideas and to other disciplines.

M2P4.a. Recognize and use connections among mathematical ideas.

M2P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

M2P4.c. Recognize and apply mathematics in contexts outside of mathematics.

M2P5. Students will represent mathematics in multiple ways.

M2P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

M2P5.b. Select, apply, and translate among mathematical representations to solve problems.

M2P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.M3N. NUMBER AND OPERATIONS: Students will use decimal fractions and common fractions to represent parts of a whole. They will also understand the four arithmetic operations for whole numbers and use them in basic calculations, and apply them in problem solving situations.

M3N1. Students will further develop their understanding of whole numbers and decimals and ways of representing them.

M3N1.a. Identify place values from tenths through ten thousands.

M3N1.b. Understand the relative sizes of digits in place value notation (10 times, 100 times, 1/10 of a single digit whole number) and ways to represent them including word name, standard form, and expanded form.

M3N2. Students will further develop their skills of addition and subtraction and apply them in problem solving.

M3N2.a. Use the properties of addition and subtraction to compute and verify the results of computation.

M3N2.b. Use mental math and estimation strategies to add and subtract.

M3N2.c. Solve problems requiring addition and subtraction.

M3N2.d. Model addition and subtraction by counting back change using the fewest number of coins.

M3N3. Students will further develop their understanding of multiplication of whole numbers and develop the ability to apply it in problem solving.

M3N3.a. Describe the relationship between addition and multiplication, i.e. multiplication is defined as repeated addition.

M3N3.b. Know the multiplication facts with understanding and fluency to 10 x 10.

M3N3.c. Use arrays and area models to develop understanding of the distributive property and to determine partial products for multiplication of 2- or 3-digit numbers by a 1-digit number.

M3N3.d. Understand the effect on the product when multiplying by multiples of 10.

M3N3.e. Apply the identity, commutative, and associative properties of multiplication and verify the results.

M3N3.f. Use mental math and estimation strategies to multiply.

M3N3.g. Solve problems requiring multiplication.

M3N4. Students will understand the meaning of division and develop the ability to apply it in problem solving.

M3N4.a. Understand the relationship between division and multiplication and between division and subtraction.

M3N4.b. Recognize that division may be two situations: the first is determining how many equal parts of a given size or amount may be taken away from the whole as in repeated subtraction, and the second is determining the size of the parts when the whole is separated into a given number of equal parts as in a sharing model.

M3N4.c. Recognize problem-solving situations in which division may be applied and write corresponding mathematical expressions.

M3N4.d. Explain the meaning of a remainder in division in different circumstances.

M3N4.e. Divide a 2 and 3-digit number by a 1-digit divisor.

M3N4.f. Solve problems requiring division.

M3N4.g. Use mental math strategies to divide.

M3N5. Students will understand the meaning of decimal fractions and common fractions in simple cases and apply them in problem-solving situations.

M3N5.a. Identify fractions that are decimal fractions and/or common fractions.

M3N5.b. Understand that a decimal fraction (i.e. 3/10) can be written as a decimal (i.e. 0.3).

M3N5.c. Understand the fraction a/b represents a equal sized parts of a whole that is divided into b equal sized parts.

M3N5.d. Know and use decimal fractions and common fractions to represent the size of parts created by equal divisions of a whole.

M3N5.e. Understand the concept of addition and subtraction of decimal fractions and common fractions with like denominators.

M3N5.f. Model addition and subtraction of decimal fractions and common fractions with like denominators.

M3N5.g. Use mental math and estimation strategies to add and subtract decimal fractions and common fractions with like denominators.

M3N5.h. Solve problems involving decimal fractions and common fractions with like denominators.

GA.M3M. MEASUREMENT: Students will understand and measure time and length. They will also model and calculate perimeter and area of simple geometric figures.

M3M1. Students will further develop their understanding of the concept of time by determining elapsed time of a full, half, and quarter-hour.

M3M2. Students will measure length choosing appropriate units and tools.

M3M2.a. Use the units kilometer (km) and mile (mi.) to discuss the measure of long distances.

M3M2.b. Measure to the nearest 1/4 inch, 1/2 inch and millimeter (mm) in addition to the previously learned inch, foot, yard, centimeter, and meter.

M3M2.c. Estimate length and represent it using appropriate units.

M3M2.d. Compare one unit to another within a single system of measurement.

M3M3. Students will understand and measure the perimeter of geometric figures.

M3M3.a. Understand the meaning of the linear unit and measurement in perimeter.

M3M3.b. Understand the concept of perimeter as being the length of the boundary of a geometric figure.

M3M3.c. Determine the perimeter of a geometric figure by measuring and summing the lengths of the sides.

M3M4. Students will understand and measure the area of simple geometric figures (squares and rectangles).

M3M4.a. Understand the meaning of the square unit and measurement in area.

M3M4.b. Model (by tiling) the area of a simple geometric figure using square units (square inch, square foot, etc.).

M3M4.c. Determine the area of squares and rectangles by counting, addition, and multiplication with models.

GA.M3G. GEOMETRY: Students will further develop their understanding of characteristics of previously studied geometric figures.

M3G1. Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties.

M3G1.a. Draw and classify previously learned fundamental geometric figures and scalene, isosceles, and equilateral triangles.

M3G1.b. Identify and compare the properties of fundamental geometric figures.

M3G1.c. Examine and compare angles of fundamental geometric figures.

M3G1.d. Identify the center, diameter, and radius of a circle.

GA.M3A. ALGEBRA: Students will understand how to express relationships as mathematical expressions.

M3A1. Students will use mathematical expressions to represent relationships between quantities and interpret given expressions.

M3A1.a. Describe and extend numeric and geometric patterns.

M3A1.b. Describe and explain a quantitative relationship represented by a formula (such as the perimeter of a geometric figure).

M3A1.c. Use a symbol, such as a square and triangle, to represent an unknown and find the value of the unknown in a number sentence.

GA.M3D. DATA ANALYSIS AND PROBABILITY: Students will gather, organize, and display data and interpret graphs.

M3D1. Students will create and interpret simple tables and graphs.

M3D1.a. Solve problems by organizing and displaying data in charts, tables, and graphs.

M3D1.b. Construct and interpret line plot graphs, pictographs, Venn diagrams, and bar graphs using scale increments of 1, 2, 5, and 10.

GA.M3P. PROCESS STANDARDS

M3P1. Students will solve problems (using appropriate technology).

M3P1.a. Build new mathematical knowledge through problem solving.

M3P1.b. Solve problems that arise in mathematics and in other contexts.

M3P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

M3P1.d. Monitor and reflect on the process of mathematical problem solving.

M3P2. Students will reason and evaluate mathematical arguments.

M3P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

M3P2.b. Make and investigate mathematical conjectures.

M3P2.c. Develop and evaluate mathematical arguments and proofs.

M3P2.d. Select and use various types of reasoning and methods of proof.

M3P3. Students will communicate mathematically.

M3P3.a. Organize and consolidate their mathematical thinking through communication.

M3P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

M3P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

M3P3.d. Use the language of mathematics to express mathematical ideas precisely.

M3P4. Students will make connections among mathematical ideas and to other disciplines.

M3P4.a. Recognize and use connections among mathematical ideas.

M3P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

M3P4.c. Recognize and apply mathematics in contexts outside of mathematics.

M3P5. Students will represent mathematics in multiple ways.

M3P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

M3P5.b. Select, apply, and translate among mathematical representations to solve problems.

M3P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.M4N. NUMBER AND OPERATIONS: Students will further develop their understanding of whole numbers and master the four basic operations with whole numbers by solving problems. They will also understand rounding and when to use it appropriately. Students will further develop their understanding of addition and subtraction of decimal fractions and common fractions with like denominators.

M4N1. Students will further develop their understanding of how whole numbers and decimals are represented in the base-ten numeration system.

M4N1.a. Identify place value names and places from hundredths through one million.

M4N1.b. Equate a number's word name, its standard form, and its expanded form.

M4N2. Students will understand and apply the concept of rounding numbers.

M4N2.a. Round numbers to the nearest ten, hundred, or thousand.

M4N2.b. Describe situations in which rounding numbers would be appropriate and determine whether to round to the nearest ten, hundred, or thousand.

M4N2.c. Determine to which whole number or tenth a given decimal is closest using tools such as a number line, and/or charts.

M4N2.d. Round a decimal to the nearest whole number or tenth.

M4N2.e. Represent the results of computation as a rounded number when appropriate and estimate a sum or difference by rounding numbers.

M4N3. Students will solve problems involving multiplication of 2-3 digit numbers by 1 or 2 digit numbers.

M4N4. Students will further develop their understanding of division of whole numbers and divide in problem solving situations without calculators.

M4N4.a. Know the division facts with understanding and fluency.

M4N4.b. Solve problems involving division by 1 or 2-digit numbers (including those that generate a remainder).

M4N4.c. Understand the relationship between dividend, divisor, quotient, and remainder.

M4N4.d. Understand and explain the effect on the quotient of multiplying or dividing both the divisor and dividend by the same number. (2050 / 50 yields the same answer as 205 / 5).

M4N5. Students will further develop their understanding of the meaning of decimals and use them in computations.

M4N5.a. Understand decimals are a part of the base-ten system.

M4N5.b. Understand the relative size of numbers and order two digit decimals.

M4N5.c. Add and subtract both one and two digit decimals.

M4N5.d. Model multiplication and division of decimals by whole numbers.

M4N5.e. Multiply and divide both one and two digit decimals by whole numbers.

M4N6. Students will further develop their understanding of the meaning of decimal fractions and common fractions and use them in computations.

M4N6.a. Understand representations of equivalent common fractions and/or decimal fractions.

M4N6.b. Add and subtract fractions and mixed numbers with like denominators. (Denominators should not exceed twelve.)

M4N6.c. Use mixed numbers and improper fractions interchangeably.

M4N7. Students will explain and use properties of the four arithmetic operations to solve and check problems.

M4N7.a. Describe situations in which the four operations may be used and the relationships among them.

M4N7.b. Compute using the order of operations, including parentheses.

M4N7.c. Compute using the commutative, associative, and distributive properties.

M4N7.d. Use mental math and estimation strategies to compute.

GA.M4M. MEASUREMENT: Students will measure weight in appropriate metric and standard units. They will also measure angles.

M4M1. Students will understand the concept of weight and how to measure weight.

M4M1.a. Use standard and metric units to measure the weight of objects.

M4M1.b. Know units used to measure weight (gram, kilogram, ounces, pounds, and tons).

M4M1.c. Compare one unit to another within a single system of measurement.

M4M2. Students will understand the concept of angles and how to measure them.

M4M2.a. Use tools, such as a protractor or angle ruler, and other methods such as paper folding, drawing a diagonal in a square, to measure angles.

M4M2.b. Understand the meaning and measure of a half rotation (180 degrees) and a full rotation (360 degrees).

M4M2.c. Determine that the sum of the three angles of a triangle is always 180 degrees.

GA.M4G. GEOMETRY: Students will understand and build plane and solid geometric figures. They will also graph points on the coordinate plane.

M4G1. Students will define and identify the characteristics of geometric figures through examination and construction.

M4G1.a. Examine and compare angles in order to classify and identify triangles by their angles.

M4G1.b. Describe parallel and perpendicular lines in plane geometric figures.

M4G1.c. Examine and classify quadrilaterals (including parallelograms, squares, rectangles, trapezoids, and rhombi) by their properties.

M4G1.d. Compare and contrast the relationships among quadrilaterals.

M4G2. Students will understand fundamental solid figures.

M4G2.a. Compare and contrast a cube and a rectangular prism in terms of the number and shape of their faces, edges, and vertices.

M4G2.b. Describe parallel and perpendicular lines and planes in connection with the rectangular prism.

M4G2.c. Build/collect models for solid geometric figures (cubes, prisms, cylinders, pyramids, spheres, and cones) using nets and other representations.

M4G3. Students will use the coordinate system.

M4G3.a. Understand and apply ordered pairs in the first quadrant of the coordinate system.

M4G3.b. Locate a point in the first quadrant in the coordinate plane and name the ordered pair.

M4G3.c. Graph ordered pairs in the first quadrant.

GA.M4A. ALGEBRA: Students will investigate and represent mathematical relationships between quantities using mathematical expressions in problem-solving situations.

M4A1. Students will represent and interpret mathematical relationships in quantitative expressions.

M4A1.a. Understand and apply patterns and rules to describe relationships and solve problems.

M4A1.b. Represent unknowns using symbols, such as a square and a triangle.

M4A1.c. Write and evaluate mathematical expressions using symbols and different values.

GA.M4D. DATA ANALYSIS AND PROBABILITY: Students will gather, organize, and display data. They will also compare features of graphs.

M4D1. Students will gather, organize, and display data according to the situation and compare related features.

M4D1.a. Construct and interpret line graphs, line plot graphs, pictographs, Venn diagrams, and bar graphs.

M4D1.b. Investigate the features and tendencies of graphs.

M4D1.c. Compare different graphical representations for a given set of data.

M4D1.d. Identify missing information and duplications in data.

M4D1.e. Determine and justify the range, mode, and median of a set of data.

GA.M4P. PROCESS STANDARDS

M4P1. Students will solve problems (using appropriate technology).

M4P1.a. Build new mathematical knowledge through problem solving.

M4P1.b. Solve problems that arise in mathematics and in other contexts.

M4P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

M4P1.d. Monitor and reflect on the process of mathematical problem solving.

M4P2. Students will reason and evaluate mathematical arguments.

M4P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

M4P2.b. Make and investigate mathematical conjectures.

M4P2.c. Develop and evaluate mathematical arguments and proofs.

M4P2.d. Select and use various types of reasoning and methods of proof.

M4P3. Students will communicate mathematically.

M4P3.a. Organize and consolidate their mathematical thinking through communication.

M4P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

M4P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

M4P3.d. Use the language of mathematics to express mathematical ideas precisely.

M4P4. Students will make connections among mathematical ideas and to other disciplines.

M4P4.a. Recognize and use connections among mathematical ideas.

M4P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

M4P4.c. Recognize and apply mathematics in contexts outside of mathematics.

M4P5. Students will represent mathematics in multiple ways.

M4P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

M4P5.b. Select, apply, and translate among mathematical representations to solve problems.

M4P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.M5N. NUMBER AND OPERATIONS: Students will further develop their understanding of the concept of whole numbers. They will also understand the meanings of multiplication and division of decimals and use decimals and common fractions in computation, as well as in problem solving situations.

M5N1. Students will further develop their understanding of whole numbers.

M5N1.a. Classify the set of counting numbers into subsets with distinguishing characteristics (odd/even, prime/composite).

M5N1.b. Find multiples and factors.

M5N1.c. Analyze and use divisibility rules.

M5N2. Students will further develop their understanding of decimals as part of the base-ten number system.

M5N2.a. Understand place value.

M5N2.b. Analyze the effect on the product when a number is multiplied by 10, 100, 1000, 0.1, 0.01, and .001.

M5N2.c. Use <, >, or = to compare decimals and justify the comparison.

M5N3. Students will further develop their understanding of the meaning of multiplication and division with decimals and use them.

M5N3.a. Model multiplication and division of decimals.

M5N3.b. Explain the process of multiplication and division, including situations in which the multiplier and divisor are both whole numbers and decimals.

M5N3.c. Multiply and divide with decimals including decimals less than one and greater than one.

M5N3.d. Understand the relationships and rules for multiplication and division of whole numbers also apply to decimals.

M5N4. Students will continue to develop their understanding of the meaning of common fractions and compute with them.

M5N4.a. Understand division of whole numbers can be represented as a fraction (a/b= a / b).

M5N4.b. Understand the value of a fraction is not changed when both its numerator and denominator are multiplied or divided by the same number because it is the same as multiplying or dividing by one.

M5N4.c. Find equivalent fractions and simplify fractions.

M5N4.d. Model the multiplication and division of common fractions.

M5N4.e. Explore finding common denominators using concrete, pictorial, and computational models.

M5N4.f. Use <, >, or = to compare fractions and justify the comparison.

M5N4.g. Add and subtract common fractions and mixed numbers with unlike denominators.

M5N4.h. Use fractions (proper and improper) and decimals interchangeably.

M5N4.i. Estimate products and quotients.

M5N5. Students will understand the meaning of percentage.

M5N5.a. Explore and model percents using multiple representations.

M5N5.b. Apply percents to circle graphs.

GA.M5M. MEASUREMENT: Students will compute the area of geometric plane figures. They will also understand the concept of volume and compute the volume of simple geometric solids and measure capacity. Students will convert from one unit to another within one system of measurement.

M5M1. Students will extend their understanding of area of geometric plane figures.

M5M1.a. Estimate the area of geometric plane figures.

M5M1.b. Derive the formula for the area of a parallelogram.

M5M1.c. Derive the formula for the area of a triangle.

M5M1.d. Find the areas of triangles and parallelograms using formulae.

M5M1.e. Estimate the area of a circle through partitioning and tiling.

M5M1.f. Find the area of a polygon (regular and irregular) by dividing it into squares, rectangles, and/or triangles and find the sum of the areas of those shapes.

M5M1.g. Derive the formula for the area of a circle.

M5M1.h. Find the area of a circle using the formula and pi is approximately equal to 3.14.

M5M2. Students will extend their understanding of perimeter to include circumference.

M5M2.a. Derive the formula for the circumference of a circle.

M5M2.b. Find the circumference of a circle using the formula and pi is approximately equal to 3.14.

M5M3. Students will measure capacity with appropriately chosen units and tools.

M5M3.a. Use milliliters, liters, fluid ounces, cups, pints, quarts, and gallons to measure capacity.

M5M3.b. Compare one unit to another within a single system of measurement.

M5M4. Students will understand and compute the volume of a simple geometric solid.

M5M4.a. Understand a cubic unit (u^3) is represented by a cube in which each edge has the length of 1 unit.

M5M4.b. Identify the units used in computing volume as cubic centimeters (cm^3), cubic meters (m^3), cubic inches (in^3), cubic feet (ft^3), and cubic yards (yd^3).

M5M4.c. Derive the formula for finding the volume of a cube and a rectangular prism using manipulatives.

M5M4.d. Compute the volume of a cube and a rectangular prism using formulae.

M5M4.e. Estimate the volume of a simple geometric solid.

M5M4.f. Understand the similarities and differences between volume and capacity.

GA.M5G. GEOMETRY: Students will further develop their understanding of geometric figures.

M5G1. Students will understand congruence of geometric figures and the correspondence of their vertices, sides, and angles.

M5G2. Students will understand the relationship of the circumference of a circle to its diameter is pi (pi is approximately equal to 3.14).

GA.M5A. ALGEBRA: Students will represent and investigate mathematical expressions algebraically by using variables.

M5A1. Students will represent and interpret the relationships between quantities algebraically.

M5A1.a. Use variables, such as n or x, for unknown quantities in algebraic expressions.

M5A1.b. Investigate simple algebraic expressions by substituting numbers for the unknown.

M5A1.c. Determine that a formula will be reliable regardless of the type of number (whole numbers or decimals) substituted for the variable.

GA.M5D. DATA ANALYSIS AND PROBABILITY: Students will gather, organize, and display data and interpret graphs.

M5D1. Students will analyze graphs.

M5D1.a. Analyze data presented in a graph.

M5D1.b. Compare and contrast multiple graphic representations (circle graphs, line graphs, line plot graphs, pictographs, Venn diagrams, and bar graphs) for a single set of data and discuss the advantages/disadvantages of each.

M5D1.c. Determine and justify the mean, range, mode, and median of a set of data.

M5D2. Students will collect, organize, and display data using the most appropriate graph.

GA.M5P. PROCESS STANDARDS

M5P1. Students will solve problems (using appropriate technology).

M5P1.a. Build new mathematical knowledge through problem solving.

M5P1.b. Solve problems that arise in mathematics and in other contexts.

M5P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

M5P1.d. Monitor and reflect on the process of mathematical problem solving.

M5P2. Students will reason and evaluate mathematical arguments.

M5P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

M5P2.b. Make and investigate mathematical conjectures.

M5P2.c. Develop and evaluate mathematical arguments and proofs.

M5P2.d. Select and use various types of reasoning and methods of proof.

M5P3. Students will communicate mathematically.

M5P3.a. Organize and consolidate their mathematical thinking through communication.

M5P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

M5P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

M5P3.d. Use the language of mathematics to express mathematical ideas precisely.

M5P4. Students will make connections among mathematical ideas and to other disciplines.

M5P4.a. Recognize and use connections among mathematical ideas.

M5P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

M5P4.c. Recognize and apply mathematics in contexts outside of mathematics.

M5P5. Students will represent mathematics in multiple ways.

M5P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

M5P5.b. Select, apply, and translate among mathematical representations to solve problems.

M5P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.M6N. Numbers and Operations: Students will understand the meaning of the four arithmetic operations as they relate to positive rational numbers and will apply these concepts and associated skills in real world situations.

M6N1. Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and will use these concepts to solve problems.

M6N1.a. Apply factors and multiples.

M6N1.b. Decompose numbers into their prime factorization (Fundamental Theorem of Arithmetic).

M6N1.c. Determine the greatest common factor (GCF) and the least common multiple (LCM) for a set of numbers.

M6N1.d. Add and subtract fractions and mixed numbers with unlike denominators.

M6N1.e. Multiply and divide fractions and mixed numbers.

M6N1.f. Use fractions, decimals, and percents interchangeably.

M6N1.g. Solve problems involving fractions, decimals, and percents.

GA.M6M. Measurement: Students will understand how to determine the volume and surface area of solid figures. They will understand and use the customary and metric systems of measurement to measure quantities efficiently and to represent volume and surface area appropriately.

M6M1. Students will convert from one unit to another within one system of measurement (customary or metric) by using proportional relationships.

M6M2. Students will use appropriate units of measure for finding length, perimeter, area, and volume and will express each quantity using the appropriate unit.

M6M2.a. Measure length to the nearest half, fourth, eighth, and sixteenth of an inch.

M6M2.b. Select and use units of appropriate size and type to measure length, perimeter, area, and volume.

M6M2.c. Compare and contrast units of measure for perimeter, area, and volume.

M6M3. Students will determine the volume of fundamental solid figures (right rectangular prisms, cylinders, pyramids, and cones).

M6M3.a. Determine the formula for finding the volume of fundamental solid figures.

M6M3.b. Compute the volumes of fundamental solid figures, using appropriate units of measure.

M6M3.c. Estimate the volumes of simple geometric solids.

M6M3.d. Solve application problems involving the volume of fundamental solid figures.

M6M4. Students will determine the surface area of solid figures (right rectangular prisms and cylinders).

M6M4.a. Find the surface area of right rectangular prisms and cylinders using manipulatives and constructing nets.

M6M4.b. Compute the surface area of right rectangular prisms and cylinders using formulae.

M6M4.c. Estimate the surface areas of simple geometric solids.

M6M4.d. Solve application problems involving surface area of right rectangular prisms and cylinders.

GA.M6G. Geometry: Students will further develop their understanding of plane and solid geometric figures, incorporating the use of appropriate technology and using this knowledge to solve authentic problems.

M6G1. Students will further develop their understanding of plane figures.

M6G1.a. Determine and use lines of symmetry.

M6G1.b. Investigate rotational symmetry, including degree of rotation.

M6G1.c. Use the concepts of ratio, proportion, and scale factor to demonstrate the relationships between similar plane figures.

M6G1.d. Interpret and sketch simple scale drawings.

M6G1.e. Solve problems involving scale drawings.

M6G2. Students will further develop their understanding of solid figures.

M6G2.a. Compare and contrast right prisms and pyramids.

M6G2.b. Compare and contrast cylinders and cones.

M6G2.c. Interpret and sketch front, back, top, bottom, and side views of solid figures.

M6G2.d. Construct nets for prisms, cylinders, pyramids, and cones.

GA.M6A. Algebra: Students will investigate relationships between two quantities. They will write and solve proportions and simple one-step equations that result from problem situations.

M6A1. Students will understand the concept of ratio and use it to represent quantitative relationships.

M6A2. Students will consider relationships between varying quantities.

M6A2.a. Analyze and describe patterns arising from mathematical rules, tables, and graphs.

M6A2.b. Use manipulatives or draw pictures to solve problems involving proportional relationships.

M6A2.c. Use proportions (a/b = c/d) to describe relationships and solve problems, including percent problems.

M6A2.d. Describe proportional relationships mathematically using y = kx, where k is the constant of proportionality.

M6A2.e. Graph proportional relationships in the form y = kx and describe characteristics of the graphs.

M6A2.f. In a proportional relationship expressed as y = kx, solve for one quantity given values of the other two. Given quantities may be whole numbers, decimals, or fractions. Solve problems using the relationship y = kx.

M6A2.g. Use proportional reasoning (a/b = c/d and y = kx) to solve problems.

M6A3. Students will evaluate algebraic expressions, including those with exponents, and solve simple one-step equations using each of the four basic operations.

GA.M6D. Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. They will represent, investigate, and use data to answer those questions. Students will understand experimental and theoretical probability.

M6D1. Students will pose questions, collect data, represent and analyze the data, and interpret results.

M6D1.a. Formulate questions that can be answered by data. Students should collect data by using samples from a larger population (surveys), or by conducting experiments.

M6D1.b. Using data, construct frequency distributions, frequency tables, and graphs.

M6D1.c. Choose appropriate graphs to be consistent with the nature of the data (categorical or numerical). Graphs should include pictographs, histograms, bar graphs, line graphs, circle graphs, and line plots.

M6D1.d. Use tables and graphs to examine variation that occurs within a group and variation that occurs between groups.

M6D1.e. Relate the data analysis to the context of the questions posed.

M6D2. Students will use experimental and simple theoretical probability and will understand the nature of sampling. They will also make predictions from investigations.

M6D2.a. Predict the probability of a given event through trials/simulations (experimental probability), and represent the probability as a ratio.

M6D2.b. Determine, and use a ratio to represent, the theoretical probability of a given event.

M6D2.c. Discover that experimental probability approaches theoretical probability when the number of trials is large.

GA.M6P. Process Standards: Each topic studied in this course should be developed with careful thought toward helping every student achieve the following process standards.

M6P1. Students will solve problems (using appropriate technology).

M6P1.a. Build new mathematical knowledge through problem solving.

M6P1.b. Solve problems that arise in mathematics and in other contexts.

M6P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

M6P1.d. Monitor and reflect on the process of mathematical problem solving.

M6P2. Students will reason and evaluate mathematical arguments.

M6P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

M6P2.b. Make and investigate mathematical conjectures.

M6P2.c. Develop and evaluate mathematical arguments and proofs.

M6P2.d. Select and use various types of reasoning and methods of proof.

M6P3. Students will communicate mathematically.

M6P3.a. Organize and consolidate their mathematical thinking through communication.

M6P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

M6P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

M6P3.d. Use the language of mathematics to express mathematical ideas precisely.

M6P4. Students will make connections among mathematical ideas and to other disciplines.

M6P4.a. Recognize and use connections among mathematical ideas.

M6P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

M6P4.c. Recognize and apply mathematics in contexts outside of mathematics.

M6P5. Students will represent mathematics in multiple ways.

M6P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

M6P5.b. Select, apply, and translate among mathematical representations to solve problems.

M6P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.M6RC. Reading Across the Curriculum: Reading across curriculum content develops both academic and personal interests in students. As students read, they develop both content and contextual vocabulary. They also build good habits for reading, researching, and learning. The Reading Across the Curriculum standard focuses on the academic and personal skills students acquire as they read in all areas of learning.

M6RC1. Students will enhance reading in all curriculum areas by:

M6RC1.a. Reading in All Curriculum Areas: Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areas; Read both informational and fictional texts in a variety of genres and modes of discourse; Read technical texts related to various subject areas.

M6RC1.b. Discussing books: Discuss messages and themes from books in all subject areas; Respond to a variety of texts in multiple modes of discourse; Relate messages and themes from one subject area to messages and themes in another area; Evaluate the merit of texts in every subject discipline; Examine author's purpose in writing; Recognize the features of disciplinary texts.

M6RC1.c. Building vocabulary knowledge: Demonstrate an understanding of contextual vocabulary in various subjects; Use content vocabulary in writing and speaking; Explore understanding of new words found in subject area texts.

M6RC1.d. Establishing context: Explore life experiences related to subject area content; Discuss in both writing and speaking how certain words are subject area related; Determine strategies for finding content and contextual meaning for unknown words.

GA.M7N. Numbers and Operations: Students will further develop their understanding of the concept of rational numbers and apply them to real world situations.

M7N1. Students will understand the meaning of positive and negative rational numbers and use them in computation.

M7N1.a. Find the absolute value of a number and understand it as the distance from zero on a number line.

M7N1.b. Compare and order rational numbers, including repeating decimals.

M7N1.c. Add, subtract, multiply, and divide positive and negative rational numbers.

M7N1.d. Solve problems using rational numbers.

GA.M7G. Geometry: Students will further develop and apply their understanding of plane and solid geometric figures through the use of constructions and transformations. Students will explore the properties of similarity and further develop their understanding of 3-dimensional figures.

M7G1. Students will construct plane figures that meet given conditions.

M7G1.a. Perform basic constructions using both compass and straight edge, and appropriate technology. Constructions should include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

M7G1.b. Recognize that many constructions are based on the creation of congruent triangles.

M7G2. Students will demonstrate understanding of transformations.

M7G2.a. Demonstrate understanding of translations, dilations, rotations, reflections, and relate symmetry to appropriate transformations.

M7G2.b. Given a figure in the coordinate plane, determine the coordinates resulting from a translation, dilation, rotation, or reflection.

M7G3. Students will use the properties of similarity and apply these concepts to geometric figures.

M7G3.a. Understand the meaning of similarity, visually compare geometric figures for similarity, and describe similarities by listing corresponding parts.

M7G3.b. Understand the relationships among scale factors, length ratios, and area ratios between similar figures. Use scale factors, length ratios, and area ratios to determine side lengths and areas of similar geometric figures.

M7G3.c. Understand congruence of geometric figures as a special case of similarity: The figures have the same size and shape.

M7G4. Students will further develop their understanding of three-dimensional figures.

M7G4.a. Describe three-dimensional figures formed by translations and rotations of plane figures through space.

M7G4.b. Sketch, model, and describe cross-sections of cones, cylinders, pyramids, and prisms.

GA.M7A. Algebra: Students will demonstrate an understanding of linear relations and fundamental algebraic concepts.

M7A1. Students will represent and evaluate quantities using algebraic expressions.

M7A1.a. Translate verbal phrases to algebraic expressions.

M7A1.b. Simplify and evaluate algebraic expressions, using commutative, associative, and distributive properties as appropriate.

M7A1.c. Add and subtract linear expressions.

M7A2. Students will understand and apply linear equations in one variable.

M7A2.a. Given a problem, define a variable, write an equation, solve the equation, and interpret the solution.

M7A2.b. Use the addition and multiplication properties of equality to solve one- and two-step linear equations.

M7A3. Students will understand relationships between two variables.

M7A3.a. Plot points on a coordinate plane.

M7A3.b. Represent, describe, and analyze relations from tables, graphs, and formulas.

M7A3.c. Describe how change in one variable affects the other variable.

M7A3.d. Describe patterns in the graphs of proportional relationships, both direct (y = kx) and inverse (y = k/x).

GA.M7D. Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions, collecting data, analyzing the data using measures of central tendency and variation, and using the data to answer the questions posed. Students will understand the role of probability in sampling.

M7D1. Students will pose questions, collect data, represent and analyze the data, and interpret results.

M7D1.a. Formulate questions and collect data from a census of at least 30 objects and from samples of varying sizes.

M7D1.b. Construct frequency distributions.

M7D1.c. Analyze data using measures of central tendency (mean, median, and mode), including recognition of outliers.

M7D1.d. Analyze data with respect to measures of variation (range, quartiles, interquartile range).

M7D1.e. Compare measures of central tendency and variation from samples to those from a census. Observe that sample statistics are more likely to approximate the population parameters as sample size increases.

M7D1.f. Analyze data using appropriate graphs, including pictographs, histograms, bar graphs, line graphs, circle graphs, and line plots introduced earlier, and using box-and-whisker plots and scatter plots.

M7D1.g. Analyze and draw conclusions about data, including a description of the relationship between two variables.

GA.M7P. Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

M7P1. Students will solve problems (using appropriate technology).

M7P1.a. Build new mathematical knowledge through problem solving.

M7P1.b. Solve problems that arise in mathematics and in other contexts.

M7P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

M7P1.d. Monitor and reflect on the process of mathematical problem solving.

M7P2. Students will reason and evaluate mathematical arguments.

M7P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

M7P2.b. Make and investigate mathematical conjectures.

M7P2.c. Develop and evaluate mathematical arguments and proofs.

M7P2.d. Select and use various types of reasoning and methods of proof.

M7P3. Students will communicate mathematically.

M7P3.a. Organize and consolidate their mathematical thinking through communication.

M7P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

M7P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

M7P3.d. Use the language of mathematics to express mathematical ideas precisely.

M7P4. Students will make connections among mathematical ideas and to other disciplines.

M7P4.a. Recognize and use connections among mathematical ideas.

M7P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

M7P4.c. Recognize and apply mathematics in contexts outside of mathematics.

M7P5. Students will represent mathematics in multiple ways.

M7P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

M7P5.b. Select, apply, and translate among mathematical representations to solve problems.

M7P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.M7RC. Reading Across the Curriculum: Reading across curriculum content develops both academic and personal interests in students. As students read, they develop both content and contextual vocabulary. They also build good habits for reading, researching, and learning. The Reading Across the Curriculum standard focuses on the academic and personal skills students acquire as they read in all areas of learning.

M7RC1. Students will enhance reading in all curriculum areas by:

M7RC1.a. Reading in All Curriculum Areas: Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areas; Read both informational and fictional texts in a variety of genres and modes of discourse; Read technical texts related to various subject areas.

M7RC1.b. Discussing books: Discuss messages and themes from books in all subject areas; Respond to a variety of texts in multiple modes of discourse; Relate messages and themes from one subject area to messages and themes in another area; Evaluate the merit of texts in every subject discipline; Examine author's purpose in writing; Recognize the features of disciplinary texts.

M7RC1.c. Building vocabulary knowledge: Demonstrate an understanding of contextual vocabulary in various subjects; Use content vocabulary in writing and speaking; Explore understanding of new words found in subject area texts.

M7RC1.d. Establishing context: Explore life experiences related to subject area content; Discuss in both writing and speaking how certain words are subject area related; Determine strategies for finding content and contextual meaning for unknown words.

GA.M8N. Numbers and Operations: Students will understand the numeric and geometric meaning of square root, apply properties of integer exponents, and use scientific notation.

M8N1. Students will understand different representations of numbers including square roots, exponents, and scientific notation.

M8N1.a. Find square roots of perfect squares.

M8N1.b. Recognize the (positive) square root of a number as a length of a side of a square with a given area.

M8N1.c. Recognize square roots as points and as lengths on a number line.

M8N1.d. Understand that the square root of 0 is 0 and that every positive number has two square roots that are opposite in sign.

M8N1.e. Recognize and use the radical symbol to denote the positive square root of a positive number.

M8N1.f. Estimate square roots of positive numbers.

M8N1.g. Simplify, add, subtract, multiply, and divide expressions containing square roots.

M8N1.h. Distinguish between rational and irrational numbers.

M8N1.i. Simplify expressions containing integer exponents.

M8N1.j. Express and use numbers in scientific notation.

M8N1.k. Use appropriate technologies to solve problems involving square roots, exponents, and scientific notation.

GA.M8G. Geometry: Students will use and apply geometric properties of plane figures, including congruence and the Pythagorean theorem.

M8G1. Students will understand and apply the properties of parallel and perpendicular lines and understand the meaning of congruence.

M8G1.a. Investigate characteristics of parallel and perpendicular lines both algebraically and geometrically.

M8G1.b. Apply properties of angle pairs formed by parallel lines cut by a transversal.

M8G1.c. Understand the properties of the ratio of segments of parallel lines cut by one or more transversals.

M8G1.d. Understand the meaning of congruence: that all corresponding angles are congruent and all corresponding sides are congruent.

M8G2. Students will understand and use the Pythagorean theorem.

M8G2.a. Apply properties of right triangles, including the Pythagorean theorem.

M8G2.b. Recognize and interpret the Pythagorean theorem as a statement about areas of squares on the sides of a right triangle.

GA.M8A. Algebra: Students will use linear algebra to represent, analyze and solve problems. They will use equations, tables, and graphs to investigate linear relations and functions, paying particular attention to slope as a rate of change.

M8A1. Students will use algebra to represent, analyze, and solve problems.

M8A1.a. Represent a given situation using algebraic expressions or equations in one variable.

M8A1.b. Simplify and evaluate algebraic expressions.

M8A1.c. Solve algebraic equations in one variable, including equations involving absolute values.

M8A1.d. Solve equations involving several variables for one variable in terms of the others.

M8A1.e. Interpret solutions in problem contexts.

M8A2. Students will understand and graph inequalities in one variable.

M8A2.a. Represent a given situation using an inequality in one variable.

M8A2.b. Use the properties of inequality to solve inequalities.

M8A2.c. Graph the solution of an inequality on a number line.

M8A2.d. Interpret solutions in problem contexts.

M8A3. Students will understand relations and linear functions.

M8A3.a. Recognize a relation as a correspondence between varying quantities.

M8A3.b. Recognize a function as a correspondence between inputs and outputs where the output for each input must be unique.

M8A3.c. Distinguish between relations that are functions and those that are not functions.

M8A3.d. Recognize functions in a variety of representations and a variety of contexts.

M8A3.e. Use tables to describe sequences recursively and with a formula in closed form.

M8A3.f. Understand and recognize arithmetic sequences as linear functions with whole-number input values.

M8A3.h. Interpret the constant difference in an arithmetic sequence as the slope of the associated linear function.

M8A3.i. Identify relations and functions as linear or nonlinear.

M8A3.j. Translate among verbal, tabular, graphic, and algebraic representations of functions.

M8A4. Students will graph and analyze graphs of linear equations and inequalities.

M8A4.a. Interpret slope as a rate of change.

M8A4.b. Determine the meaning of the slope and y-intercept in a given situation.

M8A4.c. Graph equations of the form y = mx + b.

M8A4.d. Graph equations of the form ax + by = c.

M8A4.e. Graph the solution set of a linear inequality, identifying whether the solution set is an open or a closed half-plane.

M8A4.f. Determine the equation of a line given a graph, numerical information that defines the line, or a context involving a linear relationship.

M8A4.g. Solve problems involving linear relationships.

M8A5. Students will understand systems of linear equations and inequalities and use them to solve problems.

M8A5.a. Given a problem context, write an appropriate system of linear equations or inequalities.

M8A5.b. Solve systems of equations graphically and algebraically, using technology as appropriate.

M8A5.c. Graph the solution set of a system of linear inequalities in two variables.

M8A5.d. Interpret solutions in problem contexts.

GA.M8D. Data Analysis and Probability: Students will use and understand set theory and simple counting techniques; determine the theoretical probability of simple events; and make inferences from data, particularly data that can be modeled by linear functions.

M8D1. Students will apply basic concepts of set theory.

M8D1.a. Demonstrate relationships among sets through use of Venn diagrams.

M8D1.b. Determine subsets, complements, intersection, and union of sets.

M8D1.c. Use set notation to denote elements of a set.

M8D2. Students will determine the number of outcomes related to a given event.

M8D2.a. Use tree diagrams to find the number of outcomes.

M8D2.b. Apply the addition and multiplication principles of counting.

M8D3. Students will use the basic laws of probability.

M8D3.a. Find the probability of simple independent events.

M8D3.b. Find the probability of compound independent events

M8D4. Students will organize, interpret, and make inferences from statistical data.

M8D4.a. Gather data that can be modeled with a linear function.

M8D4.b. Estimate and determine a line of best fit from a scatter plot.

GA.M8P. Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

M8P1. Students will solve problems (using appropriate technology).

M8P1.a. Build new mathematical knowledge through problem solving.

M8P1.b. Solve problems that arise in mathematics and in other contexts.

M8P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

M8P1.d. Monitor and reflect on the process of mathematical problem solving.

M8P2. Students will reason and evaluate mathematical arguments.

M8P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

M8P2.b. Make and investigate mathematical conjectures.

M8P2.c. Develop and evaluate mathematical arguments and proofs.

M8P2.d. Select and use various types of reasoning and methods of proof.

M8P3. Students will communicate mathematically.

M8P3.a. Organize and consolidate their mathematical thinking through communication.

M8P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

M8P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

M8P3.d. Use the language of mathematics to express mathematical ideas precisely.

M8P4. Students will make connections among mathematical ideas and to other disciplines.

M8P4.a. Recognize and use connections among mathematical ideas.

M8P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

M8P4.c. Recognize and apply mathematics in contexts outside of mathematics.

M8P5. Students will represent mathematics in multiple ways.

M8P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

M8P5.b. Select, apply, and translate among mathematical representations to solve problems.

M8P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.M8RC. Reading Across the Curriculum: Reading across curriculum content develops both academic and personal interests in students. As students read, they develop both content and contextual vocabulary. They also build good habits for reading, researching, and learning. The Reading Across the Curriculum standard focuses on the academic and personal skills students acquire as they read in all areas of learning.

M8RC1. Students will enhance reading in all curriculum areas by:

M8RC1.a. Reading in All Curriculum Areas: Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areas; Read both informational and fictional texts in a variety of genres and modes of discourse; Read technical texts related to various subject areas.

M8RC1.b. Discussing books: Discuss messages and themes from books in all subject areas; Respond to a variety of texts in multiple modes of discourse; Relate messages and themes from one subject area to messages and themes in another area; Evaluate the merit of texts in every subject discipline; Examine author's purpose in writing; Recognize the features of disciplinary texts.

M8RC1.c. Building vocabulary knowledge: Demonstrate an understanding of contextual vocabulary in various subjects; Use content vocabulary in writing and speaking; Explore understanding of new words found in subject area texts.

M8RC1.d. Establishing context: Explore life experiences related to subject area content; Discuss in both writing and speaking how certain words are subject area related; Determine strategies for finding content and contextual meaning for unknown words.

GA.MM1A. Mathematics 1 - Algebra: Students will explore functions and solve simple equations. Students will simplify and operate with radical, polynomial, and rational expressions.

MM1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MM1A1.a. Represent functions using function notation.

MM1A1.b. Graph the basic functions f(x) = x^n, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

MM1A1.c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

MM1A1.d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

MM1A1.e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

MM1A1.f. Recognize sequences as functions with domains that are whole numbers.

MM1A1.g. Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

MM1A1.h. Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

MM1A1.i. Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

MM1A2. Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MM1A2.a. Simplify algebraic and numeric expressions involving square root.

MM1A2.b. Perform operations with square roots.

MM1A2.c. Add, subtract, multiply, and divide polynomials.

MM1A2.d. Expand binomials using the Binomial Theorem.

MM1A2.e. Add, subtract, multiply, and divide rational expressions.

MM1A2.f. Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas: (x + y)^2 = x^2 + 2xy + y^2; (x - y)^2 = x^2 - 2xy + y^2; (x + y)(x - y) = x^2 - y^2; (x + a)(x + b) = x^2 + (a + b)x + ab; (x + y)^3 = x^3 + 3 x^2y + 3xy^2 + y^3; (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3

MM1A2.g. Use area and volume models for polynomial arithmetic.

MM1A3. Students will solve simple equations.

MM1A3.a. Solve quadratic equations in the form ax^2 + bx + c = 0, where a = 1, by using factorization and finding square roots where applicable.

MM1A3.b. Solve equations involving radicals such as square root of x + b = c, using algebraic techniques.

MM1A3.c. Use a variety of techniques, including technology, tables, and graphs to solve equations resulting from the investigation of x^2 + bx + c = 0.

MM1A3.d. Solve simple rational equations that result in linear equations or quadratic equations with leading coefficient of 1.

GA.MM1G. Mathematics 1 - Geometry: Students will explore, understand, and use the formal language of reasoning and justification. Students will apply properties of polygons and determine distances and points of concurrence.

MM1G1. Students will investigate properties of geometric figures in the coordinate plane.

MM1G1.a. Determine the distance between two points.

MM1G1.b. Determine the distance between a point and a line.

MM1G1.c. Determine the midpoint of a segment.

MM1G1.d. Understand the distance formula as an application of the Pythagorean theorem.

MM1G1.e. Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

MM1G2. Students will understand and use the language of mathematical argument and justification.

MM1G2.a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.

MM1G2.b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

MM1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.

MM1G3.a. Determine the sum of interior and exterior angles in a polygon.

MM1G3.b. Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.

MM1G3.c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

MM1G3.d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

MM1G3.e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

GA.MM1D. Mathematics 1 - Data Analysis and Probability: Students will use counting techniques and determine probability. Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data.

MM1D1. Students will determine the number of outcomes related to a given event.

MM1D1.a. Apply the addition and multiplication principles of counting.

MM1D1.b. Calculate and use simple permutations and combinations.

MM1D2. Students will use the basic laws of probability.

MM1D2.a. Find the probabilities of mutually exclusive events.

MM1D2.b. Find the probabilities of dependent events.

MM1D2.c. Calculate conditional probabilities.

MM1D2.d. Use expected value to predict outcomes.

MM1D3. Students will relate samples to a population.

MM1D3.a. Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.

MM1D3.b. Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.

MM1D3.c. Understand that a random sample is used to improve the chance of selecting a representative sample.

MM1D4. Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

GA.MM1P. Mathematics 1 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM1P1. Students will solve problems (using appropriate technology).

MM1P1.a. Build new mathematical knowledge through problem solving.

MM1P1.b. Solve problems that arise in mathematics and in other contexts.

MM1P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM1P1.d. Monitor and reflect on the process of mathematical problem solving.

MM1P2. Students will reason and evaluate mathematical arguments.

MM1P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM1P2.b. Make and investigate mathematical conjectures.

MM1P2.c. Develop and evaluate mathematical arguments and proofs.

MM1P2.d. Select and use various types of reasoning and methods of proof.

MM1P3. Students will communicate mathematically.

MM1P3.a. Organize and consolidate their mathematical thinking through communication.

MM1P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM1P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM1P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM1P4. Students will make connections among mathematical ideas and to other disciplines.

MM1P4.a. Recognize and use connections among mathematical ideas.

MM1P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM1P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM1P5. Students will represent mathematics in multiple ways.

MM1P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM1P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM1P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MM2N. Mathematics 2 - Number and Operations: Students will use the complex number system.

MM2N1. Students will represent and operate with complex numbers.

MM2N1.a. Write square roots of negative numbers in imaginary form.

MM2N1.b. Write complex numbers in the form a + bi.

MM2N1.c. Add, subtract, multiply, and divide complex numbers.

MM2N1.d. Simplify expressions involving complex numbers.

GA.MM2A. Mathematics 2 - Algebra: Students will investigate piecewise, exponential, and quadratic functions, using numerical, analytical, and graphical approaches, focusing on the use of these functions in problem-solving situations. Students will solve equations and inequalities and explore inverses of functions.

MM2A1. Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

MM2A1.a. Write absolute value functions as piecewise functions.

MM2A1.b. Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.

MM2A1.c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

MM2A2. Students will explore exponential functions.

MM2A2.a. Extend properties of exponents to include all integer exponents.

MM2A2.b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

MM2A2.c. Graph functions as transformations of f(x) = a^x.

MM2A2.d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

MM2A2.e. Understand and use basic exponential functions as models of real phenomena.

MM2A2.f. Understand and recognize geometric sequences as exponential functions with domains that are whole numbers.

MM2A2.g. Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

MM2A3.a. Convert between standard and vertex form.

MM2A3. Students will analyze quadratic functions in the forms f(x) = ax^2 + bx + c and f(x) = a(x - h)^2 + k.

MM2A3.b. Graph quadratic functions as transformations of the function f(x) = x^2.

MM2A3.c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

MM2A3.d. Explore arithmetic series and various ways of computing their sums.

MM2A3.e. Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

MM2A4. Students will solve quadratic equations and inequalities in one variable.

MM2A4.a. Solve equations graphically using appropriate technology.

MM2A4.b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

MM2A4.c. Analyze the nature of roots using technology and using the discriminant.

MM2A4.d. Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

MM2A5. Students will explore inverses of functions.

MM2A5.a. Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

MM2A5.b. Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.

MM2A5.c. Explore the graphs of functions and their inverses.

MM2A5.d. Use composition to verify that functions are inverses of each other.

GA.MM2G. Mathematics 2 - Geometry: Students will explore right triangles and right-triangle trigonometry. They will understand and apply properties of circles and spheres, and use them in determining related measures.

MM2G1. Students will identify and use special right triangles.

MM2G1.a. Determine the lengths of sides of 30 degree - 60 degree - 90 degree triangles.

MM2G1.b. Determine the lengths of sides of 45 degree - 45 degree - 90 degree triangles.

MM2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.

MM2G2.a. Discover the relationship of the trigonometric ratios for similar triangles.

MM2G2.b. Explain the relationship between the trigonometric ratios of complementary angles.

MM2G2.c. Solve application problems using the trigonometric ratios.

MM2G3. Students will understand the properties of circles.

MM2G3.a. Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

MM2G3.b. Understand and use properties of central, inscribed, and related angles.

MM2G3.c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

MM2G3.d. Justify measurements and relationships in circles using geometric and algebraic properties.

MM2G4. Students will find and compare the measures of spheres.

MM2G4.a. Use and apply surface area and volume of a sphere.

MM2G4.b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

GA.MM2D. Mathematics 2 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data. They will use regression to analyze data and to make inferences.

MM2D1. Using sample data, students will make informal inferences about population means and standard deviations.

MM2D1.a. Pose a question and collect sample data from at least two different populations.

MM2D1.b. Understand and calculate the means and standard deviations of sets of data.

MM2D1.c. Use means and standard deviations to compare data sets.

MM2D1.d. Compare the means and standard deviations of random samples with the corresponding population parameters, including those population parameters for normal distributions. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

MM2D2. Students will determine an algebraic model to quantify the association between two quantitative variables.

MM2D2.a. Gather and plot data that can be modeled with linear and quadratic functions.

MM2D2.b. Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and 'eyeballing.'

MM2D2.c. Understand and apply the processes of linear and quadratic regression for curve fitting using appropriate technology.

MM2D2.d. Investigate issues that arise when using data to explore the relationship between two variables, including confusion between correlation and causation.

GA.MM2P. Mathematics 2 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM2P1. Students will solve problems (using appropriate technology).

MM2P1.a. Build new mathematical knowledge through problem solving.

MM2P1.b. Solve problems that arise in mathematics and in other contexts.

MM2P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM2P1.d. Monitor and reflect on the process of mathematical problem solving.

MM2P2. Students will reason and evaluate mathematical arguments.

MM2P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM2P2.b. Make and investigate mathematical conjectures.

MM2P2.c. Develop and evaluate mathematical arguments and proofs.

MM2P2.d. Select and use various types of reasoning and methods of proof.

MM2P3. Students will communicate mathematically.

MM2P3.a. Organize and consolidate their mathematical thinking through communication.

MM2P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM2P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM2P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM2P4. Students will make connections among mathematical ideas and to other disciplines.

MM2P4.a. Recognize and use connections among mathematical ideas.

MM2P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM2P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM2P5. Students will represent mathematics in multiple ways.

MM2P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM2P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM2P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MM3A. Mathematics 3 - Algebra: Students will investigate exponential, logarithmic and polynomial functions of degree higher than 2. Students will understand matrices and use them to solve problems.

MM3A1. Students will analyze graphs of polynomial functions of higher degree.

MM3A1.a. Graph simple polynomial functions as translations of the function f(x) = ax^n.

MM3A1.b. Understand the effects of the following on the graph of a polynomial function: degree, lead coefficient, and multiplicity of real zeros.

MM3A1.c. Determine whether a polynomial function has symmetry and whether it is even, odd, or neither.

MM3A1.d. Investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.

MM3A2. Students will explore logarithmic functions as inverses of exponential functions.

MM3A2.a. Define and understand the properties of nth roots.

MM3A2.b. Extend properties of exponents to include rational exponents.

MM3A2.c. Define logarithmic functions as inverses of exponential functions.

MM3A2.d. Understand and use properties of logarithms by extending laws of exponents.

MM3A2.e. Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

MM3A2.f. Graph functions as transformations of f(x) = a^x, f(x) = log ax, f(x) = e^x, f(x) = ln x.

MM3A2.g. Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

MM3A3. Students will solve a variety of equations and inequalities.

MM3A3.a. Find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical conjugates.

MM3A3.b. Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

MM3A3.c. Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

MM3A3.d. Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology.

MM3A4. Students will perform basic operations with matrices.

MM3A4.a. Add, subtract, multiply, and invert matrices, when possible, choosing appropriate methods, including technology.

MM3A4.b. Find the inverses of two-by-two matrices using pencil and paper, and find inverses of larger matrices using technology.

MM3A4.c. Examine the properties of matrices, contrasting them with properties of real numbers.

MM3A5. Students will use matrices to formulate and solve problems.

MM3A5.a. Represent a system of linear equations as a matrix equation.

MM3A5.b. Solve matrix equations using inverse matrices.

MM3A5.c. Represent and solve realistic problems using systems of linear equations.

MM3A6. Students will solve linear programming problems in two variables.

MM3A6.a. Solve systems of inequalities in two variables, showing the solutions graphically.

MM3A6.b. Represent and solve realistic problems using linear programming.

MM3A7. Students will understand and apply matrix representations of vertex-edge graphs.

MM3A7.a. Use graphs to represent realistic situations.

MM3A7.b. Use matrices to represent graphs, and solve problems that can be represented by graphs.

GA.MM3G. Mathematics 3 - Geometry: Students will understand and use the analytic geometry of conic sections and of planes and spheres in space.

MM3G1. Students will investigate the relationships between lines and circles.

MM3G1.a. Find equations of circles.

MM3G1.b. Graph a circle given an equation in general form.

MM3G1.c. Find the equation of a tangent line to a circle at a given point.

MM3G1.d. Solve a system of equations involving a circle and a line.

MM3G1.e. Solve a system of equations involving two circles.

MM3G2. Students will recognize, analyze, and graph the equations of the conic sections (parabolas, circles, ellipses, and hyperbolas).

MM3G2.a. Convert equations of conics by completing the square.

MM3G2.b. Graph conic sections, identifying fundamental characteristics.

MM3G2.c. Write equations of conic sections given appropriate information.

MM3G3. Students will investigate planes and spheres.

MM3G3.a. Plot the point (x, y, z) and understand it as a vertex of a rectangular prism.

MM3G3.b. Apply the distance formula in 3-space.

MM3G3.c. Recognize and understand equations of planes and spheres.

GA.MM3D. Mathematics 3 - Data Analysis and Probability: Students will use a normal distribution to calculate probabilities. They will organize, represent, investigate, interpret, and make inferences using data from both observational studies and experiments.

MM3D1. Students will create probability histograms of discrete random variables, using both experimental and theoretical probabilities.

MM3D2. Students will solve problems involving probabilities by interpreting a normal distribution as a probability histogram for a continuous random variable (z-scores are used for a general normal distribution).

MM3D2.a. Determine intervals about the mean that include a given percent of data.

MM3D2.b. Determine the probability that a given value falls within a specified interval.

MM3D2.c. Estimate how many items in a population fall within a specified interval.

MM3D3. Students will understand the differences between experimental and observational studies by posing questions and collecting, analyzing, and interpreting data.

GA.MM3P. Mathematics 3 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM3P1. Students will solve problems (using appropriate technology).

MM3P1.a. Build new mathematical knowledge through problem solving.

MM3P1.b. Solve problems that arise in mathematics and in other contexts.

MM3P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM3P1.d. Monitor and reflect on the process of mathematical problem solving.

MM3P2. Students will reason and evaluate mathematical arguments.

MM3P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM3P2.b. Make and investigate mathematical conjectures.

MM3P2.c. Develop and evaluate mathematical arguments and proofs.

MM3P2.d. Select and use various types of reasoning and methods of proof.

MM3P3. Students will communicate mathematically.

MM3P3.a. Organize and consolidate their mathematical thinking through communication.

MM3P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM3P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM3P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM3P4. Students will make connections among mathematical ideas and to other disciplines.

MM3P4.a. Recognize and use connections among mathematical ideas.

MM3P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM3P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM3P5. Students will represent mathematics in multiple ways.

MM3P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM3P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM3P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MM4A. Mathematics 4 - Algebra: Students will analyze rational and trigonometric functions. Students will investigate and apply sequences and series and will understand and use vectors.

MM4A1. Students will explore rational functions.

MM4A1.a. Investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior.

MM4A1.b. Find inverses of rational functions, discussing domain and range, symmetry, and function composition.

MM4A1.c. Solve rational equations and inequalities analytically, graphically, and by using appropriate technology.

MM4A2. Students will use the circle to define the trigonometric functions.

MM4A2.a. Define and understand angles measured in degrees and radians, including but not limited to 0 degrees, 30 degrees, 45 degrees, 60 degrees, 90 degrees, their multiples, and equivalences.

MM4A2.b. Understand and apply the six trigonometric functions as functions of general angles in standard position.

MM4A2.c. Find values of trigonometric functions using points on the terminal sides of angles in the standard position.

MM4A2.d. Understand and apply the six trigonometric functions as functions of arc length on the unit circle.

MM4A2.e. Find values of trigonometric functions using the unit circle.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

MM4A3.a. Understand and apply the six basic trigonometric functions as functions of real numbers.

MM4A3.b. Determine the characteristics of the graphs of the six basic trigonometric functions.

MM4A3.c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3.d. Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena.

MM4A4. Students will investigate functions.

MM4A4.a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

MM4A4.b. Investigate transformations of functions.

MM4A4.c. Investigate characteristics of functions built through sum, difference, product, quotient, and composition.

MM4A5. Students will establish trigonometric identities and use them to simplify trigonometric expressions and verify equivalence statements.

MM4A6. Students will solve trigonometric equations both graphically and algebraically.

MM4A6.a. Solve trigonometric equations over a variety of domains, using technology as appropriate.

MM4A6.b. Use the coordinates of a point on the terminal side of an angle to express x and y as polar coordinates.

MM4A6.d. Apply the law of sines and the law of cosines.

MM4A7. Students will verify and apply 1/2 ab sinC to find the area of a triangle.

MM4A8. Students will investigate and use inverse sine, inverse cosine, and inverse tangent functions.

MM4A8.a. Find values of the above functions using technology as appropriate.

MM4A8.b. Determine characteristics of the above functions and their graphs.

MM4A9. Students will use sequences and series

MM4A9.a. Use and find recursive and explicit formulae for the terms of sequences.

MM4A9.b. Recognize and use simple arithmetic and geometric sequences.

MM4A9.c. Find and apply the sums of finite and, where appropriate, infinite arithmetic and geometric series.

MM4A9.d. Use summation notation to explore finite series.

MM4A10. Students will understand and use vectors.

MM4A10.a. Represent vectors algebraically and geometrically.

MM4A10.b. Convert between vectors expressed using rectangular coordinates and expressed using magnitude and direction.

MM4A10.c. Add, subtract, and compute scalar multiples of vectors.

MM4A10.d. Use vectors to solve realistic problems.

GA.MM4D. Mathematics 4 - Data Analysis and Probability: Students will organize, represent, investigate, interpret, and make inferences from data, using the central limit theorem and the standard normal distribution. Students will apply the Central Limit Theorem to calculate confidence intervals for a population mean using data from large samples. Students will use sample data and confidence intervals to draw conclusions about populations.

MM4D1. Using simulation, students will develop the idea of the central limit theorem.

MM4D2. Using student-generated data from random samples of at least 30 members, students will determine the margin of error and confidence interval for a specified level of confidence.

MM4D3. Students will use confidence intervals and margins of error to make inferences from data about a population. Technology is used to evaluate confidence intervals, but students will be aware of the ideas involved.

GA.MM4P. Mathematics 4 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM4P1. Students will solve problems (using appropriate technology).

MM4P1.a. Build new mathematical knowledge through problem solving.

MM4P1.b. Solve problems that arise in mathematics and in other contexts.

MM4P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM4P1.d. Monitor and reflect on the process of mathematical problem solving.

MM4P2. Students will reason and evaluate mathematical arguments.

MM4P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM4P2.b. Make and investigate mathematical conjectures.

MM4P2.c. Develop and evaluate mathematical arguments and proofs.

MM4P2.d. Select and use various types of reasoning and methods of proof.

MM4P3. Students will communicate mathematically.

MM4P3.a. Organize and consolidate their mathematical thinking through communication.

MM4P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM4P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM4P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM4P4. Students will make connections among mathematical ideas and to other disciplines.

MM4P4.a. Recognize and use connections among mathematical ideas.

MM4P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM4P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM4P5. Students will represent mathematics in multiple ways.

MM4P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM4P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM4P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC1A. Core Mathematics 1 - Algebra: Students will explore and interpret the characteristics of functions.

MC1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MC1A1.a. Represent functions using function notation.

MC1A1.b. Graph the basic functions f(x) = x^n, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

MC1A1.c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

MC1A1.d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

MC1A1.e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

MC1A1.f. Recognize sequences as functions with domains that are whole numbers.

MC1A1.g. Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

MC1A1.h. Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

MC1A1.i. Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

GA.MC1G. Core Mathematics 1 - Geometry: The student will apply properties of polygons and determine distances.

MC1G1. Students will investigate properties of geometric figures in the coordinate plane.

MC1G1.a. Determine the distance between two points.

MC1G1.b. Determine the distance between a point and a line.

MC1G1.c. Determine the midpoint of a segment.

MC1G1.d. Understand the distance formula as an application of the Pythagorean theorem.

MC1G1.e. Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

GA.MC1D. Core Mathematics 1 - Data Analysis and Probability: Students will use counting techniques and determine probability.

MC1D1. Students will determine the number of outcomes related to a given event

MC1D1.a. Apply addition and multiplication principles of counting.

MC1D1.b. Calculate and use simple permutations and combinations.

MC1D2. Students will use the basic laws of probability

MC1D2.a. Find the probabilities of mutually exclusive events.

MC1D2.b. Find the probabilities of dependent events.

MC1D2.c. Calculate conditional probabilities.

MC1D2.d. Use expected value to predict outcomes.

GA.MC1P. Core Mathematics 1 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC1P1. Students will solve problems (using appropriate technology).

MC1P1.a. Build new mathematical knowledge through problem solving.

MC1P1.b. Solve problems that arise in mathematics and in other contexts.

MC1P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC1P1.d. Monitor and reflect on the process of mathematical problem solving.

MC1P2. Students will reason and evaluate mathematical arguments.

MC1P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC1P2.b. Make and investigate mathematical conjectures.

MC1P2.c. Develop and evaluate mathematical arguments and proofs.

MC1P2.d. Select and use various types of reasoning and methods of proof.

MC1P3. Students will communicate mathematically.

MC1P3.a. Organize and consolidate their mathematical thinking through communication.

MC1P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC1P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC1P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC1P4. Students will make connections among mathematical ideas and to other disciplines.

MC1P4.a. Recognize and use connections among mathematical ideas.

MC1P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC1P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MC1P5. Students will represent mathematics in multiple ways.

MC1P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC1P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC1P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC2A. Core Mathematics 2 - Algebra: Students will simplify and operate with radical expressions, polynomials, and rational expressions. Students will solve simple equations.

MC2A1. Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MC2A1.a. Simplify algebraic and numeric expressions involving square root.

MC2A1.b. Perform operations with square roots.

MC2A1.c. Add, subtract, multiply, and divide polynomials.

MC2A1.d. Add, subtract, multiply, and divide rational expressions.

MC2A1.e. Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas: (x + y)^2 = x^2 + 2xy + y^2; (x - y)^2 = x^2 - 2xy + y^2; (x + y)(x - y) = x^2 - y^2; (x + a)(x + b) = x^2 + (a + b)x + ab; (x + y)^3 = x^3 + 3 x^2y + 3xy^2 + y^3; (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y3

MC2A1.f. Use area and volume models for polynomial arithmetic.

MC2A2. Students will solve simple equations.

MC2A2.a. Solve quadratic equations in the form ax^2 + bx + c = 0, where a = 1, by using factorization and finding square roots where applicable.

MC2A2.b. Solve equations involving radicals such as square root of x + b = c, using algebraic techniques.

MC2A2.c. Use a variety of techniques, including technology, tables, and graphs to solve equations resulting from the investigation of x^2 + bx + c = 0.

MC2A2.d. Solve simple rational equations that result in linear equations or quadratic equations with leading coefficient of 1.

GA.MC2G. Core Mathematics 2 - Geometry: Students will explore, understand and use the formal language of reasoning and justification. Students will apply properties of polygons.

MC2G1. Students will understand and use the language of mathematical argument and justification.

MC2G1.a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.

MC2G1.b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

MC2G1.c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

MC2G1.d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

MC2G1.e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

GA.MC2D. Core Mathematics 2 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data.

MC2D1. Students will relate samples to a population.

MC2D1.a. Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.

MC2D1.b. Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.

MC2D1.c. Understand that a random sample is used to improve the chance of selecting a representative sample.

MC2D2. Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

GA.MC2P. Core Mathematics 2 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC2P1. Students will solve problems (using appropriate technology).

MC2P1.a. Build new mathematical knowledge through problem solving.

MC2P1.b. Solve problems that arise in mathematics and in other contexts.

MC2P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC2P1.d. Monitor and reflect on the process of mathematical problem solving.

MC2P2. Students will reason and evaluate mathematical arguments.

MC2P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC2P2.b. Make and investigate mathematical conjectures.

MC2P2.c. Develop and evaluate mathematical arguments and proofs.

MC2P2.d. Select and use various types of reasoning and methods of proof.

MC2P3. Students will communicate mathematically.

MC2P3.a. Organize and consolidate their mathematical thinking through communication.

MC2P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC2P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC2P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC2P4. Students will make connections among mathematical ideas and to other disciplines.

MC2P4.a. Recognize and use connections among mathematical ideas.

MC2P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC2P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MC2P5. Students will represent mathematics in multiple ways.

MC2P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC2P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC2P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC3A. Core Mathematics 3 - Algebra: Students will investigate piecewise and exponential functions from numerical, analytical and graphical approaches, focusing on the use of these functions in problem-solving situations.

MC3A1. Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

MC3A1.a. Write absolute value functions as piecewise functions.

MC3A1.b. Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.

MC3A1.c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

MC3A2. Students will explore exponential functions.

MC3A2.a. Extend properties of exponents to include all integer exponents.

MC3A2.b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

MC3A2.c. Graph functions as transformations of f(x) = a^x.

MC3A2.d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

MC3A2.e. Understand and use basic exponential functions as models of real phenomena.

MC3A2.f. Understand and recognize geometric sequences as exponential functions with domains that are sets of whole numbers.

MC3A2.g. Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

GA.MC3G. Core Mathematics 3 - Geometry: Students will explore right triangles and right triangular trigonometry.

MC3G1. Students will identify and use special right triangles.

MC3G1.a. Determine the lengths of sides of 30 degree - 60 degree - 90 degree triangles.

MC3G1.b. Determine the lengths of sides of 45 degree - 45 degree - 90 degree triangles.

MC3G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.

MC3G2.a. Discover the relationship of the trigonometric ratios for similar triangles.

MC3G2.b. Explain the relationship between the trigonometric ratios of complementary angles.

MC3G2.c. Solve application problems using the trigonometric ratios.

GA.MC3D. Core Mathematics 3 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data. Students will use regression to analyze data, and to make inferences.

MC3D1. Using sample data, students will make informal inferences about population means and standard deviations.

MC3D1.a. Pose a question and collect sample data from at least two different populations.

MC3D1.b. Understand and calculate the means and standard deviations of sets of data.

MC3D1.c. Use means and standard deviations to compare data sets.

MC3D1.d. Compare the means and standard deviations of random samples with the corresponding population parameters. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

MC3D2. Students will determine an algebraic model to quantify the association between two quantitative variables.

MC3D2.a. Gather and plot data that can be modeled with linear functions.

MC3D2.b. Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and 'eyeballing.'

MC3D2.c. Understand and apply the processes of linear regression for curve fitting using appropriate technology.

GA.MC3P. Core Mathematics 3 - Process Standards: The following process standards are essential mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC3P1. Students will solve problems (using appropriate technology).

MC3P1.a. Build new mathematical knowledge through problem solving.

MC3P1.b. Solve problems that arise in mathematics and in other contexts.

MC3P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC3P1.d. Monitor and reflect on the process of mathematical problem solving.

MC3P2. Students will reason and evaluate mathematical arguments.

MC3P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC3P2.b. Make and investigate mathematical conjectures.

MC3P2.c. Develop and evaluate mathematical arguments and proofs.

MC3P2.d. Select and use various types of reasoning and methods of proof.

MC3P3. Students will communicate mathematically.

MC3P3.a. Organize and consolidate their mathematical thinking through communication.

MC3P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC3P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC3P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC3P4. Students will make connections among mathematical ideas and to other disciplines.

MC3P4.a. Recognize and use connections among mathematical ideas.

MC3P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC3P4.c. Recognize and apply mathematics in context outside of mathematics.

MC3P5. Students will represent mathematics in multiple ways.

MC3P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC3P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC3P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC4N. Core Mathematics 4 - Number and Operations: Students will use the complex number system.

MC4N1. Students will represent and operate with complex numbers.

MC4N1.a. Write square roots of negative numbers in imaginary form.

MC4N1.b. Write complex numbers in the form a + bi.

MC4N1.c. Add, subtract, multiply, and divide complex numbers.

MC4N1.d. Simplify expressions involving complex numbers.

GA.MC4A. Core Mathematics 4 - Algebra: Students will investigate quadratic functions from numerical, analytical and graphical approaches, focusing on the use of these functions in problem-solving situations. Students will solve quadratic equations and inequalities and explore inverses of functions.

MC4A1. Students will analyze quadratic functions in the forms f(x) = ax^2 + bx + c and f(x) = a(x - h)^2 + k.

MC4A1.a. Convert between standard and vertex form.

MC4A1.b. Graph quadratic functions as transformations of the function f(x) = x^2.

MC4A1.c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

MC4A1.d. Explore arithmetic series and various ways of computing their sums.

MC4A1.e. Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

MC4A2. Students will solve quadratic equations and inequalities in one variable.

MC4A2.a. Solve equations graphically using appropriate technology.

MC4A2.b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

MC4A2.c. Analyze the nature of roots using technology and using the discriminant.

MC4A2.d. Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

MC4A3. Students will explore inverses of functions.

MC4A3.a. Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

MC4A3.b. Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.

MC4A3.c. Explore the graphs of functions and their inverses.

MC4A3.d. Use composition to verify that functions are inverses of each other.

GA.MC4G. Core Mathematics 4 - Geometry: Students will understand and apply properties of circles and spheres and use them in determining related measures.

MC4G1. Students will understand the properties of circles.

MC4G1.a. Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

MC4G1.b. Understand and use properties of central, inscribed, and related angles.

MC4G1.c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

MC4G1.d. Justify measurements and relationships in circles using geometric and algebraic properties.

MC4G2. Students will find and compare the measures of spheres.

MC4G2.a. Use and apply surface area and volume of a sphere.

MC4G2.b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

GA.MC4D. Core Mathematics 4 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will use regression to analyze data, and to make inferences.

MC4D1. Students will determine an algebraic model to quantify the association between two quantitative variables.

MC4D1.a. Gather and plot data that can be modeled with quadratic functions.

MC4D1.b. Understand and apply the processes of quadratic regression for curve fitting using appropriate technology.

GA.MC4P. Core Mathematics 4 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC4P1. Students will solve problems (using appropriate technology).

MC4P1.a. Build new mathematical knowledge through problem solving.

MC4P1.b. Solve problems that arise in mathematics and in other contexts.

MC4P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC4P1.d. Monitor and reflect on the process of mathematical problem solving.

MC4P2. Students will reason and evaluate mathematical arguments.

MC4P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC4P2.b. Make and investigate mathematical conjectures.

MC4P2.c. Develop and evaluate mathematical arguments and proofs.

MC4P2.d. Select and use various types of reasoning and methods of proof.

MC4P3. Students will communicate mathematically.

MC4P3.a. Organize and consolidate their mathematical thinking through communication.

MC4P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC4P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC4P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC4P4. Students will make connections among mathematical ideas and to other disciplines.

MC4P4.a. Recognize and use connections among mathematical ideas.

MC4P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC4P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MC4P5. Students will represent mathematics in multiple ways.

MC4P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC4P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC4P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MA1N. Accelerated Mathematics 1 - Number and Operations: Students will use the complex number system.

MA1N1. Students will represent and operate with complex numbers.

MA1N1.a. Write square roots of negative numbers in imaginary form.

MA1N1.b. Write complex numbers in the form a + bi.

MA1N1.c. Add, subtract, multiply, and divide complex numbers.

MA1N1.d. Simplify expressions involving complex numbers.

GA.MA1A. Accelerated Mathematics 1 - Algebra: Students will explore functions, solve equations and operate with radical, polynomial and rational expressions.

MA1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MA1A1.a. Represent functions using function notation.

MA1A1.b. Graph the basic functions f(x) = x^n, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

MA1A1.c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

MA1A1.d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

MA1A1.e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

MA1A1.f. Recognize sequences as functions with domains that are sets of whole numbers.

MA1A1.g. Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

MA1A1.h. Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

MA1A1.i. Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

MA1A2. Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MA1A2.a. Simplify algebraic and numeric expressions involving square root.

MA1A2.b. Perform operations with square roots.

MA1A2.c. Add, subtract, multiply, and divide polynomials.

MA1A2.d. Add, subtract, multiply, and divide rational expressions.

MA1A2.e. Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas: (x + y)^2 = x^2 + 2xy + y^2; (x - y)^2 = x^2 - 2xy + y^2; (x + y)(x - y) = x^2 - y^2; (x + a)(x + b) = x^2 + (a + b)x + ab; (x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3; (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3

MA1A2.f. Use area and volume models for polynomial arithmetic.

MA1A3. Students will analyze quadratic functions in the forms f(x) = ax^2 + bx + c and f(x) = a(x - h)^2 + k.

MA1A3.a. Convert between standard and vertex form.

MA1A3.b. Graph quadratic functions as transformations of the function f(x) = x^2.

MA1A3.c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

MA1A3.d. Explore arithmetic series and various ways of computing their sums.

MA1A3.e. Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

MA1A4. Students will solve quadratic equations and inequalities in one variable.

MA1A4.a. Solve equations graphically using appropriate technology.

MA1A4.b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

MA1A4.c. Analyze the nature of roots using technology and using the discriminant.

MA1A4.d. Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

MA1A5. Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

MA1A5.a. Write absolute value functions as piecewise functions.

MA1A5.b. Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.

MA1A5.c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

GA.MA1G. Accelerated Mathematics 1 - Geometry: Students will explore, understand and use the formal language of reasoning and justification. Students will apply properties of polygons, circles and spheres, and determine distances and points of concurrence.

MA1G1. Students will investigate properties of geometric figures in the coordinate plane.

MA1G1.a. Determine the distance between two points.

MA1G1.b. Determine the distance between a point and a line.

MA1G1.c. Determine the midpoint of a segment.

MA1G1.d. Understand the distance formula as an application of the Pythagorean theorem.

MA1G1.e. Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

MA1G2. Students will understand and use the language of mathematical argument and justification.

MA1G2.a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.

MA1G2.b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

MA1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.

MA1G3.a. Determine the sum of interior and exterior angles in a polygon.

MA1G3.b. Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.

MA1G3.c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

MA1G3.d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

MA1G3.e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

MA1G4. Students will understand the properties of circles.

MA1G4.a. Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

MA1G4.b. Understand and use properties of central, inscribed, and related angles.

MA1G4.c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

MA1G4.d. Justify measurements and relationships in circles using geometric and algebraic properties.

MA1G5. Students will find and compare the measures of spheres.

MA1G5.a. Use and apply surface area and volume of a sphere.

MA1G5.b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

GA.MA1D. Accelerated Mathematics 1 - Data Analysis and Probability: Students will use counting techniques and determine probability. Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data. Students will determine algebraic models from data.

MA1D1. Students will determine the number of outcomes related to a given event.

MA1D1.a. Apply the addition and multiplication principles of counting.

MA1D1.b. Calculate and use simple permutations and combinations.

MA1D2. Students will use the basic laws of probability.

MA1D2.a. Find the probabilities of mutually exclusive events.

MA1D2.b. Find the probabilities of dependent events.

MA1D2.c. Calculate conditional probabilities.

MA1D2.d. Use expected value to predict outcomes.

MA1D3. Students will relate samples to a population.

MA1D3.a. Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.

MA1D3.b. Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.

MA1D3.c. Understand that a random sample is used to improve the chance of selecting a representative sample.

MA1D4. Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

MA1D5. Students will determine an algebraic model to quantify the association between two quantitative variables.

MA1D5.a. Gather and plot data that can be modeled with linear and quadratic functions.

MA1D5.b. Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and .eyeballing..

MA1D5.c. Understand and apply the processes of linear and quadratic regression for curve fitting using appropriate technology.

GA.MA1P. Accelerated Mathematics 1 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MA1P1. Students will solve problems (using appropriate technology).

MA1P1.a. Build new mathematical knowledge through problem solving.

MA1P1.b. Solve problems that arise in mathematics and in other contexts.

MA1P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MA1P1.d. Monitor and reflect on the process of mathematical problem solving.

MA1P2. Students will reason and evaluate mathematical arguments.

MA1P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MA1P2.b. Make and investigate mathematical conjectures.

MA1P2.c. Develop and evaluate mathematical arguments and proofs.

MA1P2.d. Select and use various types of reasoning and methods of proof.

MA1P3. Students will communicate mathematically.

MA1P3.a. Organize and consolidate their mathematical thinking through communication.

MA1P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MA1P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MA1P3.d. Use the language of mathematics to express mathematical ideas precisely.

MA1P4. Students will make connections among mathematical ideas and to other disciplines.

MA1P4.a. Recognize and use connections among mathematical ideas.

MA1P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MA1P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MA1P5. Students will represent mathematics in multiple ways.

MA1P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MA1P5.b. Select, apply, and translate among mathematical representations to solve problems.

MA1P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MA2A. Accelerated Mathematics 2 - Algebra: Students will investigate exponential, logarithmic, and polynomial functions of higher degree; understand matrices and use them to solve problems; and solve linear programming problems in two variables.

MA2A1. Students will explore exponential functions.

MA2A1.a. Extend properties of exponents to include all integer exponents.

MA2A1.b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

MA2A1.c. Graph functions as transformations of f(x) = a^x.

MA2A1.d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

MA2A1.e. Understand and use basic exponential functions as models of real phenomena.

MA2A1.f. Understand and recognize geometric sequences as exponential functions with domains that are sets of whole numbers.

MA2A1.g. Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

MA2A2. Students will explore inverses of functions.

MA2A2.a. Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

MA2A2.b. Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.

MA2A2.c. Explore the graphs of functions and their inverses.

MA2A2.d. Use composition to verify that functions are inverses of each other.

MA2A3. Students will analyze graphs of polynomial functions of higher degree.

MA2A3.a. Graph simple polynomial functions as translations of the function f(x) = ax^n.

MA2A3.b. Understand the effects of the following on the graph of a polynomial function: degree, lead coefficient, and multiplicity of real zeros.

MA2A3.c. Determine whether a polynomial function has symmetry and whether it is even, odd, or neither.

MA2A3.d. Investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.

MA2A4. Students will explore logarithmic functions as inverses of exponential functions.

MA2A4.a. Define and understand the properties of nth roots.

MA2A4.b. Extend properties of exponents to include rational exponents.

MA2A4.c. Define logarithmic functions as inverses of exponential functions.

MA2A4.d. Understand and use properties of logarithms by extending laws of exponents.

MA2A4.e. Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

MA2A4.f. Graph functions as transformations of f(x) = a^x, f(x) = log ax, f(x) = e^x, f(x) = ln x.

MA2A4.g. Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

MA2A5. Students will solve a variety of equations and inequalities.

MA2A5.a. Find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical conjugates.

MA2A5.b. Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

MA2A5.c. Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

MA2A5.d. Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology.

MA2A6. Students will perform basic operations with matrices.

MA2A6.a. Add, subtract, multiply, and invert matrices, when possible, choosing appropriate methods, including technology.

MA2A6.b. Find the inverses of two-by-two matrices using pencil and paper, and find inverses of larger matrices using technology.

MA2A6.c. Examine the properties of matrices, contrasting them with properties of real numbers.

MA2A7. Students will use matrices to formulate and solve problems.

MA2A7.a. Represent a system of linear equations as a matrix equation.

MA2A7.b. Solve matrix equations using inverse matrices.

MA2A7.c. Represent and solve realistic problems using systems of linear equations.

MA2A8. Students will solve linear programming problems in two variables.

MA2A8.a. Solve systems of inequalities in two variables, showing the solutions graphically.

MA2A8.b. Represent and solve realistic problems using linear programming.

MA2A9. Students will understand and apply matrix representations of vertex-edge graphs.

MA2A9.a. Use graphs to represent realistic situations.

MA2A9.b. Use matrices to represent graphs, and solve problems that can be represented by graphs.

GA.MA2G. Accelerated Mathematics 2 - Geometry: Students will explore right triangles and right triangular trigonometry. They will understand and apply properties of conic sections, planes, and spheres.

MA2G1. Students will identify and use special right triangles.

MA2G1.a. Determine the lengths of sides of 30 degree - 60 degree - 90 degree triangles.

MA2G1.b. Determine the lengths of sides of 45 degree - 45 degree - 90 degree triangles.

MA2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.

MA2G2.a. Discover the relationship of the trigonometric ratios for similar triangles.

MA2G2.b. Explain the relationship between the trigonometric ratios of complementary angles.

MA2G2.c. Solve application problems using the trigonometric ratios.

MA2G3. Students will investigate the relationships between lines and circles.

MA2G3.a. Find equations of circles.

MA2G3.b. Graph a circle given an equation in general form.

MA2G3.c. Find the equation of a tangent line to a circle at a given point.

MA2G3.d. Solve a system of equations involving a circle and a line.

MA2G3.e. Solve a system of equations involving two circles.

MA2G4. Students will recognize, analyze, and graph the equations of the conic sections (parabolas, circles, ellipses, and hyperbolas).

MA2G4.a. Convert equations of conics by completing the square.

MA2G4.b. Graph conic sections, identifying fundamental characteristics.

MA2G4.c. Write equations of conic sections given appropriate information.

MA2G5. Students will investigate planes and spheres.

MA2G5.a. Plot the point (x, y, z) and understand it as a vertex of a rectangular prism.

MA2G5.b. Apply the distance formula in 3-space.

MA2G5.c. Recognize and understand equations of planes and spheres.

GA.MA2D. Accelerated Mathematics 2 - Data Analysis and Probability: Students will make informal inferences about means and standard deviations. Students will use a normal distribution to calculate probabilities. Students will organize, represent, investigate, interpret, and make inferences from both observational studies and experiments.

MA2D1. Using sample data, students will make informal inferences about population means and standard deviations.

MA2D1.a. Pose a question and collect sample data from at least two different populations.

MA2D1.b. Understand and calculate the means and standard deviations of sets of data.

MA2D1.c. Use means and standard deviations to compare data sets.

MA2D1.d. Compare the means and standard deviations of random samples with the corresponding population parameters. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

MA2D2. Students will create probability histograms of discrete random variables, using both experimental and theoretical probabilities.

MA2D3. Students will solve problems involving probabilities by interpreting a normal distribution as a probability histogram for a continuous random variable (z-scores are used for a general normal distribution).

MA2D3.a. Determine intervals about the mean that include a given percent of data.

MA2D3.b. Determine the probability that a given value falls within a specified interval.

MA2D3.c. Estimate how many items in a population fall within a specified interval.

MA2D4. Students will understand the differences between experimental and observational studies by posing questions and collecting, analyzing, and interpreting data.

GA.MA2P. Accelerated Mathematics 2 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MA2P1. Students will solve problems (using appropriate technology).

MA2P1.a. Build new mathematical knowledge through problem solving.

MA2P1.b. Solve problems that arise in mathematics and in other contexts.

MA2P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MA2P1.d. Monitor and reflect on the process of mathematical problem solving.

MA2P2. Students will reason and evaluate mathematical arguments.

MA2P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MA2P2.b. Make and investigate mathematical conjectures.

MA2P2.c. Develop and evaluate mathematical arguments and proofs.

MA2P2.d. Select and use various types of reasoning and methods of proof.

MA2P3. Students will communicate mathematically.

MA2P3.a. Organize and consolidate their mathematical thinking through communication.

MA2P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MA2P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MA2P3.d. Use the language of mathematics to express mathematical ideas precisely.

MA2P4. Students will make connections among mathematical ideas and to other disciplines.

MA2P4.a. Recognize and use connections among mathematical ideas.

MA2P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MA2P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MA2P5. Students will represent mathematics in multiple ways.

MA2P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MA2P5.b. Select, apply, and translate among mathematical representations to solve problems.

MA2P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MA3A. Accelerated Mathematics 3 - Algebra: Students will explore characteristics of various functions, understand and use concepts of trigonometric functions, investigate and apply sequences and series, and use parametric and polar equations to represent functions and curves.

MA3A1. Students will explore rational functions.

MA3A1.a. Investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior.

MA3A1.b. Find inverses of rational functions, discussing domain and range, symmetry, and function composition.

MA3A1.c. Solve rational equations and inequalities analytically, graphically, and by using appropriate technology.

MA3A2. Students will use the circle to define the trigonometric functions.

MA3A2.a. Define and understand angles measured in degrees and radians, including but not limited to 0 degrees, 30 degrees, 45 degrees, 60 degrees, 90 degrees, their multiples, and equivalences.

MA3A2.b. Understand and apply the six trigonometric functions as functions of general angles in standard position.

MA3A2.c. Find values of trigonometric functions using points on the terminal sides of angles in the standard position.

MA3A2.d. Understand and apply the six trigonometric functions as functions of arc length on the unit circle.

MA3A2.e. Find values of trigonometric functions using the unit circle.

MA3A3. Students will investigate and use the graphs of the six trigonometric functions.

MA3A3.a. Understand and apply the six basic trigonometric functions as functions of real numbers.

MA3A3.b. Determine the characteristics of the graphs of the six basic trigonometric functions.

MA3A3.c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MA3A3.d. Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena.

MA3A4. Students will investigate functions.

MA3A4.a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

MA3A4.b. Investigate transformations of functions.

MA3A4.c. Investigate characteristics of functions built through sum, difference, product, quotient, and composition.

MA3A5. Students will establish trigonometric identities and use them to simplify trigonometric expressions and verify equivalence statements.

MA3A6. Students will solve trigonometric equations both graphically and algebraically.

MA3A6.a. Solve trigonometric equations over a variety of domains, using technology as appropriate.

MA3A6.b. Use the coordinates of a point on the terminal side of an angle to express x and y as polar coordinates.

MA3A6.c. Apply the law of sines and the law of cosines.

MA3A7. Students will verify and apply 1/2 ab sinC to find the area of a triangle.

MA3A8. Students will investigate and use inverse sine, inverse cosine, and inverse tangent functions.

MA3A8.a. Find values of the above functions using technology as appropriate.

MA3A8.b. Determine characteristics of the above functions and their graphs.

MA3A9. Students will use sequences and series

MA3A9.a. Use and find recursive and explicit formulae for the terms of sequences.

MA3A9.b. Recognize and use simple arithmetic and geometric sequences.

MA3A9.c. Investigate limits of sequences.

MA3A9.d. Use mathematical induction to find and prove formulae for sums of finite series.

MA3A9.e. Find and apply the sums of finite and, where appropriate, infinite arithmetic and geometric series.

MA3A9.f. Use summation notation to explore series.

MA3A9.g. Determine geometric series and their limits.

MA3A10. Students will understand and use vectors.

MA3A10.a. Represent vectors algebraically and geometrically.

MA3A10.b. Convert between vectors expressed using rectangular coordinates and vectors expressed using magnitude and direction.

MA3A10.c. Add and subtract vectors and compute scalar multiples of vectors.

MA3A10.d. Use vectors to solve realistic problems.

MA3A11. Students will use complex numbers in trigonometric form.

MA3A11.a. Represent complex numbers in trigonometric form.

MA3A11.b. Find products, quotients, powers, and roots of complex numbers in trigonometric form.

MA3A12. Students will explore parametric representations of plane curves.

MA3A12.a. Convert between Cartesian and parametric form.

MA3A12.b. Graph equations in parametric form showing direction and beginning and ending points where appropriate.

MA3A13. Students will explore polar equations.

MA3A13.a. Express coordinates of points in rectangular and polar form.

MA3A13.b. Graph and identify characteristics of simple polar equations including lines, circles, cardioids, limacons, and roses.

GA.MA3D. Accelerated Mathematics 3 - Data Analysis and Probability: Students will organize, represent, investigate, interpret, and make inferences from data, using the central limit theorem and the standard normal distribution. Students will apply the Central Limit Theorem to calculate confidence intervals for a population mean using data from large samples. Students will use sample data and confidence intervals to draw conclusions about populations.

MA3D1. Using simulation, students will develop the idea of the central limit theorem.

MA3D2. Using student-generated data from random samples of at least 30 members, students will determine the margin of error and confidence interval for a specified level of confidence.

MA3D3. Students will use confidence intervals and margins of error to make inferences from data about a population. Technology is used to evaluate confidence intervals, but students will be aware of the ideas involved.

GA.MA3P. Accelerated Mathematics 3 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MA3P1. Students will solve problems (using appropriate technology).

MA3P1.a. Build new mathematical knowledge through problem solving.

MA3P1.b. Solve problems that arise in mathematics and in other contexts.

MA3P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MA3P1.d. Monitor and reflect on the process of mathematical problem solving.

MA3P2. Students will reason and evaluate mathematical arguments.

MA3P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MA3P2.b. Make and investigate mathematical conjectures.

MA3P2.c. Develop and evaluate mathematical arguments and proofs.

MA3P2.d. Select and use various types of reasoning and methods of proof.

MA3P3. Students will communicate mathematically.

MA3P3.a. Organize and consolidate their mathematical thinking through communication.

MA3P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MA3P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MA3P3.d. Use the language of mathematics to express mathematical ideas precisely.

MA3P4. Students will make connections among mathematical ideas and to other disciplines.

MA3P4.a. Recognize and use connections among mathematical ideas.

MA3P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MA3P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MA3P5. Students will represent mathematics in multiple ways.

MA3P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MA3P5.b. Select, apply, and translate among mathematical representations to solve problems.

MA3P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MRC. Reading Across the Curriculum: Reading across curriculum content develops both academic and personal interests in students. As students read, they develop both content and contextual vocabulary. They also build good habits for reading, researching, and learning. The Reading Across the Curriculum standard focuses on the academic and personal skills students acquire as they read in all areas of learning.

MRC1. Students will enhance reading in all curriculum areas by:

MRC1.a. Reading in all curriculum areas: Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areas; Read both informational and fictional texts in a variety of genres and modes of discourse; Read technical texts related to various subject areas

MRC1.b. Discussing books: Discuss messages and themes from books in all subject areas; Respond to a variety of texts in multiple modes of discourse; Relate messages and themes from one subject area to messages and themes in another area; Evaluate the merit of texts in every subject discipline; Examine author's purpose in writing; Recognize the features of disciplinary texts.

MRC1.c. Building vocabulary knowledge: Demonstrate an understanding of contextual vocabulary in various subjects; Use content vocabulary in writing and speaking; Explore understanding of new words found in subject area texts.

MRC1.d. Establishing context: Explore life experiences related to subject area content; Discuss in both writing and speaking how certain words are subject area related; Determine strategies for finding content and contextual meaning for unknown words.

GA.MM1A. Mathematics 1 - Algebra: Students will explore functions and solve simple equations. Students will simplify and operate with radical, polynomial, and rational expressions.

MM1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MM1A1.a. Represent functions using function notation.

MM1A1.b. Graph the basic functions f(x) = x^n, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

MM1A1.c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

MM1A1.d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

MM1A1.e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

MM1A1.f. Recognize sequences as functions with domains that are whole numbers.

MM1A1.g. Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

MM1A1.h. Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

MM1A1.i. Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

MM1A2. Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MM1A2.a. Simplify algebraic and numeric expressions involving square root.

MM1A2.b. Perform operations with square roots.

MM1A2.c. Add, subtract, multiply, and divide polynomials.

MM1A2.d. Expand binomials using the Binomial Theorem.

MM1A2.e. Add, subtract, multiply, and divide rational expressions.

MM1A2.f. Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas: (x + y)^2 = x^2 + 2xy + y^2; (x - y)^2 = x^2 - 2xy + y^2; (x + y)(x - y) = x^2 - y^2; (x + a)(x + b) = x^2 + (a + b)x + ab; (x + y)^3 = x^3 + 3 x^2y + 3xy^2 + y^3; (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3

MM1A2.g. Use area and volume models for polynomial arithmetic.

MM1A3. Students will solve simple equations.

MM1A3.a. Solve quadratic equations in the form ax^2 + bx + c = 0, where a = 1, by using factorization and finding square roots where applicable.

MM1A3.b. Solve equations involving radicals such as square root of x + b = c, using algebraic techniques.

MM1A3.c. Use a variety of techniques, including technology, tables, and graphs to solve equations resulting from the investigation of x^2 + bx + c = 0.

MM1A3.d. Solve simple rational equations that result in linear equations or quadratic equations with leading coefficient of 1.

GA.MM1G. Mathematics 1 - Geometry: Students will explore, understand, and use the formal language of reasoning and justification. Students will apply properties of polygons and determine distances and points of concurrence.

MM1G1. Students will investigate properties of geometric figures in the coordinate plane.

MM1G1.a. Determine the distance between two points.

MM1G1.b. Determine the distance between a point and a line.

MM1G1.c. Determine the midpoint of a segment.

MM1G1.d. Understand the distance formula as an application of the Pythagorean theorem.

MM1G1.e. Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

MM1G2. Students will understand and use the language of mathematical argument and justification.

MM1G2.a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.

MM1G2.b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

MM1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.

MM1G3.a. Determine the sum of interior and exterior angles in a polygon.

MM1G3.b. Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.

MM1G3.c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

MM1G3.d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

MM1G3.e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

GA.MM1D. Mathematics 1 - Data Analysis and Probability: Students will use counting techniques and determine probability. Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data.

MM1D1. Students will determine the number of outcomes related to a given event.

MM1D1.a. Apply the addition and multiplication principles of counting.

MM1D1.b. Calculate and use simple permutations and combinations.

MM1D2. Students will use the basic laws of probability.

MM1D2.a. Find the probabilities of mutually exclusive events.

MM1D2.b. Find the probabilities of dependent events.

MM1D2.c. Calculate conditional probabilities.

MM1D2.d. Use expected value to predict outcomes.

MM1D3. Students will relate samples to a population.

MM1D3.a. Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.

MM1D3.b. Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.

MM1D3.c. Understand that a random sample is used to improve the chance of selecting a representative sample.

MM1D4. Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

GA.MM1P. Mathematics 1 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM1P1. Students will solve problems (using appropriate technology).

MM1P1.a. Build new mathematical knowledge through problem solving.

MM1P1.b. Solve problems that arise in mathematics and in other contexts.

MM1P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM1P1.d. Monitor and reflect on the process of mathematical problem solving.

MM1P2. Students will reason and evaluate mathematical arguments.

MM1P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM1P2.b. Make and investigate mathematical conjectures.

MM1P2.c. Develop and evaluate mathematical arguments and proofs.

MM1P2.d. Select and use various types of reasoning and methods of proof.

MM1P3. Students will communicate mathematically.

MM1P3.a. Organize and consolidate their mathematical thinking through communication.

MM1P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM1P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM1P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM1P4. Students will make connections among mathematical ideas and to other disciplines.

MM1P4.a. Recognize and use connections among mathematical ideas.

MM1P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM1P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM1P5. Students will represent mathematics in multiple ways.

MM1P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM1P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM1P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MM2N. Mathematics 2 - Number and Operations: Students will use the complex number system.

MM2N1. Students will represent and operate with complex numbers.

MM2N1.a. Write square roots of negative numbers in imaginary form.

MM2N1.b. Write complex numbers in the form a + bi.

MM2N1.c. Add, subtract, multiply, and divide complex numbers.

MM2N1.d. Simplify expressions involving complex numbers.

GA.MM2A. Mathematics 2 - Algebra: Students will investigate piecewise, exponential, and quadratic functions, using numerical, analytical, and graphical approaches, focusing on the use of these functions in problem-solving situations. Students will solve equations and inequalities and explore inverses of functions.

MM2A1. Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

MM2A1.a. Write absolute value functions as piecewise functions.

MM2A1.b. Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.

MM2A1.c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

MM2A2. Students will explore exponential functions.

MM2A2.a. Extend properties of exponents to include all integer exponents.

MM2A2.b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

MM2A2.c. Graph functions as transformations of f(x) = a^x.

MM2A2.d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

MM2A2.e. Understand and use basic exponential functions as models of real phenomena.

MM2A2.f. Understand and recognize geometric sequences as exponential functions with domains that are whole numbers.

MM2A2.g. Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

MM2A3.a. Convert between standard and vertex form.

MM2A3. Students will analyze quadratic functions in the forms f(x) = ax^2 + bx + c and f(x) = a(x - h)^2 + k.

MM2A3.b. Graph quadratic functions as transformations of the function f(x) = x^2.

MM2A3.c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

MM2A3.d. Explore arithmetic series and various ways of computing their sums.

MM2A3.e. Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

MM2A4. Students will solve quadratic equations and inequalities in one variable.

MM2A4.a. Solve equations graphically using appropriate technology.

MM2A4.b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

MM2A4.c. Analyze the nature of roots using technology and using the discriminant.

MM2A4.d. Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

MM2A5. Students will explore inverses of functions.

MM2A5.a. Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

MM2A5.b. Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.

MM2A5.c. Explore the graphs of functions and their inverses.

MM2A5.d. Use composition to verify that functions are inverses of each other.

GA.MM2G. Mathematics 2 - Geometry: Students will explore right triangles and right-triangle trigonometry. They will understand and apply properties of circles and spheres, and use them in determining related measures.

MM2G1. Students will identify and use special right triangles.

MM2G1.a. Determine the lengths of sides of 30 degree - 60 degree - 90 degree triangles.

MM2G1.b. Determine the lengths of sides of 45 degree - 45 degree - 90 degree triangles.

MM2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.

MM2G2.a. Discover the relationship of the trigonometric ratios for similar triangles.

MM2G2.b. Explain the relationship between the trigonometric ratios of complementary angles.

MM2G2.c. Solve application problems using the trigonometric ratios.

MM2G3. Students will understand the properties of circles.

MM2G3.a. Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

MM2G3.b. Understand and use properties of central, inscribed, and related angles.

MM2G3.c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

MM2G3.d. Justify measurements and relationships in circles using geometric and algebraic properties.

MM2G4. Students will find and compare the measures of spheres.

MM2G4.a. Use and apply surface area and volume of a sphere.

MM2G4.b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

GA.MM2D. Mathematics 2 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data. They will use regression to analyze data and to make inferences.

MM2D1. Using sample data, students will make informal inferences about population means and standard deviations.

MM2D1.a. Pose a question and collect sample data from at least two different populations.

MM2D1.b. Understand and calculate the means and standard deviations of sets of data.

MM2D1.c. Use means and standard deviations to compare data sets.

MM2D1.d. Compare the means and standard deviations of random samples with the corresponding population parameters, including those population parameters for normal distributions. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

MM2D2. Students will determine an algebraic model to quantify the association between two quantitative variables.

MM2D2.a. Gather and plot data that can be modeled with linear and quadratic functions.

MM2D2.b. Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and 'eyeballing.'

MM2D2.c. Understand and apply the processes of linear and quadratic regression for curve fitting using appropriate technology.

MM2D2.d. Investigate issues that arise when using data to explore the relationship between two variables, including confusion between correlation and causation.

GA.MM2P. Mathematics 2 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM2P1. Students will solve problems (using appropriate technology).

MM2P1.a. Build new mathematical knowledge through problem solving.

MM2P1.b. Solve problems that arise in mathematics and in other contexts.

MM2P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM2P1.d. Monitor and reflect on the process of mathematical problem solving.

MM2P2. Students will reason and evaluate mathematical arguments.

MM2P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM2P2.b. Make and investigate mathematical conjectures.

MM2P2.c. Develop and evaluate mathematical arguments and proofs.

MM2P2.d. Select and use various types of reasoning and methods of proof.

MM2P3. Students will communicate mathematically.

MM2P3.a. Organize and consolidate their mathematical thinking through communication.

MM2P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM2P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM2P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM2P4. Students will make connections among mathematical ideas and to other disciplines.

MM2P4.a. Recognize and use connections among mathematical ideas.

MM2P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM2P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM2P5. Students will represent mathematics in multiple ways.

MM2P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM2P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM2P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MM3A. Mathematics 3 - Algebra: Students will investigate exponential, logarithmic and polynomial functions of degree higher than 2. Students will understand matrices and use them to solve problems.

MM3A1. Students will analyze graphs of polynomial functions of higher degree.

MM3A1.a. Graph simple polynomial functions as translations of the function f(x) = ax^n.

MM3A1.b. Understand the effects of the following on the graph of a polynomial function: degree, lead coefficient, and multiplicity of real zeros.

MM3A1.c. Determine whether a polynomial function has symmetry and whether it is even, odd, or neither.

MM3A1.d. Investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.

MM3A2. Students will explore logarithmic functions as inverses of exponential functions.

MM3A2.a. Define and understand the properties of nth roots.

MM3A2.b. Extend properties of exponents to include rational exponents.

MM3A2.c. Define logarithmic functions as inverses of exponential functions.

MM3A2.d. Understand and use properties of logarithms by extending laws of exponents.

MM3A2.e. Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

MM3A2.f. Graph functions as transformations of f(x) = a^x, f(x) = log ax, f(x) = e^x, f(x) = ln x.

MM3A2.g. Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

MM3A3. Students will solve a variety of equations and inequalities.

MM3A3.a. Find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical conjugates.

MM3A3.b. Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

MM3A3.c. Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

MM3A3.d. Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology.

MM3A4. Students will perform basic operations with matrices.

MM3A4.a. Add, subtract, multiply, and invert matrices, when possible, choosing appropriate methods, including technology.

MM3A4.b. Find the inverses of two-by-two matrices using pencil and paper, and find inverses of larger matrices using technology.

MM3A4.c. Examine the properties of matrices, contrasting them with properties of real numbers.

MM3A5. Students will use matrices to formulate and solve problems.

MM3A5.a. Represent a system of linear equations as a matrix equation.

MM3A5.b. Solve matrix equations using inverse matrices.

MM3A5.c. Represent and solve realistic problems using systems of linear equations.

MM3A6. Students will solve linear programming problems in two variables.

MM3A6.a. Solve systems of inequalities in two variables, showing the solutions graphically.

MM3A6.b. Represent and solve realistic problems using linear programming.

MM3A7. Students will understand and apply matrix representations of vertex-edge graphs.

MM3A7.a. Use graphs to represent realistic situations.

MM3A7.b. Use matrices to represent graphs, and solve problems that can be represented by graphs.

GA.MM3G. Mathematics 3 - Geometry: Students will understand and use the analytic geometry of conic sections and of planes and spheres in space.

MM3G1. Students will investigate the relationships between lines and circles.

MM3G1.a. Find equations of circles.

MM3G1.b. Graph a circle given an equation in general form.

MM3G1.c. Find the equation of a tangent line to a circle at a given point.

MM3G1.d. Solve a system of equations involving a circle and a line.

MM3G1.e. Solve a system of equations involving two circles.

MM3G2. Students will recognize, analyze, and graph the equations of the conic sections (parabolas, circles, ellipses, and hyperbolas).

MM3G2.a. Convert equations of conics by completing the square.

MM3G2.b. Graph conic sections, identifying fundamental characteristics.

MM3G2.c. Write equations of conic sections given appropriate information.

MM3G3. Students will investigate planes and spheres.

MM3G3.a. Plot the point (x, y, z) and understand it as a vertex of a rectangular prism.

MM3G3.b. Apply the distance formula in 3-space.

MM3G3.c. Recognize and understand equations of planes and spheres.

GA.MM3D. Mathematics 3 - Data Analysis and Probability: Students will use a normal distribution to calculate probabilities. They will organize, represent, investigate, interpret, and make inferences using data from both observational studies and experiments.

MM3D1. Students will create probability histograms of discrete random variables, using both experimental and theoretical probabilities.

MM3D2. Students will solve problems involving probabilities by interpreting a normal distribution as a probability histogram for a continuous random variable (z-scores are used for a general normal distribution).

MM3D2.a. Determine intervals about the mean that include a given percent of data.

MM3D2.b. Determine the probability that a given value falls within a specified interval.

MM3D2.c. Estimate how many items in a population fall within a specified interval.

MM3D3. Students will understand the differences between experimental and observational studies by posing questions and collecting, analyzing, and interpreting data.

GA.MM3P. Mathematics 3 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM3P1. Students will solve problems (using appropriate technology).

MM3P1.a. Build new mathematical knowledge through problem solving.

MM3P1.b. Solve problems that arise in mathematics and in other contexts.

MM3P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM3P1.d. Monitor and reflect on the process of mathematical problem solving.

MM3P2. Students will reason and evaluate mathematical arguments.

MM3P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM3P2.b. Make and investigate mathematical conjectures.

MM3P2.c. Develop and evaluate mathematical arguments and proofs.

MM3P2.d. Select and use various types of reasoning and methods of proof.

MM3P3. Students will communicate mathematically.

MM3P3.a. Organize and consolidate their mathematical thinking through communication.

MM3P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM3P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM3P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM3P4. Students will make connections among mathematical ideas and to other disciplines.

MM3P4.a. Recognize and use connections among mathematical ideas.

MM3P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM3P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM3P5. Students will represent mathematics in multiple ways.

MM3P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM3P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM3P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MM4A. Mathematics 4 - Algebra: Students will analyze rational and trigonometric functions. Students will investigate and apply sequences and series and will understand and use vectors.

MM4A1. Students will explore rational functions.

MM4A1.a. Investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior.

MM4A1.b. Find inverses of rational functions, discussing domain and range, symmetry, and function composition.

MM4A1.c. Solve rational equations and inequalities analytically, graphically, and by using appropriate technology.

MM4A2. Students will use the circle to define the trigonometric functions.

MM4A2.a. Define and understand angles measured in degrees and radians, including but not limited to 0 degrees, 30 degrees, 45 degrees, 60 degrees, 90 degrees, their multiples, and equivalences.

MM4A2.b. Understand and apply the six trigonometric functions as functions of general angles in standard position.

MM4A2.c. Find values of trigonometric functions using points on the terminal sides of angles in the standard position.

MM4A2.d. Understand and apply the six trigonometric functions as functions of arc length on the unit circle.

MM4A2.e. Find values of trigonometric functions using the unit circle.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

MM4A3.a. Understand and apply the six basic trigonometric functions as functions of real numbers.

MM4A3.b. Determine the characteristics of the graphs of the six basic trigonometric functions.

MM4A3.c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3.d. Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena.

MM4A4. Students will investigate functions.

MM4A4.a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

MM4A4.b. Investigate transformations of functions.

MM4A4.c. Investigate characteristics of functions built through sum, difference, product, quotient, and composition.

MM4A5. Students will establish trigonometric identities and use them to simplify trigonometric expressions and verify equivalence statements.

MM4A6. Students will solve trigonometric equations both graphically and algebraically.

MM4A6.a. Solve trigonometric equations over a variety of domains, using technology as appropriate.

MM4A6.b. Use the coordinates of a point on the terminal side of an angle to express x and y as polar coordinates.

MM4A6.d. Apply the law of sines and the law of cosines.

MM4A7. Students will verify and apply 1/2 ab sinC to find the area of a triangle.

MM4A8. Students will investigate and use inverse sine, inverse cosine, and inverse tangent functions.

MM4A8.a. Find values of the above functions using technology as appropriate.

MM4A8.b. Determine characteristics of the above functions and their graphs.

MM4A9. Students will use sequences and series

MM4A9.a. Use and find recursive and explicit formulae for the terms of sequences.

MM4A9.b. Recognize and use simple arithmetic and geometric sequences.

MM4A9.c. Find and apply the sums of finite and, where appropriate, infinite arithmetic and geometric series.

MM4A9.d. Use summation notation to explore finite series.

MM4A10. Students will understand and use vectors.

MM4A10.a. Represent vectors algebraically and geometrically.

MM4A10.b. Convert between vectors expressed using rectangular coordinates and expressed using magnitude and direction.

MM4A10.c. Add, subtract, and compute scalar multiples of vectors.

MM4A10.d. Use vectors to solve realistic problems.

GA.MM4D. Mathematics 4 - Data Analysis and Probability: Students will organize, represent, investigate, interpret, and make inferences from data, using the central limit theorem and the standard normal distribution. Students will apply the Central Limit Theorem to calculate confidence intervals for a population mean using data from large samples. Students will use sample data and confidence intervals to draw conclusions about populations.

MM4D1. Using simulation, students will develop the idea of the central limit theorem.

MM4D2. Using student-generated data from random samples of at least 30 members, students will determine the margin of error and confidence interval for a specified level of confidence.

MM4D3. Students will use confidence intervals and margins of error to make inferences from data about a population. Technology is used to evaluate confidence intervals, but students will be aware of the ideas involved.

GA.MM4P. Mathematics 4 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM4P1. Students will solve problems (using appropriate technology).

MM4P1.a. Build new mathematical knowledge through problem solving.

MM4P1.b. Solve problems that arise in mathematics and in other contexts.

MM4P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM4P1.d. Monitor and reflect on the process of mathematical problem solving.

MM4P2. Students will reason and evaluate mathematical arguments.

MM4P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM4P2.b. Make and investigate mathematical conjectures.

MM4P2.c. Develop and evaluate mathematical arguments and proofs.

MM4P2.d. Select and use various types of reasoning and methods of proof.

MM4P3. Students will communicate mathematically.

MM4P3.a. Organize and consolidate their mathematical thinking through communication.

MM4P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM4P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM4P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM4P4. Students will make connections among mathematical ideas and to other disciplines.

MM4P4.a. Recognize and use connections among mathematical ideas.

MM4P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM4P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM4P5. Students will represent mathematics in multiple ways.

MM4P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM4P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM4P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC1A. Core Mathematics 1 - Algebra: Students will explore and interpret the characteristics of functions.

MC1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MC1A1.a. Represent functions using function notation.

MC1A1.b. Graph the basic functions f(x) = x^n, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

MC1A1.c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

MC1A1.d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

MC1A1.e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

MC1A1.f. Recognize sequences as functions with domains that are whole numbers.

MC1A1.g. Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

MC1A1.h. Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

MC1A1.i. Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

GA.MC1G. Core Mathematics 1 - Geometry: The student will apply properties of polygons and determine distances.

MC1G1. Students will investigate properties of geometric figures in the coordinate plane.

MC1G1.a. Determine the distance between two points.

MC1G1.b. Determine the distance between a point and a line.

MC1G1.c. Determine the midpoint of a segment.

MC1G1.d. Understand the distance formula as an application of the Pythagorean theorem.

MC1G1.e. Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

GA.MC1D. Core Mathematics 1 - Data Analysis and Probability: Students will use counting techniques and determine probability.

MC1D1. Students will determine the number of outcomes related to a given event

MC1D1.a. Apply addition and multiplication principles of counting.

MC1D1.b. Calculate and use simple permutations and combinations.

MC1D2. Students will use the basic laws of probability

MC1D2.a. Find the probabilities of mutually exclusive events.

MC1D2.b. Find the probabilities of dependent events.

MC1D2.c. Calculate conditional probabilities.

MC1D2.d. Use expected value to predict outcomes.

GA.MC1P. Core Mathematics 1 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC1P1. Students will solve problems (using appropriate technology).

MC1P1.a. Build new mathematical knowledge through problem solving.

MC1P1.b. Solve problems that arise in mathematics and in other contexts.

MC1P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC1P1.d. Monitor and reflect on the process of mathematical problem solving.

MC1P2. Students will reason and evaluate mathematical arguments.

MC1P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC1P2.b. Make and investigate mathematical conjectures.

MC1P2.c. Develop and evaluate mathematical arguments and proofs.

MC1P2.d. Select and use various types of reasoning and methods of proof.

MC1P3. Students will communicate mathematically.

MC1P3.a. Organize and consolidate their mathematical thinking through communication.

MC1P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC1P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC1P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC1P4. Students will make connections among mathematical ideas and to other disciplines.

MC1P4.a. Recognize and use connections among mathematical ideas.

MC1P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC1P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MC1P5. Students will represent mathematics in multiple ways.

MC1P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC1P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC1P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC2A. Core Mathematics 2 - Algebra: Students will simplify and operate with radical expressions, polynomials, and rational expressions. Students will solve simple equations.

MC2A1. Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MC2A1.a. Simplify algebraic and numeric expressions involving square root.

MC2A1.b. Perform operations with square roots.

MC2A1.c. Add, subtract, multiply, and divide polynomials.

MC2A1.d. Add, subtract, multiply, and divide rational expressions.

MC2A1.e. Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas: (x + y)^2 = x^2 + 2xy + y^2; (x - y)^2 = x^2 - 2xy + y^2; (x + y)(x - y) = x^2 - y^2; (x + a)(x + b) = x^2 + (a + b)x + ab; (x + y)^3 = x^3 + 3 x^2y + 3xy^2 + y^3; (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y3

MC2A1.f. Use area and volume models for polynomial arithmetic.

MC2A2. Students will solve simple equations.

MC2A2.a. Solve quadratic equations in the form ax^2 + bx + c = 0, where a = 1, by using factorization and finding square roots where applicable.

MC2A2.b. Solve equations involving radicals such as square root of x + b = c, using algebraic techniques.

MC2A2.c. Use a variety of techniques, including technology, tables, and graphs to solve equations resulting from the investigation of x^2 + bx + c = 0.

MC2A2.d. Solve simple rational equations that result in linear equations or quadratic equations with leading coefficient of 1.

GA.MC2G. Core Mathematics 2 - Geometry: Students will explore, understand and use the formal language of reasoning and justification. Students will apply properties of polygons.

MC2G1. Students will understand and use the language of mathematical argument and justification.

MC2G1.a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.

MC2G1.b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

MC2G1.c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

MC2G1.d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

MC2G1.e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

GA.MC2D. Core Mathematics 2 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data.

MC2D1. Students will relate samples to a population.

MC2D1.a. Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.

MC2D1.b. Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.

MC2D1.c. Understand that a random sample is used to improve the chance of selecting a representative sample.

MC2D2. Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

GA.MC2P. Core Mathematics 2 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC2P1. Students will solve problems (using appropriate technology).

MC2P1.a. Build new mathematical knowledge through problem solving.

MC2P1.b. Solve problems that arise in mathematics and in other contexts.

MC2P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC2P1.d. Monitor and reflect on the process of mathematical problem solving.

MC2P2. Students will reason and evaluate mathematical arguments.

MC2P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC2P2.b. Make and investigate mathematical conjectures.

MC2P2.c. Develop and evaluate mathematical arguments and proofs.

MC2P2.d. Select and use various types of reasoning and methods of proof.

MC2P3. Students will communicate mathematically.

MC2P3.a. Organize and consolidate their mathematical thinking through communication.

MC2P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC2P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC2P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC2P4. Students will make connections among mathematical ideas and to other disciplines.

MC2P4.a. Recognize and use connections among mathematical ideas.

MC2P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC2P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MC2P5. Students will represent mathematics in multiple ways.

MC2P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC2P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC2P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC3A. Core Mathematics 3 - Algebra: Students will investigate piecewise and exponential functions from numerical, analytical and graphical approaches, focusing on the use of these functions in problem-solving situations.

MC3A1. Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

MC3A1.a. Write absolute value functions as piecewise functions.

MC3A1.b. Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.

MC3A1.c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

MC3A2. Students will explore exponential functions.

MC3A2.a. Extend properties of exponents to include all integer exponents.

MC3A2.b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

MC3A2.c. Graph functions as transformations of f(x) = a^x.

MC3A2.d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

MC3A2.e. Understand and use basic exponential functions as models of real phenomena.

MC3A2.f. Understand and recognize geometric sequences as exponential functions with domains that are sets of whole numbers.

MC3A2.g. Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

GA.MC3G. Core Mathematics 3 - Geometry: Students will explore right triangles and right triangular trigonometry.

MC3G1. Students will identify and use special right triangles.

MC3G1.a. Determine the lengths of sides of 30 degree - 60 degree - 90 degree triangles.

MC3G1.b. Determine the lengths of sides of 45 degree - 45 degree - 90 degree triangles.

MC3G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.

MC3G2.a. Discover the relationship of the trigonometric ratios for similar triangles.

MC3G2.b. Explain the relationship between the trigonometric ratios of complementary angles.

MC3G2.c. Solve application problems using the trigonometric ratios.

GA.MC3D. Core Mathematics 3 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data. Students will use regression to analyze data, and to make inferences.

MC3D1. Using sample data, students will make informal inferences about population means and standard deviations.

MC3D1.a. Pose a question and collect sample data from at least two different populations.

MC3D1.b. Understand and calculate the means and standard deviations of sets of data.

MC3D1.c. Use means and standard deviations to compare data sets.

MC3D1.d. Compare the means and standard deviations of random samples with the corresponding population parameters. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

MC3D2. Students will determine an algebraic model to quantify the association between two quantitative variables.

MC3D2.a. Gather and plot data that can be modeled with linear functions.

MC3D2.b. Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and 'eyeballing.'

MC3D2.c. Understand and apply the processes of linear regression for curve fitting using appropriate technology.

GA.MC3P. Core Mathematics 3 - Process Standards: The following process standards are essential mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC3P1. Students will solve problems (using appropriate technology).

MC3P1.a. Build new mathematical knowledge through problem solving.

MC3P1.b. Solve problems that arise in mathematics and in other contexts.

MC3P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC3P1.d. Monitor and reflect on the process of mathematical problem solving.

MC3P2. Students will reason and evaluate mathematical arguments.

MC3P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC3P2.b. Make and investigate mathematical conjectures.

MC3P2.c. Develop and evaluate mathematical arguments and proofs.

MC3P2.d. Select and use various types of reasoning and methods of proof.

MC3P3. Students will communicate mathematically.

MC3P3.a. Organize and consolidate their mathematical thinking through communication.

MC3P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC3P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC3P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC3P4. Students will make connections among mathematical ideas and to other disciplines.

MC3P4.a. Recognize and use connections among mathematical ideas.

MC3P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC3P4.c. Recognize and apply mathematics in context outside of mathematics.

MC3P5. Students will represent mathematics in multiple ways.

MC3P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC3P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC3P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC4N. Core Mathematics 4 - Number and Operations: Students will use the complex number system.

MC4N1. Students will represent and operate with complex numbers.

MC4N1.a. Write square roots of negative numbers in imaginary form.

MC4N1.b. Write complex numbers in the form a + bi.

MC4N1.c. Add, subtract, multiply, and divide complex numbers.

MC4N1.d. Simplify expressions involving complex numbers.

GA.MC4A. Core Mathematics 4 - Algebra: Students will investigate quadratic functions from numerical, analytical and graphical approaches, focusing on the use of these functions in problem-solving situations. Students will solve quadratic equations and inequalities and explore inverses of functions.

MC4A1. Students will analyze quadratic functions in the forms f(x) = ax^2 + bx + c and f(x) = a(x - h)^2 + k.

MC4A1.a. Convert between standard and vertex form.

MC4A1.b. Graph quadratic functions as transformations of the function f(x) = x^2.

MC4A1.c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

MC4A1.d. Explore arithmetic series and various ways of computing their sums.

MC4A1.e. Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

MC4A2. Students will solve quadratic equations and inequalities in one variable.

MC4A2.a. Solve equations graphically using appropriate technology.

MC4A2.b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

MC4A2.c. Analyze the nature of roots using technology and using the discriminant.

MC4A2.d. Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

MC4A3. Students will explore inverses of functions.

MC4A3.a. Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

MC4A3.b. Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.

MC4A3.c. Explore the graphs of functions and their inverses.

MC4A3.d. Use composition to verify that functions are inverses of each other.

GA.MC4G. Core Mathematics 4 - Geometry: Students will understand and apply properties of circles and spheres and use them in determining related measures.

MC4G1. Students will understand the properties of circles.

MC4G1.a. Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

MC4G1.b. Understand and use properties of central, inscribed, and related angles.

MC4G1.c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

MC4G1.d. Justify measurements and relationships in circles using geometric and algebraic properties.

MC4G2. Students will find and compare the measures of spheres.

MC4G2.a. Use and apply surface area and volume of a sphere.

MC4G2.b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

GA.MC4D. Core Mathematics 4 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will use regression to analyze data, and to make inferences.

MC4D1. Students will determine an algebraic model to quantify the association between two quantitative variables.

MC4D1.a. Gather and plot data that can be modeled with quadratic functions.

MC4D1.b. Understand and apply the processes of quadratic regression for curve fitting using appropriate technology.

GA.MC4P. Core Mathematics 4 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC4P1. Students will solve problems (using appropriate technology).

MC4P1.a. Build new mathematical knowledge through problem solving.

MC4P1.b. Solve problems that arise in mathematics and in other contexts.

MC4P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC4P1.d. Monitor and reflect on the process of mathematical problem solving.

MC4P2. Students will reason and evaluate mathematical arguments.

MC4P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC4P2.b. Make and investigate mathematical conjectures.

MC4P2.c. Develop and evaluate mathematical arguments and proofs.

MC4P2.d. Select and use various types of reasoning and methods of proof.

MC4P3. Students will communicate mathematically.

MC4P3.a. Organize and consolidate their mathematical thinking through communication.

MC4P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC4P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC4P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC4P4. Students will make connections among mathematical ideas and to other disciplines.

MC4P4.a. Recognize and use connections among mathematical ideas.

MC4P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC4P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MC4P5. Students will represent mathematics in multiple ways.

MC4P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC4P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC4P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MA1N. Accelerated Mathematics 1 - Number and Operations: Students will use the complex number system.

MA1N1. Students will represent and operate with complex numbers.

MA1N1.a. Write square roots of negative numbers in imaginary form.

MA1N1.b. Write complex numbers in the form a + bi.

MA1N1.c. Add, subtract, multiply, and divide complex numbers.

MA1N1.d. Simplify expressions involving complex numbers.

GA.MA1A. Accelerated Mathematics 1 - Algebra: Students will explore functions, solve equations and operate with radical, polynomial and rational expressions.

MA1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MA1A1.a. Represent functions using function notation.

MA1A1.b. Graph the basic functions f(x) = x^n, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

MA1A1.c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

MA1A1.d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

MA1A1.e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

MA1A1.f. Recognize sequences as functions with domains that are sets of whole numbers.

MA1A1.g. Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

MA1A1.h. Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

MA1A1.i. Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

MA1A2. Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MA1A2.a. Simplify algebraic and numeric expressions involving square root.

MA1A2.b. Perform operations with square roots.

MA1A2.c. Add, subtract, multiply, and divide polynomials.

MA1A2.d. Add, subtract, multiply, and divide rational expressions.

MA1A2.e. Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas: (x + y)^2 = x^2 + 2xy + y^2; (x - y)^2 = x^2 - 2xy + y^2; (x + y)(x - y) = x^2 - y^2; (x + a)(x + b) = x^2 + (a + b)x + ab; (x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3; (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3

MA1A2.f. Use area and volume models for polynomial arithmetic.

MA1A3. Students will analyze quadratic functions in the forms f(x) = ax^2 + bx + c and f(x) = a(x - h)^2 + k.

MA1A3.a. Convert between standard and vertex form.

MA1A3.b. Graph quadratic functions as transformations of the function f(x) = x^2.

MA1A3.c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

MA1A3.d. Explore arithmetic series and various ways of computing their sums.

MA1A3.e. Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

MA1A4. Students will solve quadratic equations and inequalities in one variable.

MA1A4.a. Solve equations graphically using appropriate technology.

MA1A4.b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

MA1A4.c. Analyze the nature of roots using technology and using the discriminant.

MA1A4.d. Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

MA1A5. Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

MA1A5.a. Write absolute value functions as piecewise functions.

MA1A5.b. Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.

MA1A5.c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

GA.MA1G. Accelerated Mathematics 1 - Geometry: Students will explore, understand and use the formal language of reasoning and justification. Students will apply properties of polygons, circles and spheres, and determine distances and points of concurrence.

MA1G1. Students will investigate properties of geometric figures in the coordinate plane.

MA1G1.a. Determine the distance between two points.

MA1G1.b. Determine the distance between a point and a line.

MA1G1.c. Determine the midpoint of a segment.

MA1G1.d. Understand the distance formula as an application of the Pythagorean theorem.

MA1G1.e. Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

MA1G2. Students will understand and use the language of mathematical argument and justification.

MA1G2.a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.

MA1G2.b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

MA1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.

MA1G3.a. Determine the sum of interior and exterior angles in a polygon.

MA1G3.b. Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.

MA1G3.c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

MA1G3.d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

MA1G3.e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

MA1G4. Students will understand the properties of circles.

MA1G4.a. Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

MA1G4.b. Understand and use properties of central, inscribed, and related angles.

MA1G4.c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

MA1G4.d. Justify measurements and relationships in circles using geometric and algebraic properties.

MA1G5. Students will find and compare the measures of spheres.

MA1G5.a. Use and apply surface area and volume of a sphere.

MA1G5.b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

GA.MA1D. Accelerated Mathematics 1 - Data Analysis and Probability: Students will use counting techniques and determine probability. Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data. Students will determine algebraic models from data.

MA1D1. Students will determine the number of outcomes related to a given event.

MA1D1.a. Apply the addition and multiplication principles of counting.

MA1D1.b. Calculate and use simple permutations and combinations.

MA1D2. Students will use the basic laws of probability.

MA1D2.a. Find the probabilities of mutually exclusive events.

MA1D2.b. Find the probabilities of dependent events.

MA1D2.c. Calculate conditional probabilities.

MA1D2.d. Use expected value to predict outcomes.

MA1D3. Students will relate samples to a population.

MA1D3.a. Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.

MA1D3.b. Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.

MA1D3.c. Understand that a random sample is used to improve the chance of selecting a representative sample.

MA1D4. Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

MA1D5. Students will determine an algebraic model to quantify the association between two quantitative variables.

MA1D5.a. Gather and plot data that can be modeled with linear and quadratic functions.

MA1D5.b. Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and .eyeballing..

MA1D5.c. Understand and apply the processes of linear and quadratic regression for curve fitting using appropriate technology.

GA.MA1P. Accelerated Mathematics 1 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MA1P1. Students will solve problems (using appropriate technology).

MA1P1.a. Build new mathematical knowledge through problem solving.

MA1P1.b. Solve problems that arise in mathematics and in other contexts.

MA1P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MA1P1.d. Monitor and reflect on the process of mathematical problem solving.

MA1P2. Students will reason and evaluate mathematical arguments.

MA1P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MA1P2.b. Make and investigate mathematical conjectures.

MA1P2.c. Develop and evaluate mathematical arguments and proofs.

MA1P2.d. Select and use various types of reasoning and methods of proof.

MA1P3. Students will communicate mathematically.

MA1P3.a. Organize and consolidate their mathematical thinking through communication.

MA1P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MA1P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MA1P3.d. Use the language of mathematics to express mathematical ideas precisely.

MA1P4. Students will make connections among mathematical ideas and to other disciplines.

MA1P4.a. Recognize and use connections among mathematical ideas.

MA1P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MA1P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MA1P5. Students will represent mathematics in multiple ways.

MA1P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MA1P5.b. Select, apply, and translate among mathematical representations to solve problems.

MA1P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MA2A. Accelerated Mathematics 2 - Algebra: Students will investigate exponential, logarithmic, and polynomial functions of higher degree; understand matrices and use them to solve problems; and solve linear programming problems in two variables.

MA2A1. Students will explore exponential functions.

MA2A1.a. Extend properties of exponents to include all integer exponents.

MA2A1.b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

MA2A1.c. Graph functions as transformations of f(x) = a^x.

MA2A1.d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

MA2A1.e. Understand and use basic exponential functions as models of real phenomena.

MA2A1.f. Understand and recognize geometric sequences as exponential functions with domains that are sets of whole numbers.

MA2A1.g. Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

MA2A2. Students will explore inverses of functions.

MA2A2.a. Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

MA2A2.b. Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.

MA2A2.c. Explore the graphs of functions and their inverses.

MA2A2.d. Use composition to verify that functions are inverses of each other.

MA2A3. Students will analyze graphs of polynomial functions of higher degree.

MA2A3.a. Graph simple polynomial functions as translations of the function f(x) = ax^n.

MA2A3.b. Understand the effects of the following on the graph of a polynomial function: degree, lead coefficient, and multiplicity of real zeros.

MA2A3.c. Determine whether a polynomial function has symmetry and whether it is even, odd, or neither.

MA2A3.d. Investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.

MA2A4. Students will explore logarithmic functions as inverses of exponential functions.

MA2A4.a. Define and understand the properties of nth roots.

MA2A4.b. Extend properties of exponents to include rational exponents.

MA2A4.c. Define logarithmic functions as inverses of exponential functions.

MA2A4.d. Understand and use properties of logarithms by extending laws of exponents.

MA2A4.e. Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

MA2A4.f. Graph functions as transformations of f(x) = a^x, f(x) = log ax, f(x) = e^x, f(x) = ln x.

MA2A4.g. Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

MA2A5. Students will solve a variety of equations and inequalities.

MA2A5.a. Find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical conjugates.

MA2A5.b. Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

MA2A5.c. Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

MA2A5.d. Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology.

MA2A6. Students will perform basic operations with matrices.

MA2A6.a. Add, subtract, multiply, and invert matrices, when possible, choosing appropriate methods, including technology.

MA2A6.b. Find the inverses of two-by-two matrices using pencil and paper, and find inverses of larger matrices using technology.

MA2A6.c. Examine the properties of matrices, contrasting them with properties of real numbers.

MA2A7. Students will use matrices to formulate and solve problems.

MA2A7.a. Represent a system of linear equations as a matrix equation.

MA2A7.b. Solve matrix equations using inverse matrices.

MA2A7.c. Represent and solve realistic problems using systems of linear equations.

MA2A8. Students will solve linear programming problems in two variables.

MA2A8.a. Solve systems of inequalities in two variables, showing the solutions graphically.

MA2A8.b. Represent and solve realistic problems using linear programming.

MA2A9. Students will understand and apply matrix representations of vertex-edge graphs.

MA2A9.a. Use graphs to represent realistic situations.

MA2A9.b. Use matrices to represent graphs, and solve problems that can be represented by graphs.

GA.MA2G. Accelerated Mathematics 2 - Geometry: Students will explore right triangles and right triangular trigonometry. They will understand and apply properties of conic sections, planes, and spheres.

MA2G1. Students will identify and use special right triangles.

MA2G1.a. Determine the lengths of sides of 30 degree - 60 degree - 90 degree triangles.

MA2G1.b. Determine the lengths of sides of 45 degree - 45 degree - 90 degree triangles.

MA2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.

MA2G2.a. Discover the relationship of the trigonometric ratios for similar triangles.

MA2G2.b. Explain the relationship between the trigonometric ratios of complementary angles.

MA2G2.c. Solve application problems using the trigonometric ratios.

MA2G3. Students will investigate the relationships between lines and circles.

MA2G3.a. Find equations of circles.

MA2G3.b. Graph a circle given an equation in general form.

MA2G3.c. Find the equation of a tangent line to a circle at a given point.

MA2G3.d. Solve a system of equations involving a circle and a line.

MA2G3.e. Solve a system of equations involving two circles.

MA2G4. Students will recognize, analyze, and graph the equations of the conic sections (parabolas, circles, ellipses, and hyperbolas).

MA2G4.a. Convert equations of conics by completing the square.

MA2G4.b. Graph conic sections, identifying fundamental characteristics.

MA2G4.c. Write equations of conic sections given appropriate information.

MA2G5. Students will investigate planes and spheres.

MA2G5.a. Plot the point (x, y, z) and understand it as a vertex of a rectangular prism.

MA2G5.b. Apply the distance formula in 3-space.

MA2G5.c. Recognize and understand equations of planes and spheres.

GA.MA2D. Accelerated Mathematics 2 - Data Analysis and Probability: Students will make informal inferences about means and standard deviations. Students will use a normal distribution to calculate probabilities. Students will organize, represent, investigate, interpret, and make inferences from both observational studies and experiments.

MA2D1. Using sample data, students will make informal inferences about population means and standard deviations.

MA2D1.a. Pose a question and collect sample data from at least two different populations.

MA2D1.b. Understand and calculate the means and standard deviations of sets of data.

MA2D1.c. Use means and standard deviations to compare data sets.

MA2D1.d. Compare the means and standard deviations of random samples with the corresponding population parameters. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

MA2D2. Students will create probability histograms of discrete random variables, using both experimental and theoretical probabilities.

MA2D3. Students will solve problems involving probabilities by interpreting a normal distribution as a probability histogram for a continuous random variable (z-scores are used for a general normal distribution).

MA2D3.a. Determine intervals about the mean that include a given percent of data.

MA2D3.b. Determine the probability that a given value falls within a specified interval.

MA2D3.c. Estimate how many items in a population fall within a specified interval.

MA2D4. Students will understand the differences between experimental and observational studies by posing questions and collecting, analyzing, and interpreting data.

GA.MA2P. Accelerated Mathematics 2 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MA2P1. Students will solve problems (using appropriate technology).

MA2P1.a. Build new mathematical knowledge through problem solving.

MA2P1.b. Solve problems that arise in mathematics and in other contexts.

MA2P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MA2P1.d. Monitor and reflect on the process of mathematical problem solving.

MA2P2. Students will reason and evaluate mathematical arguments.

MA2P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MA2P2.b. Make and investigate mathematical conjectures.

MA2P2.c. Develop and evaluate mathematical arguments and proofs.

MA2P2.d. Select and use various types of reasoning and methods of proof.

MA2P3. Students will communicate mathematically.

MA2P3.a. Organize and consolidate their mathematical thinking through communication.

MA2P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MA2P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MA2P3.d. Use the language of mathematics to express mathematical ideas precisely.

MA2P4. Students will make connections among mathematical ideas and to other disciplines.

MA2P4.a. Recognize and use connections among mathematical ideas.

MA2P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MA2P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MA2P5. Students will represent mathematics in multiple ways.

MA2P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MA2P5.b. Select, apply, and translate among mathematical representations to solve problems.

MA2P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MA3A. Accelerated Mathematics 3 - Algebra: Students will explore characteristics of various functions, understand and use concepts of trigonometric functions, investigate and apply sequences and series, and use parametric and polar equations to represent functions and curves.

MA3A1. Students will explore rational functions.

MA3A1.a. Investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior.

MA3A1.b. Find inverses of rational functions, discussing domain and range, symmetry, and function composition.

MA3A1.c. Solve rational equations and inequalities analytically, graphically, and by using appropriate technology.

MA3A2. Students will use the circle to define the trigonometric functions.

MA3A2.a. Define and understand angles measured in degrees and radians, including but not limited to 0 degrees, 30 degrees, 45 degrees, 60 degrees, 90 degrees, their multiples, and equivalences.

MA3A2.b. Understand and apply the six trigonometric functions as functions of general angles in standard position.

MA3A2.c. Find values of trigonometric functions using points on the terminal sides of angles in the standard position.

MA3A2.d. Understand and apply the six trigonometric functions as functions of arc length on the unit circle.

MA3A2.e. Find values of trigonometric functions using the unit circle.

MA3A3. Students will investigate and use the graphs of the six trigonometric functions.

MA3A3.a. Understand and apply the six basic trigonometric functions as functions of real numbers.

MA3A3.b. Determine the characteristics of the graphs of the six basic trigonometric functions.

MA3A3.c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MA3A3.d. Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena.

MA3A4. Students will investigate functions.

MA3A4.a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

MA3A4.b. Investigate transformations of functions.

MA3A4.c. Investigate characteristics of functions built through sum, difference, product, quotient, and composition.

MA3A5. Students will establish trigonometric identities and use them to simplify trigonometric expressions and verify equivalence statements.

MA3A6. Students will solve trigonometric equations both graphically and algebraically.

MA3A6.a. Solve trigonometric equations over a variety of domains, using technology as appropriate.

MA3A6.b. Use the coordinates of a point on the terminal side of an angle to express x and y as polar coordinates.

MA3A6.c. Apply the law of sines and the law of cosines.

MA3A7. Students will verify and apply 1/2 ab sinC to find the area of a triangle.

MA3A8. Students will investigate and use inverse sine, inverse cosine, and inverse tangent functions.

MA3A8.a. Find values of the above functions using technology as appropriate.

MA3A8.b. Determine characteristics of the above functions and their graphs.

MA3A9. Students will use sequences and series

MA3A9.a. Use and find recursive and explicit formulae for the terms of sequences.

MA3A9.b. Recognize and use simple arithmetic and geometric sequences.

MA3A9.c. Investigate limits of sequences.

MA3A9.d. Use mathematical induction to find and prove formulae for sums of finite series.

MA3A9.e. Find and apply the sums of finite and, where appropriate, infinite arithmetic and geometric series.

MA3A9.f. Use summation notation to explore series.

MA3A9.g. Determine geometric series and their limits.

MA3A10. Students will understand and use vectors.

MA3A10.a. Represent vectors algebraically and geometrically.

MA3A10.b. Convert between vectors expressed using rectangular coordinates and vectors expressed using magnitude and direction.

MA3A10.c. Add and subtract vectors and compute scalar multiples of vectors.

MA3A10.d. Use vectors to solve realistic problems.

MA3A11. Students will use complex numbers in trigonometric form.

MA3A11.a. Represent complex numbers in trigonometric form.

MA3A11.b. Find products, quotients, powers, and roots of complex numbers in trigonometric form.

MA3A12. Students will explore parametric representations of plane curves.

MA3A12.a. Convert between Cartesian and parametric form.

MA3A12.b. Graph equations in parametric form showing direction and beginning and ending points where appropriate.

MA3A13. Students will explore polar equations.

MA3A13.a. Express coordinates of points in rectangular and polar form.

MA3A13.b. Graph and identify characteristics of simple polar equations including lines, circles, cardioids, limacons, and roses.

GA.MA3D. Accelerated Mathematics 3 - Data Analysis and Probability: Students will organize, represent, investigate, interpret, and make inferences from data, using the central limit theorem and the standard normal distribution. Students will apply the Central Limit Theorem to calculate confidence intervals for a population mean using data from large samples. Students will use sample data and confidence intervals to draw conclusions about populations.

MA3D1. Using simulation, students will develop the idea of the central limit theorem.

MA3D2. Using student-generated data from random samples of at least 30 members, students will determine the margin of error and confidence interval for a specified level of confidence.

MA3D3. Students will use confidence intervals and margins of error to make inferences from data about a population. Technology is used to evaluate confidence intervals, but students will be aware of the ideas involved.

GA.MA3P. Accelerated Mathematics 3 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MA3P1. Students will solve problems (using appropriate technology).

MA3P1.a. Build new mathematical knowledge through problem solving.

MA3P1.b. Solve problems that arise in mathematics and in other contexts.

MA3P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MA3P1.d. Monitor and reflect on the process of mathematical problem solving.

MA3P2. Students will reason and evaluate mathematical arguments.

MA3P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MA3P2.b. Make and investigate mathematical conjectures.

MA3P2.c. Develop and evaluate mathematical arguments and proofs.

MA3P2.d. Select and use various types of reasoning and methods of proof.

MA3P3. Students will communicate mathematically.

MA3P3.a. Organize and consolidate their mathematical thinking through communication.

MA3P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MA3P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MA3P3.d. Use the language of mathematics to express mathematical ideas precisely.

MA3P4. Students will make connections among mathematical ideas and to other disciplines.

MA3P4.a. Recognize and use connections among mathematical ideas.

MA3P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MA3P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MA3P5. Students will represent mathematics in multiple ways.

MA3P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MA3P5.b. Select, apply, and translate among mathematical representations to solve problems.

MA3P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MRC. Reading Across the Curriculum: Reading across curriculum content develops both academic and personal interests in students. As students read, they develop both content and contextual vocabulary. They also build good habits for reading, researching, and learning. The Reading Across the Curriculum standard focuses on the academic and personal skills students acquire as they read in all areas of learning.

MRC1. Students will enhance reading in all curriculum areas by:

MRC1.a. Reading in all curriculum areas: Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areas; Read both informational and fictional texts in a variety of genres and modes of discourse; Read technical texts related to various subject areas

MRC1.b. Discussing books: Discuss messages and themes from books in all subject areas; Respond to a variety of texts in multiple modes of discourse; Relate messages and themes from one subject area to messages and themes in another area; Evaluate the merit of texts in every subject discipline; Examine author's purpose in writing; Recognize the features of disciplinary texts.

MRC1.c. Building vocabulary knowledge: Demonstrate an understanding of contextual vocabulary in various subjects; Use content vocabulary in writing and speaking; Explore understanding of new words found in subject area texts.

MRC1.d. Establishing context: Explore life experiences related to subject area content; Discuss in both writing and speaking how certain words are subject area related; Determine strategies for finding content and contextual meaning for unknown words.

GA.MM1A. Mathematics 1 - Algebra: Students will explore functions and solve simple equations. Students will simplify and operate with radical, polynomial, and rational expressions.

MM1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MM1A1.a. Represent functions using function notation.

MM1A1.b. Graph the basic functions f(x) = x^n, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

MM1A1.c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

MM1A1.d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

MM1A1.e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

MM1A1.f. Recognize sequences as functions with domains that are whole numbers.

MM1A1.g. Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

MM1A1.h. Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

MM1A1.i. Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

MM1A2. Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MM1A2.a. Simplify algebraic and numeric expressions involving square root.

MM1A2.b. Perform operations with square roots.

MM1A2.c. Add, subtract, multiply, and divide polynomials.

MM1A2.d. Expand binomials using the Binomial Theorem.

MM1A2.e. Add, subtract, multiply, and divide rational expressions.

MM1A2.f. Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas: (x + y)^2 = x^2 + 2xy + y^2; (x - y)^2 = x^2 - 2xy + y^2; (x + y)(x - y) = x^2 - y^2; (x + a)(x + b) = x^2 + (a + b)x + ab; (x + y)^3 = x^3 + 3 x^2y + 3xy^2 + y^3; (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3

MM1A2.g. Use area and volume models for polynomial arithmetic.

MM1A3. Students will solve simple equations.

MM1A3.a. Solve quadratic equations in the form ax^2 + bx + c = 0, where a = 1, by using factorization and finding square roots where applicable.

MM1A3.b. Solve equations involving radicals such as square root of x + b = c, using algebraic techniques.

MM1A3.c. Use a variety of techniques, including technology, tables, and graphs to solve equations resulting from the investigation of x^2 + bx + c = 0.

MM1A3.d. Solve simple rational equations that result in linear equations or quadratic equations with leading coefficient of 1.

GA.MM1G. Mathematics 1 - Geometry: Students will explore, understand, and use the formal language of reasoning and justification. Students will apply properties of polygons and determine distances and points of concurrence.

MM1G1. Students will investigate properties of geometric figures in the coordinate plane.

MM1G1.a. Determine the distance between two points.

MM1G1.b. Determine the distance between a point and a line.

MM1G1.c. Determine the midpoint of a segment.

MM1G1.d. Understand the distance formula as an application of the Pythagorean theorem.

MM1G1.e. Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

MM1G2. Students will understand and use the language of mathematical argument and justification.

MM1G2.a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.

MM1G2.b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

MM1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.

MM1G3.a. Determine the sum of interior and exterior angles in a polygon.

MM1G3.b. Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.

MM1G3.c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

MM1G3.d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

MM1G3.e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

GA.MM1D. Mathematics 1 - Data Analysis and Probability: Students will use counting techniques and determine probability. Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data.

MM1D1. Students will determine the number of outcomes related to a given event.

MM1D1.a. Apply the addition and multiplication principles of counting.

MM1D1.b. Calculate and use simple permutations and combinations.

MM1D2. Students will use the basic laws of probability.

MM1D2.a. Find the probabilities of mutually exclusive events.

MM1D2.b. Find the probabilities of dependent events.

MM1D2.c. Calculate conditional probabilities.

MM1D2.d. Use expected value to predict outcomes.

MM1D3. Students will relate samples to a population.

MM1D3.a. Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.

MM1D3.b. Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.

MM1D3.c. Understand that a random sample is used to improve the chance of selecting a representative sample.

MM1D4. Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

GA.MM1P. Mathematics 1 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM1P1. Students will solve problems (using appropriate technology).

MM1P1.a. Build new mathematical knowledge through problem solving.

MM1P1.b. Solve problems that arise in mathematics and in other contexts.

MM1P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM1P1.d. Monitor and reflect on the process of mathematical problem solving.

MM1P2. Students will reason and evaluate mathematical arguments.

MM1P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM1P2.b. Make and investigate mathematical conjectures.

MM1P2.c. Develop and evaluate mathematical arguments and proofs.

MM1P2.d. Select and use various types of reasoning and methods of proof.

MM1P3. Students will communicate mathematically.

MM1P3.a. Organize and consolidate their mathematical thinking through communication.

MM1P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM1P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM1P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM1P4. Students will make connections among mathematical ideas and to other disciplines.

MM1P4.a. Recognize and use connections among mathematical ideas.

MM1P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM1P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM1P5. Students will represent mathematics in multiple ways.

MM1P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM1P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM1P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MM2N. Mathematics 2 - Number and Operations: Students will use the complex number system.

MM2N1. Students will represent and operate with complex numbers.

MM2N1.a. Write square roots of negative numbers in imaginary form.

MM2N1.b. Write complex numbers in the form a + bi.

MM2N1.c. Add, subtract, multiply, and divide complex numbers.

MM2N1.d. Simplify expressions involving complex numbers.

GA.MM2A. Mathematics 2 - Algebra: Students will investigate piecewise, exponential, and quadratic functions, using numerical, analytical, and graphical approaches, focusing on the use of these functions in problem-solving situations. Students will solve equations and inequalities and explore inverses of functions.

MM2A1. Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

MM2A1.a. Write absolute value functions as piecewise functions.

MM2A1.b. Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.

MM2A1.c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

MM2A2. Students will explore exponential functions.

MM2A2.a. Extend properties of exponents to include all integer exponents.

MM2A2.b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

MM2A2.c. Graph functions as transformations of f(x) = a^x.

MM2A2.d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

MM2A2.e. Understand and use basic exponential functions as models of real phenomena.

MM2A2.f. Understand and recognize geometric sequences as exponential functions with domains that are whole numbers.

MM2A2.g. Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

MM2A3.a. Convert between standard and vertex form.

MM2A3. Students will analyze quadratic functions in the forms f(x) = ax^2 + bx + c and f(x) = a(x - h)^2 + k.

MM2A3.b. Graph quadratic functions as transformations of the function f(x) = x^2.

MM2A3.c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

MM2A3.d. Explore arithmetic series and various ways of computing their sums.

MM2A3.e. Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

MM2A4. Students will solve quadratic equations and inequalities in one variable.

MM2A4.a. Solve equations graphically using appropriate technology.

MM2A4.b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

MM2A4.c. Analyze the nature of roots using technology and using the discriminant.

MM2A4.d. Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

MM2A5. Students will explore inverses of functions.

MM2A5.a. Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

MM2A5.b. Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.

MM2A5.c. Explore the graphs of functions and their inverses.

MM2A5.d. Use composition to verify that functions are inverses of each other.

GA.MM2G. Mathematics 2 - Geometry: Students will explore right triangles and right-triangle trigonometry. They will understand and apply properties of circles and spheres, and use them in determining related measures.

MM2G1. Students will identify and use special right triangles.

MM2G1.a. Determine the lengths of sides of 30 degree - 60 degree - 90 degree triangles.

MM2G1.b. Determine the lengths of sides of 45 degree - 45 degree - 90 degree triangles.

MM2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.

MM2G2.a. Discover the relationship of the trigonometric ratios for similar triangles.

MM2G2.b. Explain the relationship between the trigonometric ratios of complementary angles.

MM2G2.c. Solve application problems using the trigonometric ratios.

MM2G3. Students will understand the properties of circles.

MM2G3.a. Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

MM2G3.b. Understand and use properties of central, inscribed, and related angles.

MM2G3.c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

MM2G3.d. Justify measurements and relationships in circles using geometric and algebraic properties.

MM2G4. Students will find and compare the measures of spheres.

MM2G4.a. Use and apply surface area and volume of a sphere.

MM2G4.b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

GA.MM2D. Mathematics 2 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data. They will use regression to analyze data and to make inferences.

MM2D1. Using sample data, students will make informal inferences about population means and standard deviations.

MM2D1.a. Pose a question and collect sample data from at least two different populations.

MM2D1.b. Understand and calculate the means and standard deviations of sets of data.

MM2D1.c. Use means and standard deviations to compare data sets.

MM2D1.d. Compare the means and standard deviations of random samples with the corresponding population parameters, including those population parameters for normal distributions. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

MM2D2. Students will determine an algebraic model to quantify the association between two quantitative variables.

MM2D2.a. Gather and plot data that can be modeled with linear and quadratic functions.

MM2D2.b. Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and 'eyeballing.'

MM2D2.c. Understand and apply the processes of linear and quadratic regression for curve fitting using appropriate technology.

MM2D2.d. Investigate issues that arise when using data to explore the relationship between two variables, including confusion between correlation and causation.

GA.MM2P. Mathematics 2 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM2P1. Students will solve problems (using appropriate technology).

MM2P1.a. Build new mathematical knowledge through problem solving.

MM2P1.b. Solve problems that arise in mathematics and in other contexts.

MM2P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM2P1.d. Monitor and reflect on the process of mathematical problem solving.

MM2P2. Students will reason and evaluate mathematical arguments.

MM2P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM2P2.b. Make and investigate mathematical conjectures.

MM2P2.c. Develop and evaluate mathematical arguments and proofs.

MM2P2.d. Select and use various types of reasoning and methods of proof.

MM2P3. Students will communicate mathematically.

MM2P3.a. Organize and consolidate their mathematical thinking through communication.

MM2P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM2P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM2P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM2P4. Students will make connections among mathematical ideas and to other disciplines.

MM2P4.a. Recognize and use connections among mathematical ideas.

MM2P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM2P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM2P5. Students will represent mathematics in multiple ways.

MM2P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM2P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM2P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MM3A. Mathematics 3 - Algebra: Students will investigate exponential, logarithmic and polynomial functions of degree higher than 2. Students will understand matrices and use them to solve problems.

MM3A1. Students will analyze graphs of polynomial functions of higher degree.

MM3A1.a. Graph simple polynomial functions as translations of the function f(x) = ax^n.

MM3A1.b. Understand the effects of the following on the graph of a polynomial function: degree, lead coefficient, and multiplicity of real zeros.

MM3A1.c. Determine whether a polynomial function has symmetry and whether it is even, odd, or neither.

MM3A1.d. Investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.

MM3A2. Students will explore logarithmic functions as inverses of exponential functions.

MM3A2.a. Define and understand the properties of nth roots.

MM3A2.b. Extend properties of exponents to include rational exponents.

MM3A2.c. Define logarithmic functions as inverses of exponential functions.

MM3A2.d. Understand and use properties of logarithms by extending laws of exponents.

MM3A2.e. Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

MM3A2.f. Graph functions as transformations of f(x) = a^x, f(x) = log ax, f(x) = e^x, f(x) = ln x.

MM3A2.g. Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

MM3A3. Students will solve a variety of equations and inequalities.

MM3A3.a. Find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical conjugates.

MM3A3.b. Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

MM3A3.c. Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

MM3A3.d. Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology.

MM3A4. Students will perform basic operations with matrices.

MM3A4.a. Add, subtract, multiply, and invert matrices, when possible, choosing appropriate methods, including technology.

MM3A4.b. Find the inverses of two-by-two matrices using pencil and paper, and find inverses of larger matrices using technology.

MM3A4.c. Examine the properties of matrices, contrasting them with properties of real numbers.

MM3A5. Students will use matrices to formulate and solve problems.

MM3A5.a. Represent a system of linear equations as a matrix equation.

MM3A5.b. Solve matrix equations using inverse matrices.

MM3A5.c. Represent and solve realistic problems using systems of linear equations.

MM3A6. Students will solve linear programming problems in two variables.

MM3A6.a. Solve systems of inequalities in two variables, showing the solutions graphically.

MM3A6.b. Represent and solve realistic problems using linear programming.

MM3A7. Students will understand and apply matrix representations of vertex-edge graphs.

MM3A7.a. Use graphs to represent realistic situations.

MM3A7.b. Use matrices to represent graphs, and solve problems that can be represented by graphs.

GA.MM3G. Mathematics 3 - Geometry: Students will understand and use the analytic geometry of conic sections and of planes and spheres in space.

MM3G1. Students will investigate the relationships between lines and circles.

MM3G1.a. Find equations of circles.

MM3G1.b. Graph a circle given an equation in general form.

MM3G1.c. Find the equation of a tangent line to a circle at a given point.

MM3G1.d. Solve a system of equations involving a circle and a line.

MM3G1.e. Solve a system of equations involving two circles.

MM3G2. Students will recognize, analyze, and graph the equations of the conic sections (parabolas, circles, ellipses, and hyperbolas).

MM3G2.a. Convert equations of conics by completing the square.

MM3G2.b. Graph conic sections, identifying fundamental characteristics.

MM3G2.c. Write equations of conic sections given appropriate information.

MM3G3. Students will investigate planes and spheres.

MM3G3.a. Plot the point (x, y, z) and understand it as a vertex of a rectangular prism.

MM3G3.b. Apply the distance formula in 3-space.

MM3G3.c. Recognize and understand equations of planes and spheres.

GA.MM3D. Mathematics 3 - Data Analysis and Probability: Students will use a normal distribution to calculate probabilities. They will organize, represent, investigate, interpret, and make inferences using data from both observational studies and experiments.

MM3D1. Students will create probability histograms of discrete random variables, using both experimental and theoretical probabilities.

MM3D2. Students will solve problems involving probabilities by interpreting a normal distribution as a probability histogram for a continuous random variable (z-scores are used for a general normal distribution).

MM3D2.a. Determine intervals about the mean that include a given percent of data.

MM3D2.b. Determine the probability that a given value falls within a specified interval.

MM3D2.c. Estimate how many items in a population fall within a specified interval.

MM3D3. Students will understand the differences between experimental and observational studies by posing questions and collecting, analyzing, and interpreting data.

GA.MM3P. Mathematics 3 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM3P1. Students will solve problems (using appropriate technology).

MM3P1.a. Build new mathematical knowledge through problem solving.

MM3P1.b. Solve problems that arise in mathematics and in other contexts.

MM3P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM3P1.d. Monitor and reflect on the process of mathematical problem solving.

MM3P2. Students will reason and evaluate mathematical arguments.

MM3P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM3P2.b. Make and investigate mathematical conjectures.

MM3P2.c. Develop and evaluate mathematical arguments and proofs.

MM3P2.d. Select and use various types of reasoning and methods of proof.

MM3P3. Students will communicate mathematically.

MM3P3.a. Organize and consolidate their mathematical thinking through communication.

MM3P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM3P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM3P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM3P4. Students will make connections among mathematical ideas and to other disciplines.

MM3P4.a. Recognize and use connections among mathematical ideas.

MM3P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM3P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM3P5. Students will represent mathematics in multiple ways.

MM3P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM3P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM3P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MM4A. Mathematics 4 - Algebra: Students will analyze rational and trigonometric functions. Students will investigate and apply sequences and series and will understand and use vectors.

MM4A1. Students will explore rational functions.

MM4A1.a. Investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior.

MM4A1.b. Find inverses of rational functions, discussing domain and range, symmetry, and function composition.

MM4A1.c. Solve rational equations and inequalities analytically, graphically, and by using appropriate technology.

MM4A2. Students will use the circle to define the trigonometric functions.

MM4A2.a. Define and understand angles measured in degrees and radians, including but not limited to 0 degrees, 30 degrees, 45 degrees, 60 degrees, 90 degrees, their multiples, and equivalences.

MM4A2.b. Understand and apply the six trigonometric functions as functions of general angles in standard position.

MM4A2.c. Find values of trigonometric functions using points on the terminal sides of angles in the standard position.

MM4A2.d. Understand and apply the six trigonometric functions as functions of arc length on the unit circle.

MM4A2.e. Find values of trigonometric functions using the unit circle.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

MM4A3.a. Understand and apply the six basic trigonometric functions as functions of real numbers.

MM4A3.b. Determine the characteristics of the graphs of the six basic trigonometric functions.

MM4A3.c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3.d. Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena.

MM4A4. Students will investigate functions.

MM4A4.a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

MM4A4.b. Investigate transformations of functions.

MM4A4.c. Investigate characteristics of functions built through sum, difference, product, quotient, and composition.

MM4A5. Students will establish trigonometric identities and use them to simplify trigonometric expressions and verify equivalence statements.

MM4A6. Students will solve trigonometric equations both graphically and algebraically.

MM4A6.a. Solve trigonometric equations over a variety of domains, using technology as appropriate.

MM4A6.b. Use the coordinates of a point on the terminal side of an angle to express x and y as polar coordinates.

MM4A6.d. Apply the law of sines and the law of cosines.

MM4A7. Students will verify and apply 1/2 ab sinC to find the area of a triangle.

MM4A8. Students will investigate and use inverse sine, inverse cosine, and inverse tangent functions.

MM4A8.a. Find values of the above functions using technology as appropriate.

MM4A8.b. Determine characteristics of the above functions and their graphs.

MM4A9. Students will use sequences and series

MM4A9.a. Use and find recursive and explicit formulae for the terms of sequences.

MM4A9.b. Recognize and use simple arithmetic and geometric sequences.

MM4A9.c. Find and apply the sums of finite and, where appropriate, infinite arithmetic and geometric series.

MM4A9.d. Use summation notation to explore finite series.

MM4A10. Students will understand and use vectors.

MM4A10.a. Represent vectors algebraically and geometrically.

MM4A10.b. Convert between vectors expressed using rectangular coordinates and expressed using magnitude and direction.

MM4A10.c. Add, subtract, and compute scalar multiples of vectors.

MM4A10.d. Use vectors to solve realistic problems.

GA.MM4D. Mathematics 4 - Data Analysis and Probability: Students will organize, represent, investigate, interpret, and make inferences from data, using the central limit theorem and the standard normal distribution. Students will apply the Central Limit Theorem to calculate confidence intervals for a population mean using data from large samples. Students will use sample data and confidence intervals to draw conclusions about populations.

MM4D1. Using simulation, students will develop the idea of the central limit theorem.

MM4D2. Using student-generated data from random samples of at least 30 members, students will determine the margin of error and confidence interval for a specified level of confidence.

MM4D3. Students will use confidence intervals and margins of error to make inferences from data about a population. Technology is used to evaluate confidence intervals, but students will be aware of the ideas involved.

GA.MM4P. Mathematics 4 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM4P1. Students will solve problems (using appropriate technology).

MM4P1.a. Build new mathematical knowledge through problem solving.

MM4P1.b. Solve problems that arise in mathematics and in other contexts.

MM4P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM4P1.d. Monitor and reflect on the process of mathematical problem solving.

MM4P2. Students will reason and evaluate mathematical arguments.

MM4P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM4P2.b. Make and investigate mathematical conjectures.

MM4P2.c. Develop and evaluate mathematical arguments and proofs.

MM4P2.d. Select and use various types of reasoning and methods of proof.

MM4P3. Students will communicate mathematically.

MM4P3.a. Organize and consolidate their mathematical thinking through communication.

MM4P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM4P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM4P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM4P4. Students will make connections among mathematical ideas and to other disciplines.

MM4P4.a. Recognize and use connections among mathematical ideas.

MM4P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM4P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM4P5. Students will represent mathematics in multiple ways.

MM4P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM4P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM4P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC1A. Core Mathematics 1 - Algebra: Students will explore and interpret the characteristics of functions.

MC1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MC1A1.a. Represent functions using function notation.

MC1A1.b. Graph the basic functions f(x) = x^n, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

MC1A1.c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

MC1A1.d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

MC1A1.e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

MC1A1.f. Recognize sequences as functions with domains that are whole numbers.

MC1A1.g. Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

MC1A1.h. Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

MC1A1.i. Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

GA.MC1G. Core Mathematics 1 - Geometry: The student will apply properties of polygons and determine distances.

MC1G1. Students will investigate properties of geometric figures in the coordinate plane.

MC1G1.a. Determine the distance between two points.

MC1G1.b. Determine the distance between a point and a line.

MC1G1.c. Determine the midpoint of a segment.

MC1G1.d. Understand the distance formula as an application of the Pythagorean theorem.

MC1G1.e. Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

GA.MC1D. Core Mathematics 1 - Data Analysis and Probability: Students will use counting techniques and determine probability.

MC1D1. Students will determine the number of outcomes related to a given event

MC1D1.a. Apply addition and multiplication principles of counting.

MC1D1.b. Calculate and use simple permutations and combinations.

MC1D2. Students will use the basic laws of probability

MC1D2.a. Find the probabilities of mutually exclusive events.

MC1D2.b. Find the probabilities of dependent events.

MC1D2.c. Calculate conditional probabilities.

MC1D2.d. Use expected value to predict outcomes.

GA.MC1P. Core Mathematics 1 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC1P1. Students will solve problems (using appropriate technology).

MC1P1.a. Build new mathematical knowledge through problem solving.

MC1P1.b. Solve problems that arise in mathematics and in other contexts.

MC1P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC1P1.d. Monitor and reflect on the process of mathematical problem solving.

MC1P2. Students will reason and evaluate mathematical arguments.

MC1P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC1P2.b. Make and investigate mathematical conjectures.

MC1P2.c. Develop and evaluate mathematical arguments and proofs.

MC1P2.d. Select and use various types of reasoning and methods of proof.

MC1P3. Students will communicate mathematically.

MC1P3.a. Organize and consolidate their mathematical thinking through communication.

MC1P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC1P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC1P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC1P4. Students will make connections among mathematical ideas and to other disciplines.

MC1P4.a. Recognize and use connections among mathematical ideas.

MC1P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC1P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MC1P5. Students will represent mathematics in multiple ways.

MC1P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC1P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC1P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC2A. Core Mathematics 2 - Algebra: Students will simplify and operate with radical expressions, polynomials, and rational expressions. Students will solve simple equations.

MC2A1. Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MC2A1.a. Simplify algebraic and numeric expressions involving square root.

MC2A1.b. Perform operations with square roots.

MC2A1.c. Add, subtract, multiply, and divide polynomials.

MC2A1.d. Add, subtract, multiply, and divide rational expressions.

MC2A1.e. Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas: (x + y)^2 = x^2 + 2xy + y^2; (x - y)^2 = x^2 - 2xy + y^2; (x + y)(x - y) = x^2 - y^2; (x + a)(x + b) = x^2 + (a + b)x + ab; (x + y)^3 = x^3 + 3 x^2y + 3xy^2 + y^3; (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y3

MC2A1.f. Use area and volume models for polynomial arithmetic.

MC2A2. Students will solve simple equations.

MC2A2.a. Solve quadratic equations in the form ax^2 + bx + c = 0, where a = 1, by using factorization and finding square roots where applicable.

MC2A2.b. Solve equations involving radicals such as square root of x + b = c, using algebraic techniques.

MC2A2.c. Use a variety of techniques, including technology, tables, and graphs to solve equations resulting from the investigation of x^2 + bx + c = 0.

MC2A2.d. Solve simple rational equations that result in linear equations or quadratic equations with leading coefficient of 1.

GA.MC2G. Core Mathematics 2 - Geometry: Students will explore, understand and use the formal language of reasoning and justification. Students will apply properties of polygons.

MC2G1. Students will understand and use the language of mathematical argument and justification.

MC2G1.a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.

MC2G1.b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

MC2G1.c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

MC2G1.d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

MC2G1.e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

GA.MC2D. Core Mathematics 2 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data.

MC2D1. Students will relate samples to a population.

MC2D1.a. Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.

MC2D1.b. Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.

MC2D1.c. Understand that a random sample is used to improve the chance of selecting a representative sample.

MC2D2. Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

GA.MC2P. Core Mathematics 2 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC2P1. Students will solve problems (using appropriate technology).

MC2P1.a. Build new mathematical knowledge through problem solving.

MC2P1.b. Solve problems that arise in mathematics and in other contexts.

MC2P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC2P1.d. Monitor and reflect on the process of mathematical problem solving.

MC2P2. Students will reason and evaluate mathematical arguments.

MC2P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC2P2.b. Make and investigate mathematical conjectures.

MC2P2.c. Develop and evaluate mathematical arguments and proofs.

MC2P2.d. Select and use various types of reasoning and methods of proof.

MC2P3. Students will communicate mathematically.

MC2P3.a. Organize and consolidate their mathematical thinking through communication.

MC2P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC2P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC2P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC2P4. Students will make connections among mathematical ideas and to other disciplines.

MC2P4.a. Recognize and use connections among mathematical ideas.

MC2P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC2P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MC2P5. Students will represent mathematics in multiple ways.

MC2P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC2P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC2P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC3A. Core Mathematics 3 - Algebra: Students will investigate piecewise and exponential functions from numerical, analytical and graphical approaches, focusing on the use of these functions in problem-solving situations.

MC3A1. Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

MC3A1.a. Write absolute value functions as piecewise functions.

MC3A1.b. Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.

MC3A1.c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

MC3A2. Students will explore exponential functions.

MC3A2.a. Extend properties of exponents to include all integer exponents.

MC3A2.b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

MC3A2.c. Graph functions as transformations of f(x) = a^x.

MC3A2.d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

MC3A2.e. Understand and use basic exponential functions as models of real phenomena.

MC3A2.f. Understand and recognize geometric sequences as exponential functions with domains that are sets of whole numbers.

MC3A2.g. Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

GA.MC3G. Core Mathematics 3 - Geometry: Students will explore right triangles and right triangular trigonometry.

MC3G1. Students will identify and use special right triangles.

MC3G1.a. Determine the lengths of sides of 30 degree - 60 degree - 90 degree triangles.

MC3G1.b. Determine the lengths of sides of 45 degree - 45 degree - 90 degree triangles.

MC3G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.

MC3G2.a. Discover the relationship of the trigonometric ratios for similar triangles.

MC3G2.b. Explain the relationship between the trigonometric ratios of complementary angles.

MC3G2.c. Solve application problems using the trigonometric ratios.

GA.MC3D. Core Mathematics 3 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data. Students will use regression to analyze data, and to make inferences.

MC3D1. Using sample data, students will make informal inferences about population means and standard deviations.

MC3D1.a. Pose a question and collect sample data from at least two different populations.

MC3D1.b. Understand and calculate the means and standard deviations of sets of data.

MC3D1.c. Use means and standard deviations to compare data sets.

MC3D1.d. Compare the means and standard deviations of random samples with the corresponding population parameters. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

MC3D2. Students will determine an algebraic model to quantify the association between two quantitative variables.

MC3D2.a. Gather and plot data that can be modeled with linear functions.

MC3D2.b. Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and 'eyeballing.'

MC3D2.c. Understand and apply the processes of linear regression for curve fitting using appropriate technology.

GA.MC3P. Core Mathematics 3 - Process Standards: The following process standards are essential mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC3P1. Students will solve problems (using appropriate technology).

MC3P1.a. Build new mathematical knowledge through problem solving.

MC3P1.b. Solve problems that arise in mathematics and in other contexts.

MC3P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC3P1.d. Monitor and reflect on the process of mathematical problem solving.

MC3P2. Students will reason and evaluate mathematical arguments.

MC3P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC3P2.b. Make and investigate mathematical conjectures.

MC3P2.c. Develop and evaluate mathematical arguments and proofs.

MC3P2.d. Select and use various types of reasoning and methods of proof.

MC3P3. Students will communicate mathematically.

MC3P3.a. Organize and consolidate their mathematical thinking through communication.

MC3P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC3P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC3P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC3P4. Students will make connections among mathematical ideas and to other disciplines.

MC3P4.a. Recognize and use connections among mathematical ideas.

MC3P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC3P4.c. Recognize and apply mathematics in context outside of mathematics.

MC3P5. Students will represent mathematics in multiple ways.

MC3P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC3P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC3P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC4N. Core Mathematics 4 - Number and Operations: Students will use the complex number system.

MC4N1. Students will represent and operate with complex numbers.

MC4N1.a. Write square roots of negative numbers in imaginary form.

MC4N1.b. Write complex numbers in the form a + bi.

MC4N1.c. Add, subtract, multiply, and divide complex numbers.

MC4N1.d. Simplify expressions involving complex numbers.

GA.MC4A. Core Mathematics 4 - Algebra: Students will investigate quadratic functions from numerical, analytical and graphical approaches, focusing on the use of these functions in problem-solving situations. Students will solve quadratic equations and inequalities and explore inverses of functions.

MC4A1. Students will analyze quadratic functions in the forms f(x) = ax^2 + bx + c and f(x) = a(x - h)^2 + k.

MC4A1.a. Convert between standard and vertex form.

MC4A1.b. Graph quadratic functions as transformations of the function f(x) = x^2.

MC4A1.c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

MC4A1.d. Explore arithmetic series and various ways of computing their sums.

MC4A1.e. Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

MC4A2. Students will solve quadratic equations and inequalities in one variable.

MC4A2.a. Solve equations graphically using appropriate technology.

MC4A2.b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

MC4A2.c. Analyze the nature of roots using technology and using the discriminant.

MC4A2.d. Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

MC4A3. Students will explore inverses of functions.

MC4A3.a. Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

MC4A3.b. Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.

MC4A3.c. Explore the graphs of functions and their inverses.

MC4A3.d. Use composition to verify that functions are inverses of each other.

GA.MC4G. Core Mathematics 4 - Geometry: Students will understand and apply properties of circles and spheres and use them in determining related measures.

MC4G1. Students will understand the properties of circles.

MC4G1.a. Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

MC4G1.b. Understand and use properties of central, inscribed, and related angles.

MC4G1.c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

MC4G1.d. Justify measurements and relationships in circles using geometric and algebraic properties.

MC4G2. Students will find and compare the measures of spheres.

MC4G2.a. Use and apply surface area and volume of a sphere.

MC4G2.b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

GA.MC4D. Core Mathematics 4 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will use regression to analyze data, and to make inferences.

MC4D1. Students will determine an algebraic model to quantify the association between two quantitative variables.

MC4D1.a. Gather and plot data that can be modeled with quadratic functions.

MC4D1.b. Understand and apply the processes of quadratic regression for curve fitting using appropriate technology.

GA.MC4P. Core Mathematics 4 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC4P1. Students will solve problems (using appropriate technology).

MC4P1.a. Build new mathematical knowledge through problem solving.

MC4P1.b. Solve problems that arise in mathematics and in other contexts.

MC4P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC4P1.d. Monitor and reflect on the process of mathematical problem solving.

MC4P2. Students will reason and evaluate mathematical arguments.

MC4P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC4P2.b. Make and investigate mathematical conjectures.

MC4P2.c. Develop and evaluate mathematical arguments and proofs.

MC4P2.d. Select and use various types of reasoning and methods of proof.

MC4P3. Students will communicate mathematically.

MC4P3.a. Organize and consolidate their mathematical thinking through communication.

MC4P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC4P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC4P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC4P4. Students will make connections among mathematical ideas and to other disciplines.

MC4P4.a. Recognize and use connections among mathematical ideas.

MC4P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC4P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MC4P5. Students will represent mathematics in multiple ways.

MC4P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC4P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC4P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MA1N. Accelerated Mathematics 1 - Number and Operations: Students will use the complex number system.

MA1N1. Students will represent and operate with complex numbers.

MA1N1.a. Write square roots of negative numbers in imaginary form.

MA1N1.b. Write complex numbers in the form a + bi.

MA1N1.c. Add, subtract, multiply, and divide complex numbers.

MA1N1.d. Simplify expressions involving complex numbers.

GA.MA1A. Accelerated Mathematics 1 - Algebra: Students will explore functions, solve equations and operate with radical, polynomial and rational expressions.

MA1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MA1A1.a. Represent functions using function notation.

MA1A1.b. Graph the basic functions f(x) = x^n, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

MA1A1.c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

MA1A1.d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

MA1A1.e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

MA1A1.f. Recognize sequences as functions with domains that are sets of whole numbers.

MA1A1.g. Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

MA1A1.h. Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

MA1A1.i. Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

MA1A2. Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MA1A2.a. Simplify algebraic and numeric expressions involving square root.

MA1A2.b. Perform operations with square roots.

MA1A2.c. Add, subtract, multiply, and divide polynomials.

MA1A2.d. Add, subtract, multiply, and divide rational expressions.

MA1A2.e. Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas: (x + y)^2 = x^2 + 2xy + y^2; (x - y)^2 = x^2 - 2xy + y^2; (x + y)(x - y) = x^2 - y^2; (x + a)(x + b) = x^2 + (a + b)x + ab; (x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3; (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3

MA1A2.f. Use area and volume models for polynomial arithmetic.

MA1A3. Students will analyze quadratic functions in the forms f(x) = ax^2 + bx + c and f(x) = a(x - h)^2 + k.

MA1A3.a. Convert between standard and vertex form.

MA1A3.b. Graph quadratic functions as transformations of the function f(x) = x^2.

MA1A3.c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

MA1A3.d. Explore arithmetic series and various ways of computing their sums.

MA1A3.e. Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

MA1A4. Students will solve quadratic equations and inequalities in one variable.

MA1A4.a. Solve equations graphically using appropriate technology.

MA1A4.b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

MA1A4.c. Analyze the nature of roots using technology and using the discriminant.

MA1A4.d. Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

MA1A5. Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

MA1A5.a. Write absolute value functions as piecewise functions.

MA1A5.b. Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.

MA1A5.c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

GA.MA1G. Accelerated Mathematics 1 - Geometry: Students will explore, understand and use the formal language of reasoning and justification. Students will apply properties of polygons, circles and spheres, and determine distances and points of concurrence.

MA1G1. Students will investigate properties of geometric figures in the coordinate plane.

MA1G1.a. Determine the distance between two points.

MA1G1.b. Determine the distance between a point and a line.

MA1G1.c. Determine the midpoint of a segment.

MA1G1.d. Understand the distance formula as an application of the Pythagorean theorem.

MA1G1.e. Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

MA1G2. Students will understand and use the language of mathematical argument and justification.

MA1G2.a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.

MA1G2.b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

MA1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.

MA1G3.a. Determine the sum of interior and exterior angles in a polygon.

MA1G3.b. Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.

MA1G3.c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

MA1G3.d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

MA1G3.e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

MA1G4. Students will understand the properties of circles.

MA1G4.a. Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

MA1G4.b. Understand and use properties of central, inscribed, and related angles.

MA1G4.c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

MA1G4.d. Justify measurements and relationships in circles using geometric and algebraic properties.

MA1G5. Students will find and compare the measures of spheres.

MA1G5.a. Use and apply surface area and volume of a sphere.

MA1G5.b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

GA.MA1D. Accelerated Mathematics 1 - Data Analysis and Probability: Students will use counting techniques and determine probability. Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data. Students will determine algebraic models from data.

MA1D1. Students will determine the number of outcomes related to a given event.

MA1D1.a. Apply the addition and multiplication principles of counting.

MA1D1.b. Calculate and use simple permutations and combinations.

MA1D2. Students will use the basic laws of probability.

MA1D2.a. Find the probabilities of mutually exclusive events.

MA1D2.b. Find the probabilities of dependent events.

MA1D2.c. Calculate conditional probabilities.

MA1D2.d. Use expected value to predict outcomes.

MA1D3. Students will relate samples to a population.

MA1D3.a. Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.

MA1D3.b. Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.

MA1D3.c. Understand that a random sample is used to improve the chance of selecting a representative sample.

MA1D4. Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

MA1D5. Students will determine an algebraic model to quantify the association between two quantitative variables.

MA1D5.a. Gather and plot data that can be modeled with linear and quadratic functions.

MA1D5.b. Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and .eyeballing..

MA1D5.c. Understand and apply the processes of linear and quadratic regression for curve fitting using appropriate technology.

GA.MA1P. Accelerated Mathematics 1 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MA1P1. Students will solve problems (using appropriate technology).

MA1P1.a. Build new mathematical knowledge through problem solving.

MA1P1.b. Solve problems that arise in mathematics and in other contexts.

MA1P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MA1P1.d. Monitor and reflect on the process of mathematical problem solving.

MA1P2. Students will reason and evaluate mathematical arguments.

MA1P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MA1P2.b. Make and investigate mathematical conjectures.

MA1P2.c. Develop and evaluate mathematical arguments and proofs.

MA1P2.d. Select and use various types of reasoning and methods of proof.

MA1P3. Students will communicate mathematically.

MA1P3.a. Organize and consolidate their mathematical thinking through communication.

MA1P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MA1P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MA1P3.d. Use the language of mathematics to express mathematical ideas precisely.

MA1P4. Students will make connections among mathematical ideas and to other disciplines.

MA1P4.a. Recognize and use connections among mathematical ideas.

MA1P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MA1P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MA1P5. Students will represent mathematics in multiple ways.

MA1P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MA1P5.b. Select, apply, and translate among mathematical representations to solve problems.

MA1P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MA2A. Accelerated Mathematics 2 - Algebra: Students will investigate exponential, logarithmic, and polynomial functions of higher degree; understand matrices and use them to solve problems; and solve linear programming problems in two variables.

MA2A1. Students will explore exponential functions.

MA2A1.a. Extend properties of exponents to include all integer exponents.

MA2A1.b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

MA2A1.c. Graph functions as transformations of f(x) = a^x.

MA2A1.d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

MA2A1.e. Understand and use basic exponential functions as models of real phenomena.

MA2A1.f. Understand and recognize geometric sequences as exponential functions with domains that are sets of whole numbers.

MA2A1.g. Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

MA2A2. Students will explore inverses of functions.

MA2A2.a. Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

MA2A2.b. Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.

MA2A2.c. Explore the graphs of functions and their inverses.

MA2A2.d. Use composition to verify that functions are inverses of each other.

MA2A3. Students will analyze graphs of polynomial functions of higher degree.

MA2A3.a. Graph simple polynomial functions as translations of the function f(x) = ax^n.

MA2A3.b. Understand the effects of the following on the graph of a polynomial function: degree, lead coefficient, and multiplicity of real zeros.

MA2A3.c. Determine whether a polynomial function has symmetry and whether it is even, odd, or neither.

MA2A3.d. Investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.

MA2A4. Students will explore logarithmic functions as inverses of exponential functions.

MA2A4.a. Define and understand the properties of nth roots.

MA2A4.b. Extend properties of exponents to include rational exponents.

MA2A4.c. Define logarithmic functions as inverses of exponential functions.

MA2A4.d. Understand and use properties of logarithms by extending laws of exponents.

MA2A4.e. Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

MA2A4.f. Graph functions as transformations of f(x) = a^x, f(x) = log ax, f(x) = e^x, f(x) = ln x.

MA2A4.g. Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

MA2A5. Students will solve a variety of equations and inequalities.

MA2A5.a. Find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical conjugates.

MA2A5.b. Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

MA2A5.c. Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

MA2A5.d. Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology.

MA2A6. Students will perform basic operations with matrices.

MA2A6.a. Add, subtract, multiply, and invert matrices, when possible, choosing appropriate methods, including technology.

MA2A6.b. Find the inverses of two-by-two matrices using pencil and paper, and find inverses of larger matrices using technology.

MA2A6.c. Examine the properties of matrices, contrasting them with properties of real numbers.

MA2A7. Students will use matrices to formulate and solve problems.

MA2A7.a. Represent a system of linear equations as a matrix equation.

MA2A7.b. Solve matrix equations using inverse matrices.

MA2A7.c. Represent and solve realistic problems using systems of linear equations.

MA2A8. Students will solve linear programming problems in two variables.

MA2A8.a. Solve systems of inequalities in two variables, showing the solutions graphically.

MA2A8.b. Represent and solve realistic problems using linear programming.

MA2A9. Students will understand and apply matrix representations of vertex-edge graphs.

MA2A9.a. Use graphs to represent realistic situations.

MA2A9.b. Use matrices to represent graphs, and solve problems that can be represented by graphs.

GA.MA2G. Accelerated Mathematics 2 - Geometry: Students will explore right triangles and right triangular trigonometry. They will understand and apply properties of conic sections, planes, and spheres.

MA2G1. Students will identify and use special right triangles.

MA2G1.a. Determine the lengths of sides of 30 degree - 60 degree - 90 degree triangles.

MA2G1.b. Determine the lengths of sides of 45 degree - 45 degree - 90 degree triangles.

MA2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.

MA2G2.a. Discover the relationship of the trigonometric ratios for similar triangles.

MA2G2.b. Explain the relationship between the trigonometric ratios of complementary angles.

MA2G2.c. Solve application problems using the trigonometric ratios.

MA2G3. Students will investigate the relationships between lines and circles.

MA2G3.a. Find equations of circles.

MA2G3.b. Graph a circle given an equation in general form.

MA2G3.c. Find the equation of a tangent line to a circle at a given point.

MA2G3.d. Solve a system of equations involving a circle and a line.

MA2G3.e. Solve a system of equations involving two circles.

MA2G4. Students will recognize, analyze, and graph the equations of the conic sections (parabolas, circles, ellipses, and hyperbolas).

MA2G4.a. Convert equations of conics by completing the square.

MA2G4.b. Graph conic sections, identifying fundamental characteristics.

MA2G4.c. Write equations of conic sections given appropriate information.

MA2G5. Students will investigate planes and spheres.

MA2G5.a. Plot the point (x, y, z) and understand it as a vertex of a rectangular prism.

MA2G5.b. Apply the distance formula in 3-space.

MA2G5.c. Recognize and understand equations of planes and spheres.

GA.MA2D. Accelerated Mathematics 2 - Data Analysis and Probability: Students will make informal inferences about means and standard deviations. Students will use a normal distribution to calculate probabilities. Students will organize, represent, investigate, interpret, and make inferences from both observational studies and experiments.

MA2D1. Using sample data, students will make informal inferences about population means and standard deviations.

MA2D1.a. Pose a question and collect sample data from at least two different populations.

MA2D1.b. Understand and calculate the means and standard deviations of sets of data.

MA2D1.c. Use means and standard deviations to compare data sets.

MA2D1.d. Compare the means and standard deviations of random samples with the corresponding population parameters. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

MA2D2. Students will create probability histograms of discrete random variables, using both experimental and theoretical probabilities.

MA2D3. Students will solve problems involving probabilities by interpreting a normal distribution as a probability histogram for a continuous random variable (z-scores are used for a general normal distribution).

MA2D3.a. Determine intervals about the mean that include a given percent of data.

MA2D3.b. Determine the probability that a given value falls within a specified interval.

MA2D3.c. Estimate how many items in a population fall within a specified interval.

MA2D4. Students will understand the differences between experimental and observational studies by posing questions and collecting, analyzing, and interpreting data.

GA.MA2P. Accelerated Mathematics 2 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MA2P1. Students will solve problems (using appropriate technology).

MA2P1.a. Build new mathematical knowledge through problem solving.

MA2P1.b. Solve problems that arise in mathematics and in other contexts.

MA2P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MA2P1.d. Monitor and reflect on the process of mathematical problem solving.

MA2P2. Students will reason and evaluate mathematical arguments.

MA2P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MA2P2.b. Make and investigate mathematical conjectures.

MA2P2.c. Develop and evaluate mathematical arguments and proofs.

MA2P2.d. Select and use various types of reasoning and methods of proof.

MA2P3. Students will communicate mathematically.

MA2P3.a. Organize and consolidate their mathematical thinking through communication.

MA2P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MA2P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MA2P3.d. Use the language of mathematics to express mathematical ideas precisely.

MA2P4. Students will make connections among mathematical ideas and to other disciplines.

MA2P4.a. Recognize and use connections among mathematical ideas.

MA2P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MA2P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MA2P5. Students will represent mathematics in multiple ways.

MA2P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MA2P5.b. Select, apply, and translate among mathematical representations to solve problems.

MA2P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MA3A. Accelerated Mathematics 3 - Algebra: Students will explore characteristics of various functions, understand and use concepts of trigonometric functions, investigate and apply sequences and series, and use parametric and polar equations to represent functions and curves.

MA3A1. Students will explore rational functions.

MA3A1.a. Investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior.

MA3A1.b. Find inverses of rational functions, discussing domain and range, symmetry, and function composition.

MA3A1.c. Solve rational equations and inequalities analytically, graphically, and by using appropriate technology.

MA3A2. Students will use the circle to define the trigonometric functions.

MA3A2.a. Define and understand angles measured in degrees and radians, including but not limited to 0 degrees, 30 degrees, 45 degrees, 60 degrees, 90 degrees, their multiples, and equivalences.

MA3A2.b. Understand and apply the six trigonometric functions as functions of general angles in standard position.

MA3A2.c. Find values of trigonometric functions using points on the terminal sides of angles in the standard position.

MA3A2.d. Understand and apply the six trigonometric functions as functions of arc length on the unit circle.

MA3A2.e. Find values of trigonometric functions using the unit circle.

MA3A3. Students will investigate and use the graphs of the six trigonometric functions.

MA3A3.a. Understand and apply the six basic trigonometric functions as functions of real numbers.

MA3A3.b. Determine the characteristics of the graphs of the six basic trigonometric functions.

MA3A3.c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MA3A3.d. Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena.

MA3A4. Students will investigate functions.

MA3A4.a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

MA3A4.b. Investigate transformations of functions.

MA3A4.c. Investigate characteristics of functions built through sum, difference, product, quotient, and composition.

MA3A5. Students will establish trigonometric identities and use them to simplify trigonometric expressions and verify equivalence statements.

MA3A6. Students will solve trigonometric equations both graphically and algebraically.

MA3A6.a. Solve trigonometric equations over a variety of domains, using technology as appropriate.

MA3A6.b. Use the coordinates of a point on the terminal side of an angle to express x and y as polar coordinates.

MA3A6.c. Apply the law of sines and the law of cosines.

MA3A7. Students will verify and apply 1/2 ab sinC to find the area of a triangle.

MA3A8. Students will investigate and use inverse sine, inverse cosine, and inverse tangent functions.

MA3A8.a. Find values of the above functions using technology as appropriate.

MA3A8.b. Determine characteristics of the above functions and their graphs.

MA3A9. Students will use sequences and series

MA3A9.a. Use and find recursive and explicit formulae for the terms of sequences.

MA3A9.b. Recognize and use simple arithmetic and geometric sequences.

MA3A9.c. Investigate limits of sequences.

MA3A9.d. Use mathematical induction to find and prove formulae for sums of finite series.

MA3A9.e. Find and apply the sums of finite and, where appropriate, infinite arithmetic and geometric series.

MA3A9.f. Use summation notation to explore series.

MA3A9.g. Determine geometric series and their limits.

MA3A10. Students will understand and use vectors.

MA3A10.a. Represent vectors algebraically and geometrically.

MA3A10.b. Convert between vectors expressed using rectangular coordinates and vectors expressed using magnitude and direction.

MA3A10.c. Add and subtract vectors and compute scalar multiples of vectors.

MA3A10.d. Use vectors to solve realistic problems.

MA3A11. Students will use complex numbers in trigonometric form.

MA3A11.a. Represent complex numbers in trigonometric form.

MA3A11.b. Find products, quotients, powers, and roots of complex numbers in trigonometric form.

MA3A12. Students will explore parametric representations of plane curves.

MA3A12.a. Convert between Cartesian and parametric form.

MA3A12.b. Graph equations in parametric form showing direction and beginning and ending points where appropriate.

MA3A13. Students will explore polar equations.

MA3A13.a. Express coordinates of points in rectangular and polar form.

MA3A13.b. Graph and identify characteristics of simple polar equations including lines, circles, cardioids, limacons, and roses.

GA.MA3D. Accelerated Mathematics 3 - Data Analysis and Probability: Students will organize, represent, investigate, interpret, and make inferences from data, using the central limit theorem and the standard normal distribution. Students will apply the Central Limit Theorem to calculate confidence intervals for a population mean using data from large samples. Students will use sample data and confidence intervals to draw conclusions about populations.

MA3D1. Using simulation, students will develop the idea of the central limit theorem.

MA3D2. Using student-generated data from random samples of at least 30 members, students will determine the margin of error and confidence interval for a specified level of confidence.

MA3D3. Students will use confidence intervals and margins of error to make inferences from data about a population. Technology is used to evaluate confidence intervals, but students will be aware of the ideas involved.

GA.MA3P. Accelerated Mathematics 3 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MA3P1. Students will solve problems (using appropriate technology).

MA3P1.a. Build new mathematical knowledge through problem solving.

MA3P1.b. Solve problems that arise in mathematics and in other contexts.

MA3P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MA3P1.d. Monitor and reflect on the process of mathematical problem solving.

MA3P2. Students will reason and evaluate mathematical arguments.

MA3P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MA3P2.b. Make and investigate mathematical conjectures.

MA3P2.c. Develop and evaluate mathematical arguments and proofs.

MA3P2.d. Select and use various types of reasoning and methods of proof.

MA3P3. Students will communicate mathematically.

MA3P3.a. Organize and consolidate their mathematical thinking through communication.

MA3P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MA3P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MA3P3.d. Use the language of mathematics to express mathematical ideas precisely.

MA3P4. Students will make connections among mathematical ideas and to other disciplines.

MA3P4.a. Recognize and use connections among mathematical ideas.

MA3P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MA3P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MA3P5. Students will represent mathematics in multiple ways.

MA3P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MA3P5.b. Select, apply, and translate among mathematical representations to solve problems.

MA3P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MRC. Reading Across the Curriculum: Reading across curriculum content develops both academic and personal interests in students. As students read, they develop both content and contextual vocabulary. They also build good habits for reading, researching, and learning. The Reading Across the Curriculum standard focuses on the academic and personal skills students acquire as they read in all areas of learning.

MRC1. Students will enhance reading in all curriculum areas by:

MRC1.a. Reading in all curriculum areas: Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areas; Read both informational and fictional texts in a variety of genres and modes of discourse; Read technical texts related to various subject areas

MRC1.b. Discussing books: Discuss messages and themes from books in all subject areas; Respond to a variety of texts in multiple modes of discourse; Relate messages and themes from one subject area to messages and themes in another area; Evaluate the merit of texts in every subject discipline; Examine author's purpose in writing; Recognize the features of disciplinary texts.

MRC1.c. Building vocabulary knowledge: Demonstrate an understanding of contextual vocabulary in various subjects; Use content vocabulary in writing and speaking; Explore understanding of new words found in subject area texts.

MRC1.d. Establishing context: Explore life experiences related to subject area content; Discuss in both writing and speaking how certain words are subject area related; Determine strategies for finding content and contextual meaning for unknown words.

GA.MM1A. Mathematics 1 - Algebra: Students will explore functions and solve simple equations. Students will simplify and operate with radical, polynomial, and rational expressions.

MM1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MM1A1.a. Represent functions using function notation.

MM1A1.b. Graph the basic functions f(x) = x^n, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

MM1A1.c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

MM1A1.d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

MM1A1.e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

MM1A1.f. Recognize sequences as functions with domains that are whole numbers.

MM1A1.g. Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

MM1A1.h. Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

MM1A1.i. Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

MM1A2. Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MM1A2.a. Simplify algebraic and numeric expressions involving square root.

MM1A2.b. Perform operations with square roots.

MM1A2.c. Add, subtract, multiply, and divide polynomials.

MM1A2.d. Expand binomials using the Binomial Theorem.

MM1A2.e. Add, subtract, multiply, and divide rational expressions.

MM1A2.f. Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas: (x + y)^2 = x^2 + 2xy + y^2; (x - y)^2 = x^2 - 2xy + y^2; (x + y)(x - y) = x^2 - y^2; (x + a)(x + b) = x^2 + (a + b)x + ab; (x + y)^3 = x^3 + 3 x^2y + 3xy^2 + y^3; (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3

MM1A2.g. Use area and volume models for polynomial arithmetic.

MM1A3. Students will solve simple equations.

MM1A3.a. Solve quadratic equations in the form ax^2 + bx + c = 0, where a = 1, by using factorization and finding square roots where applicable.

MM1A3.b. Solve equations involving radicals such as square root of x + b = c, using algebraic techniques.

MM1A3.c. Use a variety of techniques, including technology, tables, and graphs to solve equations resulting from the investigation of x^2 + bx + c = 0.

MM1A3.d. Solve simple rational equations that result in linear equations or quadratic equations with leading coefficient of 1.

GA.MM1G. Mathematics 1 - Geometry: Students will explore, understand, and use the formal language of reasoning and justification. Students will apply properties of polygons and determine distances and points of concurrence.

MM1G1. Students will investigate properties of geometric figures in the coordinate plane.

MM1G1.a. Determine the distance between two points.

MM1G1.b. Determine the distance between a point and a line.

MM1G1.c. Determine the midpoint of a segment.

MM1G1.d. Understand the distance formula as an application of the Pythagorean theorem.

MM1G1.e. Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

MM1G2. Students will understand and use the language of mathematical argument and justification.

MM1G2.a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.

MM1G2.b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

MM1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.

MM1G3.a. Determine the sum of interior and exterior angles in a polygon.

MM1G3.b. Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.

MM1G3.c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

MM1G3.d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

MM1G3.e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

GA.MM1D. Mathematics 1 - Data Analysis and Probability: Students will use counting techniques and determine probability. Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data.

MM1D1. Students will determine the number of outcomes related to a given event.

MM1D1.a. Apply the addition and multiplication principles of counting.

MM1D1.b. Calculate and use simple permutations and combinations.

MM1D2. Students will use the basic laws of probability.

MM1D2.a. Find the probabilities of mutually exclusive events.

MM1D2.b. Find the probabilities of dependent events.

MM1D2.c. Calculate conditional probabilities.

MM1D2.d. Use expected value to predict outcomes.

MM1D3. Students will relate samples to a population.

MM1D3.a. Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.

MM1D3.b. Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.

MM1D3.c. Understand that a random sample is used to improve the chance of selecting a representative sample.

MM1D4. Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

GA.MM1P. Mathematics 1 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM1P1. Students will solve problems (using appropriate technology).

MM1P1.a. Build new mathematical knowledge through problem solving.

MM1P1.b. Solve problems that arise in mathematics and in other contexts.

MM1P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM1P1.d. Monitor and reflect on the process of mathematical problem solving.

MM1P2. Students will reason and evaluate mathematical arguments.

MM1P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM1P2.b. Make and investigate mathematical conjectures.

MM1P2.c. Develop and evaluate mathematical arguments and proofs.

MM1P2.d. Select and use various types of reasoning and methods of proof.

MM1P3. Students will communicate mathematically.

MM1P3.a. Organize and consolidate their mathematical thinking through communication.

MM1P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM1P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM1P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM1P4. Students will make connections among mathematical ideas and to other disciplines.

MM1P4.a. Recognize and use connections among mathematical ideas.

MM1P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM1P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM1P5. Students will represent mathematics in multiple ways.

MM1P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM1P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM1P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MM2N. Mathematics 2 - Number and Operations: Students will use the complex number system.

MM2N1. Students will represent and operate with complex numbers.

MM2N1.a. Write square roots of negative numbers in imaginary form.

MM2N1.b. Write complex numbers in the form a + bi.

MM2N1.c. Add, subtract, multiply, and divide complex numbers.

MM2N1.d. Simplify expressions involving complex numbers.

GA.MM2A. Mathematics 2 - Algebra: Students will investigate piecewise, exponential, and quadratic functions, using numerical, analytical, and graphical approaches, focusing on the use of these functions in problem-solving situations. Students will solve equations and inequalities and explore inverses of functions.

MM2A1. Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

MM2A1.a. Write absolute value functions as piecewise functions.

MM2A1.b. Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.

MM2A1.c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

MM2A2. Students will explore exponential functions.

MM2A2.a. Extend properties of exponents to include all integer exponents.

MM2A2.b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

MM2A2.c. Graph functions as transformations of f(x) = a^x.

MM2A2.d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

MM2A2.e. Understand and use basic exponential functions as models of real phenomena.

MM2A2.f. Understand and recognize geometric sequences as exponential functions with domains that are whole numbers.

MM2A2.g. Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

MM2A3.a. Convert between standard and vertex form.

MM2A3. Students will analyze quadratic functions in the forms f(x) = ax^2 + bx + c and f(x) = a(x - h)^2 + k.

MM2A3.b. Graph quadratic functions as transformations of the function f(x) = x^2.

MM2A3.c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

MM2A3.d. Explore arithmetic series and various ways of computing their sums.

MM2A3.e. Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

MM2A4. Students will solve quadratic equations and inequalities in one variable.

MM2A4.a. Solve equations graphically using appropriate technology.

MM2A4.b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

MM2A4.c. Analyze the nature of roots using technology and using the discriminant.

MM2A4.d. Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

MM2A5. Students will explore inverses of functions.

MM2A5.a. Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

MM2A5.b. Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.

MM2A5.c. Explore the graphs of functions and their inverses.

MM2A5.d. Use composition to verify that functions are inverses of each other.

GA.MM2G. Mathematics 2 - Geometry: Students will explore right triangles and right-triangle trigonometry. They will understand and apply properties of circles and spheres, and use them in determining related measures.

MM2G1. Students will identify and use special right triangles.

MM2G1.a. Determine the lengths of sides of 30 degree - 60 degree - 90 degree triangles.

MM2G1.b. Determine the lengths of sides of 45 degree - 45 degree - 90 degree triangles.

MM2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.

MM2G2.a. Discover the relationship of the trigonometric ratios for similar triangles.

MM2G2.b. Explain the relationship between the trigonometric ratios of complementary angles.

MM2G2.c. Solve application problems using the trigonometric ratios.

MM2G3. Students will understand the properties of circles.

MM2G3.a. Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

MM2G3.b. Understand and use properties of central, inscribed, and related angles.

MM2G3.c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

MM2G3.d. Justify measurements and relationships in circles using geometric and algebraic properties.

MM2G4. Students will find and compare the measures of spheres.

MM2G4.a. Use and apply surface area and volume of a sphere.

MM2G4.b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

GA.MM2D. Mathematics 2 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data. They will use regression to analyze data and to make inferences.

MM2D1. Using sample data, students will make informal inferences about population means and standard deviations.

MM2D1.a. Pose a question and collect sample data from at least two different populations.

MM2D1.b. Understand and calculate the means and standard deviations of sets of data.

MM2D1.c. Use means and standard deviations to compare data sets.

MM2D1.d. Compare the means and standard deviations of random samples with the corresponding population parameters, including those population parameters for normal distributions. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

MM2D2. Students will determine an algebraic model to quantify the association between two quantitative variables.

MM2D2.a. Gather and plot data that can be modeled with linear and quadratic functions.

MM2D2.b. Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and 'eyeballing.'

MM2D2.c. Understand and apply the processes of linear and quadratic regression for curve fitting using appropriate technology.

MM2D2.d. Investigate issues that arise when using data to explore the relationship between two variables, including confusion between correlation and causation.

GA.MM2P. Mathematics 2 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM2P1. Students will solve problems (using appropriate technology).

MM2P1.a. Build new mathematical knowledge through problem solving.

MM2P1.b. Solve problems that arise in mathematics and in other contexts.

MM2P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM2P1.d. Monitor and reflect on the process of mathematical problem solving.

MM2P2. Students will reason and evaluate mathematical arguments.

MM2P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM2P2.b. Make and investigate mathematical conjectures.

MM2P2.c. Develop and evaluate mathematical arguments and proofs.

MM2P2.d. Select and use various types of reasoning and methods of proof.

MM2P3. Students will communicate mathematically.

MM2P3.a. Organize and consolidate their mathematical thinking through communication.

MM2P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM2P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM2P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM2P4. Students will make connections among mathematical ideas and to other disciplines.

MM2P4.a. Recognize and use connections among mathematical ideas.

MM2P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM2P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM2P5. Students will represent mathematics in multiple ways.

MM2P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM2P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM2P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MM3A. Mathematics 3 - Algebra: Students will investigate exponential, logarithmic and polynomial functions of degree higher than 2. Students will understand matrices and use them to solve problems.

MM3A1. Students will analyze graphs of polynomial functions of higher degree.

MM3A1.a. Graph simple polynomial functions as translations of the function f(x) = ax^n.

MM3A1.b. Understand the effects of the following on the graph of a polynomial function: degree, lead coefficient, and multiplicity of real zeros.

MM3A1.c. Determine whether a polynomial function has symmetry and whether it is even, odd, or neither.

MM3A1.d. Investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.

MM3A2. Students will explore logarithmic functions as inverses of exponential functions.

MM3A2.a. Define and understand the properties of nth roots.

MM3A2.b. Extend properties of exponents to include rational exponents.

MM3A2.c. Define logarithmic functions as inverses of exponential functions.

MM3A2.d. Understand and use properties of logarithms by extending laws of exponents.

MM3A2.e. Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

MM3A2.f. Graph functions as transformations of f(x) = a^x, f(x) = log ax, f(x) = e^x, f(x) = ln x.

MM3A2.g. Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

MM3A3. Students will solve a variety of equations and inequalities.

MM3A3.a. Find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical conjugates.

MM3A3.b. Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

MM3A3.c. Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

MM3A3.d. Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology.

MM3A4. Students will perform basic operations with matrices.

MM3A4.a. Add, subtract, multiply, and invert matrices, when possible, choosing appropriate methods, including technology.

MM3A4.b. Find the inverses of two-by-two matrices using pencil and paper, and find inverses of larger matrices using technology.

MM3A4.c. Examine the properties of matrices, contrasting them with properties of real numbers.

MM3A5. Students will use matrices to formulate and solve problems.

MM3A5.a. Represent a system of linear equations as a matrix equation.

MM3A5.b. Solve matrix equations using inverse matrices.

MM3A5.c. Represent and solve realistic problems using systems of linear equations.

MM3A6. Students will solve linear programming problems in two variables.

MM3A6.a. Solve systems of inequalities in two variables, showing the solutions graphically.

MM3A6.b. Represent and solve realistic problems using linear programming.

MM3A7. Students will understand and apply matrix representations of vertex-edge graphs.

MM3A7.a. Use graphs to represent realistic situations.

MM3A7.b. Use matrices to represent graphs, and solve problems that can be represented by graphs.

GA.MM3G. Mathematics 3 - Geometry: Students will understand and use the analytic geometry of conic sections and of planes and spheres in space.

MM3G1. Students will investigate the relationships between lines and circles.

MM3G1.a. Find equations of circles.

MM3G1.b. Graph a circle given an equation in general form.

MM3G1.c. Find the equation of a tangent line to a circle at a given point.

MM3G1.d. Solve a system of equations involving a circle and a line.

MM3G1.e. Solve a system of equations involving two circles.

MM3G2. Students will recognize, analyze, and graph the equations of the conic sections (parabolas, circles, ellipses, and hyperbolas).

MM3G2.a. Convert equations of conics by completing the square.

MM3G2.b. Graph conic sections, identifying fundamental characteristics.

MM3G2.c. Write equations of conic sections given appropriate information.

MM3G3. Students will investigate planes and spheres.

MM3G3.a. Plot the point (x, y, z) and understand it as a vertex of a rectangular prism.

MM3G3.b. Apply the distance formula in 3-space.

MM3G3.c. Recognize and understand equations of planes and spheres.

GA.MM3D. Mathematics 3 - Data Analysis and Probability: Students will use a normal distribution to calculate probabilities. They will organize, represent, investigate, interpret, and make inferences using data from both observational studies and experiments.

MM3D1. Students will create probability histograms of discrete random variables, using both experimental and theoretical probabilities.

MM3D2. Students will solve problems involving probabilities by interpreting a normal distribution as a probability histogram for a continuous random variable (z-scores are used for a general normal distribution).

MM3D2.a. Determine intervals about the mean that include a given percent of data.

MM3D2.b. Determine the probability that a given value falls within a specified interval.

MM3D2.c. Estimate how many items in a population fall within a specified interval.

MM3D3. Students will understand the differences between experimental and observational studies by posing questions and collecting, analyzing, and interpreting data.

GA.MM3P. Mathematics 3 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM3P1. Students will solve problems (using appropriate technology).

MM3P1.a. Build new mathematical knowledge through problem solving.

MM3P1.b. Solve problems that arise in mathematics and in other contexts.

MM3P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM3P1.d. Monitor and reflect on the process of mathematical problem solving.

MM3P2. Students will reason and evaluate mathematical arguments.

MM3P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM3P2.b. Make and investigate mathematical conjectures.

MM3P2.c. Develop and evaluate mathematical arguments and proofs.

MM3P2.d. Select and use various types of reasoning and methods of proof.

MM3P3. Students will communicate mathematically.

MM3P3.a. Organize and consolidate their mathematical thinking through communication.

MM3P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM3P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM3P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM3P4. Students will make connections among mathematical ideas and to other disciplines.

MM3P4.a. Recognize and use connections among mathematical ideas.

MM3P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM3P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM3P5. Students will represent mathematics in multiple ways.

MM3P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM3P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM3P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MM4A. Mathematics 4 - Algebra: Students will analyze rational and trigonometric functions. Students will investigate and apply sequences and series and will understand and use vectors.

MM4A1. Students will explore rational functions.

MM4A1.a. Investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior.

MM4A1.b. Find inverses of rational functions, discussing domain and range, symmetry, and function composition.

MM4A1.c. Solve rational equations and inequalities analytically, graphically, and by using appropriate technology.

MM4A2. Students will use the circle to define the trigonometric functions.

MM4A2.a. Define and understand angles measured in degrees and radians, including but not limited to 0 degrees, 30 degrees, 45 degrees, 60 degrees, 90 degrees, their multiples, and equivalences.

MM4A2.b. Understand and apply the six trigonometric functions as functions of general angles in standard position.

MM4A2.c. Find values of trigonometric functions using points on the terminal sides of angles in the standard position.

MM4A2.d. Understand and apply the six trigonometric functions as functions of arc length on the unit circle.

MM4A2.e. Find values of trigonometric functions using the unit circle.

MM4A3. Students will investigate and use the graphs of the six trigonometric functions.

MM4A3.a. Understand and apply the six basic trigonometric functions as functions of real numbers.

MM4A3.b. Determine the characteristics of the graphs of the six basic trigonometric functions.

MM4A3.c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MM4A3.d. Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena.

MM4A4. Students will investigate functions.

MM4A4.a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

MM4A4.b. Investigate transformations of functions.

MM4A4.c. Investigate characteristics of functions built through sum, difference, product, quotient, and composition.

MM4A5. Students will establish trigonometric identities and use them to simplify trigonometric expressions and verify equivalence statements.

MM4A6. Students will solve trigonometric equations both graphically and algebraically.

MM4A6.a. Solve trigonometric equations over a variety of domains, using technology as appropriate.

MM4A6.b. Use the coordinates of a point on the terminal side of an angle to express x and y as polar coordinates.

MM4A6.d. Apply the law of sines and the law of cosines.

MM4A7. Students will verify and apply 1/2 ab sinC to find the area of a triangle.

MM4A8. Students will investigate and use inverse sine, inverse cosine, and inverse tangent functions.

MM4A8.a. Find values of the above functions using technology as appropriate.

MM4A8.b. Determine characteristics of the above functions and their graphs.

MM4A9. Students will use sequences and series

MM4A9.a. Use and find recursive and explicit formulae for the terms of sequences.

MM4A9.b. Recognize and use simple arithmetic and geometric sequences.

MM4A9.c. Find and apply the sums of finite and, where appropriate, infinite arithmetic and geometric series.

MM4A9.d. Use summation notation to explore finite series.

MM4A10. Students will understand and use vectors.

MM4A10.a. Represent vectors algebraically and geometrically.

MM4A10.b. Convert between vectors expressed using rectangular coordinates and expressed using magnitude and direction.

MM4A10.c. Add, subtract, and compute scalar multiples of vectors.

MM4A10.d. Use vectors to solve realistic problems.

GA.MM4D. Mathematics 4 - Data Analysis and Probability: Students will organize, represent, investigate, interpret, and make inferences from data, using the central limit theorem and the standard normal distribution. Students will apply the Central Limit Theorem to calculate confidence intervals for a population mean using data from large samples. Students will use sample data and confidence intervals to draw conclusions about populations.

MM4D1. Using simulation, students will develop the idea of the central limit theorem.

MM4D2. Using student-generated data from random samples of at least 30 members, students will determine the margin of error and confidence interval for a specified level of confidence.

MM4D3. Students will use confidence intervals and margins of error to make inferences from data about a population. Technology is used to evaluate confidence intervals, but students will be aware of the ideas involved.

GA.MM4P. Mathematics 4 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MM4P1. Students will solve problems (using appropriate technology).

MM4P1.a. Build new mathematical knowledge through problem solving.

MM4P1.b. Solve problems that arise in mathematics and in other contexts.

MM4P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MM4P1.d. Monitor and reflect on the process of mathematical problem solving.

MM4P2. Students will reason and evaluate mathematical arguments.

MM4P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MM4P2.b. Make and investigate mathematical conjectures.

MM4P2.c. Develop and evaluate mathematical arguments and proofs.

MM4P2.d. Select and use various types of reasoning and methods of proof.

MM4P3. Students will communicate mathematically.

MM4P3.a. Organize and consolidate their mathematical thinking through communication.

MM4P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MM4P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MM4P3.d. Use the language of mathematics to express mathematical ideas precisely.

MM4P4. Students will make connections among mathematical ideas and to other disciplines.

MM4P4.a. Recognize and use connections among mathematical ideas.

MM4P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MM4P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MM4P5. Students will represent mathematics in multiple ways.

MM4P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MM4P5.b. Select, apply, and translate among mathematical representations to solve problems.

MM4P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC1A. Core Mathematics 1 - Algebra: Students will explore and interpret the characteristics of functions.

MC1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MC1A1.a. Represent functions using function notation.

MC1A1.b. Graph the basic functions f(x) = x^n, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

MC1A1.c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

MC1A1.d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

MC1A1.e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

MC1A1.f. Recognize sequences as functions with domains that are whole numbers.

MC1A1.g. Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

MC1A1.h. Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

MC1A1.i. Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

GA.MC1G. Core Mathematics 1 - Geometry: The student will apply properties of polygons and determine distances.

MC1G1. Students will investigate properties of geometric figures in the coordinate plane.

MC1G1.a. Determine the distance between two points.

MC1G1.b. Determine the distance between a point and a line.

MC1G1.c. Determine the midpoint of a segment.

MC1G1.d. Understand the distance formula as an application of the Pythagorean theorem.

MC1G1.e. Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

GA.MC1D. Core Mathematics 1 - Data Analysis and Probability: Students will use counting techniques and determine probability.

MC1D1. Students will determine the number of outcomes related to a given event

MC1D1.a. Apply addition and multiplication principles of counting.

MC1D1.b. Calculate and use simple permutations and combinations.

MC1D2. Students will use the basic laws of probability

MC1D2.a. Find the probabilities of mutually exclusive events.

MC1D2.b. Find the probabilities of dependent events.

MC1D2.c. Calculate conditional probabilities.

MC1D2.d. Use expected value to predict outcomes.

GA.MC1P. Core Mathematics 1 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC1P1. Students will solve problems (using appropriate technology).

MC1P1.a. Build new mathematical knowledge through problem solving.

MC1P1.b. Solve problems that arise in mathematics and in other contexts.

MC1P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC1P1.d. Monitor and reflect on the process of mathematical problem solving.

MC1P2. Students will reason and evaluate mathematical arguments.

MC1P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC1P2.b. Make and investigate mathematical conjectures.

MC1P2.c. Develop and evaluate mathematical arguments and proofs.

MC1P2.d. Select and use various types of reasoning and methods of proof.

MC1P3. Students will communicate mathematically.

MC1P3.a. Organize and consolidate their mathematical thinking through communication.

MC1P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC1P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC1P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC1P4. Students will make connections among mathematical ideas and to other disciplines.

MC1P4.a. Recognize and use connections among mathematical ideas.

MC1P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC1P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MC1P5. Students will represent mathematics in multiple ways.

MC1P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC1P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC1P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC2A. Core Mathematics 2 - Algebra: Students will simplify and operate with radical expressions, polynomials, and rational expressions. Students will solve simple equations.

MC2A1. Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MC2A1.a. Simplify algebraic and numeric expressions involving square root.

MC2A1.b. Perform operations with square roots.

MC2A1.c. Add, subtract, multiply, and divide polynomials.

MC2A1.d. Add, subtract, multiply, and divide rational expressions.

MC2A1.e. Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas: (x + y)^2 = x^2 + 2xy + y^2; (x - y)^2 = x^2 - 2xy + y^2; (x + y)(x - y) = x^2 - y^2; (x + a)(x + b) = x^2 + (a + b)x + ab; (x + y)^3 = x^3 + 3 x^2y + 3xy^2 + y^3; (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y3

MC2A1.f. Use area and volume models for polynomial arithmetic.

MC2A2. Students will solve simple equations.

MC2A2.a. Solve quadratic equations in the form ax^2 + bx + c = 0, where a = 1, by using factorization and finding square roots where applicable.

MC2A2.b. Solve equations involving radicals such as square root of x + b = c, using algebraic techniques.

MC2A2.c. Use a variety of techniques, including technology, tables, and graphs to solve equations resulting from the investigation of x^2 + bx + c = 0.

MC2A2.d. Solve simple rational equations that result in linear equations or quadratic equations with leading coefficient of 1.

GA.MC2G. Core Mathematics 2 - Geometry: Students will explore, understand and use the formal language of reasoning and justification. Students will apply properties of polygons.

MC2G1. Students will understand and use the language of mathematical argument and justification.

MC2G1.a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.

MC2G1.b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

MC2G1.c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

MC2G1.d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

MC2G1.e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

GA.MC2D. Core Mathematics 2 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data.

MC2D1. Students will relate samples to a population.

MC2D1.a. Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.

MC2D1.b. Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.

MC2D1.c. Understand that a random sample is used to improve the chance of selecting a representative sample.

MC2D2. Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

GA.MC2P. Core Mathematics 2 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC2P1. Students will solve problems (using appropriate technology).

MC2P1.a. Build new mathematical knowledge through problem solving.

MC2P1.b. Solve problems that arise in mathematics and in other contexts.

MC2P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC2P1.d. Monitor and reflect on the process of mathematical problem solving.

MC2P2. Students will reason and evaluate mathematical arguments.

MC2P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC2P2.b. Make and investigate mathematical conjectures.

MC2P2.c. Develop and evaluate mathematical arguments and proofs.

MC2P2.d. Select and use various types of reasoning and methods of proof.

MC2P3. Students will communicate mathematically.

MC2P3.a. Organize and consolidate their mathematical thinking through communication.

MC2P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC2P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC2P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC2P4. Students will make connections among mathematical ideas and to other disciplines.

MC2P4.a. Recognize and use connections among mathematical ideas.

MC2P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC2P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MC2P5. Students will represent mathematics in multiple ways.

MC2P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC2P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC2P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC3A. Core Mathematics 3 - Algebra: Students will investigate piecewise and exponential functions from numerical, analytical and graphical approaches, focusing on the use of these functions in problem-solving situations.

MC3A1. Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

MC3A1.a. Write absolute value functions as piecewise functions.

MC3A1.b. Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.

MC3A1.c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

MC3A2. Students will explore exponential functions.

MC3A2.a. Extend properties of exponents to include all integer exponents.

MC3A2.b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

MC3A2.c. Graph functions as transformations of f(x) = a^x.

MC3A2.d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

MC3A2.e. Understand and use basic exponential functions as models of real phenomena.

MC3A2.f. Understand and recognize geometric sequences as exponential functions with domains that are sets of whole numbers.

MC3A2.g. Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

GA.MC3G. Core Mathematics 3 - Geometry: Students will explore right triangles and right triangular trigonometry.

MC3G1. Students will identify and use special right triangles.

MC3G1.a. Determine the lengths of sides of 30 degree - 60 degree - 90 degree triangles.

MC3G1.b. Determine the lengths of sides of 45 degree - 45 degree - 90 degree triangles.

MC3G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.

MC3G2.a. Discover the relationship of the trigonometric ratios for similar triangles.

MC3G2.b. Explain the relationship between the trigonometric ratios of complementary angles.

MC3G2.c. Solve application problems using the trigonometric ratios.

GA.MC3D. Core Mathematics 3 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data. Students will use regression to analyze data, and to make inferences.

MC3D1. Using sample data, students will make informal inferences about population means and standard deviations.

MC3D1.a. Pose a question and collect sample data from at least two different populations.

MC3D1.b. Understand and calculate the means and standard deviations of sets of data.

MC3D1.c. Use means and standard deviations to compare data sets.

MC3D1.d. Compare the means and standard deviations of random samples with the corresponding population parameters. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

MC3D2. Students will determine an algebraic model to quantify the association between two quantitative variables.

MC3D2.a. Gather and plot data that can be modeled with linear functions.

MC3D2.b. Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and 'eyeballing.'

MC3D2.c. Understand and apply the processes of linear regression for curve fitting using appropriate technology.

GA.MC3P. Core Mathematics 3 - Process Standards: The following process standards are essential mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC3P1. Students will solve problems (using appropriate technology).

MC3P1.a. Build new mathematical knowledge through problem solving.

MC3P1.b. Solve problems that arise in mathematics and in other contexts.

MC3P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC3P1.d. Monitor and reflect on the process of mathematical problem solving.

MC3P2. Students will reason and evaluate mathematical arguments.

MC3P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC3P2.b. Make and investigate mathematical conjectures.

MC3P2.c. Develop and evaluate mathematical arguments and proofs.

MC3P2.d. Select and use various types of reasoning and methods of proof.

MC3P3. Students will communicate mathematically.

MC3P3.a. Organize and consolidate their mathematical thinking through communication.

MC3P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC3P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC3P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC3P4. Students will make connections among mathematical ideas and to other disciplines.

MC3P4.a. Recognize and use connections among mathematical ideas.

MC3P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC3P4.c. Recognize and apply mathematics in context outside of mathematics.

MC3P5. Students will represent mathematics in multiple ways.

MC3P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC3P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC3P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MC4N. Core Mathematics 4 - Number and Operations: Students will use the complex number system.

MC4N1. Students will represent and operate with complex numbers.

MC4N1.a. Write square roots of negative numbers in imaginary form.

MC4N1.b. Write complex numbers in the form a + bi.

MC4N1.c. Add, subtract, multiply, and divide complex numbers.

MC4N1.d. Simplify expressions involving complex numbers.

GA.MC4A. Core Mathematics 4 - Algebra: Students will investigate quadratic functions from numerical, analytical and graphical approaches, focusing on the use of these functions in problem-solving situations. Students will solve quadratic equations and inequalities and explore inverses of functions.

MC4A1. Students will analyze quadratic functions in the forms f(x) = ax^2 + bx + c and f(x) = a(x - h)^2 + k.

MC4A1.a. Convert between standard and vertex form.

MC4A1.b. Graph quadratic functions as transformations of the function f(x) = x^2.

MC4A1.c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

MC4A1.d. Explore arithmetic series and various ways of computing their sums.

MC4A1.e. Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

MC4A2. Students will solve quadratic equations and inequalities in one variable.

MC4A2.a. Solve equations graphically using appropriate technology.

MC4A2.b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

MC4A2.c. Analyze the nature of roots using technology and using the discriminant.

MC4A2.d. Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

MC4A3. Students will explore inverses of functions.

MC4A3.a. Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

MC4A3.b. Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.

MC4A3.c. Explore the graphs of functions and their inverses.

MC4A3.d. Use composition to verify that functions are inverses of each other.

GA.MC4G. Core Mathematics 4 - Geometry: Students will understand and apply properties of circles and spheres and use them in determining related measures.

MC4G1. Students will understand the properties of circles.

MC4G1.a. Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

MC4G1.b. Understand and use properties of central, inscribed, and related angles.

MC4G1.c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

MC4G1.d. Justify measurements and relationships in circles using geometric and algebraic properties.

MC4G2. Students will find and compare the measures of spheres.

MC4G2.a. Use and apply surface area and volume of a sphere.

MC4G2.b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

GA.MC4D. Core Mathematics 4 - Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will use regression to analyze data, and to make inferences.

MC4D1. Students will determine an algebraic model to quantify the association between two quantitative variables.

MC4D1.a. Gather and plot data that can be modeled with quadratic functions.

MC4D1.b. Understand and apply the processes of quadratic regression for curve fitting using appropriate technology.

GA.MC4P. Core Mathematics 4 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MC4P1. Students will solve problems (using appropriate technology).

MC4P1.a. Build new mathematical knowledge through problem solving.

MC4P1.b. Solve problems that arise in mathematics and in other contexts.

MC4P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MC4P1.d. Monitor and reflect on the process of mathematical problem solving.

MC4P2. Students will reason and evaluate mathematical arguments.

MC4P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MC4P2.b. Make and investigate mathematical conjectures.

MC4P2.c. Develop and evaluate mathematical arguments and proofs.

MC4P2.d. Select and use various types of reasoning and methods of proof.

MC4P3. Students will communicate mathematically.

MC4P3.a. Organize and consolidate their mathematical thinking through communication.

MC4P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MC4P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MC4P3.d. Use the language of mathematics to express mathematical ideas precisely.

MC4P4. Students will make connections among mathematical ideas and to other disciplines.

MC4P4.a. Recognize and use connections among mathematical ideas.

MC4P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MC4P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MC4P5. Students will represent mathematics in multiple ways.

MC4P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MC4P5.b. Select, apply, and translate among mathematical representations to solve problems.

MC4P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MA1N. Accelerated Mathematics 1 - Number and Operations: Students will use the complex number system.

MA1N1. Students will represent and operate with complex numbers.

MA1N1.a. Write square roots of negative numbers in imaginary form.

MA1N1.b. Write complex numbers in the form a + bi.

MA1N1.c. Add, subtract, multiply, and divide complex numbers.

MA1N1.d. Simplify expressions involving complex numbers.

GA.MA1A. Accelerated Mathematics 1 - Algebra: Students will explore functions, solve equations and operate with radical, polynomial and rational expressions.

MA1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MA1A1.a. Represent functions using function notation.

MA1A1.b. Graph the basic functions f(x) = x^n, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

MA1A1.c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

MA1A1.d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

MA1A1.e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

MA1A1.f. Recognize sequences as functions with domains that are sets of whole numbers.

MA1A1.g. Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

MA1A1.h. Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

MA1A1.i. Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

MA1A2. Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MA1A2.a. Simplify algebraic and numeric expressions involving square root.

MA1A2.b. Perform operations with square roots.

MA1A2.c. Add, subtract, multiply, and divide polynomials.

MA1A2.d. Add, subtract, multiply, and divide rational expressions.

MA1A2.e. Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas: (x + y)^2 = x^2 + 2xy + y^2; (x - y)^2 = x^2 - 2xy + y^2; (x + y)(x - y) = x^2 - y^2; (x + a)(x + b) = x^2 + (a + b)x + ab; (x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3; (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3

MA1A2.f. Use area and volume models for polynomial arithmetic.

MA1A3. Students will analyze quadratic functions in the forms f(x) = ax^2 + bx + c and f(x) = a(x - h)^2 + k.

MA1A3.a. Convert between standard and vertex form.

MA1A3.b. Graph quadratic functions as transformations of the function f(x) = x^2.

MA1A3.c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

MA1A3.d. Explore arithmetic series and various ways of computing their sums.

MA1A3.e. Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

MA1A4. Students will solve quadratic equations and inequalities in one variable.

MA1A4.a. Solve equations graphically using appropriate technology.

MA1A4.b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

MA1A4.c. Analyze the nature of roots using technology and using the discriminant.

MA1A4.d. Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

MA1A5. Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

MA1A5.a. Write absolute value functions as piecewise functions.

MA1A5.b. Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.

MA1A5.c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

GA.MA1G. Accelerated Mathematics 1 - Geometry: Students will explore, understand and use the formal language of reasoning and justification. Students will apply properties of polygons, circles and spheres, and determine distances and points of concurrence.

MA1G1. Students will investigate properties of geometric figures in the coordinate plane.

MA1G1.a. Determine the distance between two points.

MA1G1.b. Determine the distance between a point and a line.

MA1G1.c. Determine the midpoint of a segment.

MA1G1.d. Understand the distance formula as an application of the Pythagorean theorem.

MA1G1.e. Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

MA1G2. Students will understand and use the language of mathematical argument and justification.

MA1G2.a. Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.

MA1G2.b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

MA1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.

MA1G3.a. Determine the sum of interior and exterior angles in a polygon.

MA1G3.b. Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.

MA1G3.c. Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

MA1G3.d. Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

MA1G3.e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

MA1G4. Students will understand the properties of circles.

MA1G4.a. Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

MA1G4.b. Understand and use properties of central, inscribed, and related angles.

MA1G4.c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

MA1G4.d. Justify measurements and relationships in circles using geometric and algebraic properties.

MA1G5. Students will find and compare the measures of spheres.

MA1G5.a. Use and apply surface area and volume of a sphere.

MA1G5.b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

GA.MA1D. Accelerated Mathematics 1 - Data Analysis and Probability: Students will use counting techniques and determine probability. Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data. Students will determine algebraic models from data.

MA1D1. Students will determine the number of outcomes related to a given event.

MA1D1.a. Apply the addition and multiplication principles of counting.

MA1D1.b. Calculate and use simple permutations and combinations.

MA1D2. Students will use the basic laws of probability.

MA1D2.a. Find the probabilities of mutually exclusive events.

MA1D2.b. Find the probabilities of dependent events.

MA1D2.c. Calculate conditional probabilities.

MA1D2.d. Use expected value to predict outcomes.

MA1D3. Students will relate samples to a population.

MA1D3.a. Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.

MA1D3.b. Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.

MA1D3.c. Understand that a random sample is used to improve the chance of selecting a representative sample.

MA1D4. Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

MA1D5. Students will determine an algebraic model to quantify the association between two quantitative variables.

MA1D5.a. Gather and plot data that can be modeled with linear and quadratic functions.

MA1D5.b. Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and .eyeballing..

MA1D5.c. Understand and apply the processes of linear and quadratic regression for curve fitting using appropriate technology.

GA.MA1P. Accelerated Mathematics 1 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MA1P1. Students will solve problems (using appropriate technology).

MA1P1.a. Build new mathematical knowledge through problem solving.

MA1P1.b. Solve problems that arise in mathematics and in other contexts.

MA1P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MA1P1.d. Monitor and reflect on the process of mathematical problem solving.

MA1P2. Students will reason and evaluate mathematical arguments.

MA1P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MA1P2.b. Make and investigate mathematical conjectures.

MA1P2.c. Develop and evaluate mathematical arguments and proofs.

MA1P2.d. Select and use various types of reasoning and methods of proof.

MA1P3. Students will communicate mathematically.

MA1P3.a. Organize and consolidate their mathematical thinking through communication.

MA1P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MA1P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MA1P3.d. Use the language of mathematics to express mathematical ideas precisely.

MA1P4. Students will make connections among mathematical ideas and to other disciplines.

MA1P4.a. Recognize and use connections among mathematical ideas.

MA1P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MA1P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MA1P5. Students will represent mathematics in multiple ways.

MA1P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MA1P5.b. Select, apply, and translate among mathematical representations to solve problems.

MA1P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MA2A. Accelerated Mathematics 2 - Algebra: Students will investigate exponential, logarithmic, and polynomial functions of higher degree; understand matrices and use them to solve problems; and solve linear programming problems in two variables.

MA2A1. Students will explore exponential functions.

MA2A1.a. Extend properties of exponents to include all integer exponents.

MA2A1.b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

MA2A1.c. Graph functions as transformations of f(x) = a^x.

MA2A1.d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

MA2A1.e. Understand and use basic exponential functions as models of real phenomena.

MA2A1.f. Understand and recognize geometric sequences as exponential functions with domains that are sets of whole numbers.

MA2A1.g. Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

MA2A2. Students will explore inverses of functions.

MA2A2.a. Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

MA2A2.b. Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.

MA2A2.c. Explore the graphs of functions and their inverses.

MA2A2.d. Use composition to verify that functions are inverses of each other.

MA2A3. Students will analyze graphs of polynomial functions of higher degree.

MA2A3.a. Graph simple polynomial functions as translations of the function f(x) = ax^n.

MA2A3.b. Understand the effects of the following on the graph of a polynomial function: degree, lead coefficient, and multiplicity of real zeros.

MA2A3.c. Determine whether a polynomial function has symmetry and whether it is even, odd, or neither.

MA2A3.d. Investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.

MA2A4. Students will explore logarithmic functions as inverses of exponential functions.

MA2A4.a. Define and understand the properties of nth roots.

MA2A4.b. Extend properties of exponents to include rational exponents.

MA2A4.c. Define logarithmic functions as inverses of exponential functions.

MA2A4.d. Understand and use properties of logarithms by extending laws of exponents.

MA2A4.e. Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

MA2A4.f. Graph functions as transformations of f(x) = a^x, f(x) = log ax, f(x) = e^x, f(x) = ln x.

MA2A4.g. Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

MA2A5. Students will solve a variety of equations and inequalities.

MA2A5.a. Find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical conjugates.

MA2A5.b. Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

MA2A5.c. Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

MA2A5.d. Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology.

MA2A6. Students will perform basic operations with matrices.

MA2A6.a. Add, subtract, multiply, and invert matrices, when possible, choosing appropriate methods, including technology.

MA2A6.b. Find the inverses of two-by-two matrices using pencil and paper, and find inverses of larger matrices using technology.

MA2A6.c. Examine the properties of matrices, contrasting them with properties of real numbers.

MA2A7. Students will use matrices to formulate and solve problems.

MA2A7.a. Represent a system of linear equations as a matrix equation.

MA2A7.b. Solve matrix equations using inverse matrices.

MA2A7.c. Represent and solve realistic problems using systems of linear equations.

MA2A8. Students will solve linear programming problems in two variables.

MA2A8.a. Solve systems of inequalities in two variables, showing the solutions graphically.

MA2A8.b. Represent and solve realistic problems using linear programming.

MA2A9. Students will understand and apply matrix representations of vertex-edge graphs.

MA2A9.a. Use graphs to represent realistic situations.

MA2A9.b. Use matrices to represent graphs, and solve problems that can be represented by graphs.

GA.MA2G. Accelerated Mathematics 2 - Geometry: Students will explore right triangles and right triangular trigonometry. They will understand and apply properties of conic sections, planes, and spheres.

MA2G1. Students will identify and use special right triangles.

MA2G1.a. Determine the lengths of sides of 30 degree - 60 degree - 90 degree triangles.

MA2G1.b. Determine the lengths of sides of 45 degree - 45 degree - 90 degree triangles.

MA2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.

MA2G2.a. Discover the relationship of the trigonometric ratios for similar triangles.

MA2G2.b. Explain the relationship between the trigonometric ratios of complementary angles.

MA2G2.c. Solve application problems using the trigonometric ratios.

MA2G3. Students will investigate the relationships between lines and circles.

MA2G3.a. Find equations of circles.

MA2G3.b. Graph a circle given an equation in general form.

MA2G3.c. Find the equation of a tangent line to a circle at a given point.

MA2G3.d. Solve a system of equations involving a circle and a line.

MA2G3.e. Solve a system of equations involving two circles.

MA2G4. Students will recognize, analyze, and graph the equations of the conic sections (parabolas, circles, ellipses, and hyperbolas).

MA2G4.a. Convert equations of conics by completing the square.

MA2G4.b. Graph conic sections, identifying fundamental characteristics.

MA2G4.c. Write equations of conic sections given appropriate information.

MA2G5. Students will investigate planes and spheres.

MA2G5.a. Plot the point (x, y, z) and understand it as a vertex of a rectangular prism.

MA2G5.b. Apply the distance formula in 3-space.

MA2G5.c. Recognize and understand equations of planes and spheres.

GA.MA2D. Accelerated Mathematics 2 - Data Analysis and Probability: Students will make informal inferences about means and standard deviations. Students will use a normal distribution to calculate probabilities. Students will organize, represent, investigate, interpret, and make inferences from both observational studies and experiments.

MA2D1. Using sample data, students will make informal inferences about population means and standard deviations.

MA2D1.a. Pose a question and collect sample data from at least two different populations.

MA2D1.b. Understand and calculate the means and standard deviations of sets of data.

MA2D1.c. Use means and standard deviations to compare data sets.

MA2D1.d. Compare the means and standard deviations of random samples with the corresponding population parameters. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

MA2D2. Students will create probability histograms of discrete random variables, using both experimental and theoretical probabilities.

MA2D3. Students will solve problems involving probabilities by interpreting a normal distribution as a probability histogram for a continuous random variable (z-scores are used for a general normal distribution).

MA2D3.a. Determine intervals about the mean that include a given percent of data.

MA2D3.b. Determine the probability that a given value falls within a specified interval.

MA2D3.c. Estimate how many items in a population fall within a specified interval.

MA2D4. Students will understand the differences between experimental and observational studies by posing questions and collecting, analyzing, and interpreting data.

GA.MA2P. Accelerated Mathematics 2 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MA2P1. Students will solve problems (using appropriate technology).

MA2P1.a. Build new mathematical knowledge through problem solving.

MA2P1.b. Solve problems that arise in mathematics and in other contexts.

MA2P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MA2P1.d. Monitor and reflect on the process of mathematical problem solving.

MA2P2. Students will reason and evaluate mathematical arguments.

MA2P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MA2P2.b. Make and investigate mathematical conjectures.

MA2P2.c. Develop and evaluate mathematical arguments and proofs.

MA2P2.d. Select and use various types of reasoning and methods of proof.

MA2P3. Students will communicate mathematically.

MA2P3.a. Organize and consolidate their mathematical thinking through communication.

MA2P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MA2P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MA2P3.d. Use the language of mathematics to express mathematical ideas precisely.

MA2P4. Students will make connections among mathematical ideas and to other disciplines.

MA2P4.a. Recognize and use connections among mathematical ideas.

MA2P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MA2P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MA2P5. Students will represent mathematics in multiple ways.

MA2P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MA2P5.b. Select, apply, and translate among mathematical representations to solve problems.

MA2P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MA3A. Accelerated Mathematics 3 - Algebra: Students will explore characteristics of various functions, understand and use concepts of trigonometric functions, investigate and apply sequences and series, and use parametric and polar equations to represent functions and curves.

MA3A1. Students will explore rational functions.

MA3A1.a. Investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior.

MA3A1.b. Find inverses of rational functions, discussing domain and range, symmetry, and function composition.

MA3A1.c. Solve rational equations and inequalities analytically, graphically, and by using appropriate technology.

MA3A2. Students will use the circle to define the trigonometric functions.

MA3A2.a. Define and understand angles measured in degrees and radians, including but not limited to 0 degrees, 30 degrees, 45 degrees, 60 degrees, 90 degrees, their multiples, and equivalences.

MA3A2.b. Understand and apply the six trigonometric functions as functions of general angles in standard position.

MA3A2.c. Find values of trigonometric functions using points on the terminal sides of angles in the standard position.

MA3A2.d. Understand and apply the six trigonometric functions as functions of arc length on the unit circle.

MA3A2.e. Find values of trigonometric functions using the unit circle.

MA3A3. Students will investigate and use the graphs of the six trigonometric functions.

MA3A3.a. Understand and apply the six basic trigonometric functions as functions of real numbers.

MA3A3.b. Determine the characteristics of the graphs of the six basic trigonometric functions.

MA3A3.c. Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

MA3A3.d. Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena.

MA3A4. Students will investigate functions.

MA3A4.a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

MA3A4.b. Investigate transformations of functions.

MA3A4.c. Investigate characteristics of functions built through sum, difference, product, quotient, and composition.

MA3A5. Students will establish trigonometric identities and use them to simplify trigonometric expressions and verify equivalence statements.

MA3A6. Students will solve trigonometric equations both graphically and algebraically.

MA3A6.a. Solve trigonometric equations over a variety of domains, using technology as appropriate.

MA3A6.b. Use the coordinates of a point on the terminal side of an angle to express x and y as polar coordinates.

MA3A6.c. Apply the law of sines and the law of cosines.

MA3A7. Students will verify and apply 1/2 ab sinC to find the area of a triangle.

MA3A8. Students will investigate and use inverse sine, inverse cosine, and inverse tangent functions.

MA3A8.a. Find values of the above functions using technology as appropriate.

MA3A8.b. Determine characteristics of the above functions and their graphs.

MA3A9. Students will use sequences and series

MA3A9.a. Use and find recursive and explicit formulae for the terms of sequences.

MA3A9.b. Recognize and use simple arithmetic and geometric sequences.

MA3A9.c. Investigate limits of sequences.

MA3A9.d. Use mathematical induction to find and prove formulae for sums of finite series.

MA3A9.e. Find and apply the sums of finite and, where appropriate, infinite arithmetic and geometric series.

MA3A9.f. Use summation notation to explore series.

MA3A9.g. Determine geometric series and their limits.

MA3A10. Students will understand and use vectors.

MA3A10.a. Represent vectors algebraically and geometrically.

MA3A10.b. Convert between vectors expressed using rectangular coordinates and vectors expressed using magnitude and direction.

MA3A10.c. Add and subtract vectors and compute scalar multiples of vectors.

MA3A10.d. Use vectors to solve realistic problems.

MA3A11. Students will use complex numbers in trigonometric form.

MA3A11.a. Represent complex numbers in trigonometric form.

MA3A11.b. Find products, quotients, powers, and roots of complex numbers in trigonometric form.

MA3A12. Students will explore parametric representations of plane curves.

MA3A12.a. Convert between Cartesian and parametric form.

MA3A12.b. Graph equations in parametric form showing direction and beginning and ending points where appropriate.

MA3A13. Students will explore polar equations.

MA3A13.a. Express coordinates of points in rectangular and polar form.

MA3A13.b. Graph and identify characteristics of simple polar equations including lines, circles, cardioids, limacons, and roses.

GA.MA3D. Accelerated Mathematics 3 - Data Analysis and Probability: Students will organize, represent, investigate, interpret, and make inferences from data, using the central limit theorem and the standard normal distribution. Students will apply the Central Limit Theorem to calculate confidence intervals for a population mean using data from large samples. Students will use sample data and confidence intervals to draw conclusions about populations.

MA3D1. Using simulation, students will develop the idea of the central limit theorem.

MA3D2. Using student-generated data from random samples of at least 30 members, students will determine the margin of error and confidence interval for a specified level of confidence.

MA3D3. Students will use confidence intervals and margins of error to make inferences from data about a population. Technology is used to evaluate confidence intervals, but students will be aware of the ideas involved.

GA.MA3P. Accelerated Mathematics 3 - Process Standards: The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

MA3P1. Students will solve problems (using appropriate technology).

MA3P1.a. Build new mathematical knowledge through problem solving.

MA3P1.b. Solve problems that arise in mathematics and in other contexts.

MA3P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

MA3P1.d. Monitor and reflect on the process of mathematical problem solving.

MA3P2. Students will reason and evaluate mathematical arguments.

MA3P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

MA3P2.b. Make and investigate mathematical conjectures.

MA3P2.c. Develop and evaluate mathematical arguments and proofs.

MA3P2.d. Select and use various types of reasoning and methods of proof.

MA3P3. Students will communicate mathematically.

MA3P3.a. Organize and consolidate their mathematical thinking through communication.

MA3P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

MA3P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

MA3P3.d. Use the language of mathematics to express mathematical ideas precisely.

MA3P4. Students will make connections among mathematical ideas and to other disciplines.

MA3P4.a. Recognize and use connections among mathematical ideas.

MA3P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

MA3P4.c. Recognize and apply mathematics in contexts outside of mathematics.

MA3P5. Students will represent mathematics in multiple ways.

MA3P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

MA3P5.b. Select, apply, and translate among mathematical representations to solve problems.

MA3P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.MRC. Reading Across the Curriculum: Reading across curriculum content develops both academic and personal interests in students. As students read, they develop both content and contextual vocabulary. They also build good habits for reading, researching, and learning. The Reading Across the Curriculum standard focuses on the academic and personal skills students acquire as they read in all areas of learning.

MRC1. Students will enhance reading in all curriculum areas by:

MRC1.a. Reading in all curriculum areas: Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areas; Read both informational and fictional texts in a variety of genres and modes of discourse; Read technical texts related to various subject areas

MRC1.b. Discussing books: Discuss messages and themes from books in all subject areas; Respond to a variety of texts in multiple modes of discourse; Relate messages and themes from one subject area to messages and themes in another area; Evaluate the merit of texts in every subject discipline; Examine author's purpose in writing; Recognize the features of disciplinary texts.

MRC1.c. Building vocabulary knowledge: Demonstrate an understanding of contextual vocabulary in various subjects; Use content vocabulary in writing and speaking; Explore understanding of new words found in subject area texts.

MRC1.d. Establishing context: Explore life experiences related to subject area content; Discuss in both writing and speaking how certain words are subject area related; Determine strategies for finding content and contextual meaning for unknown words.