South Carolina State Standards for Mathematics:

SC.K-1 Mathematical Processes: The student will have a basic understanding of the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

K-1.1 Apply substantive mathematical problem-solving strategies.

K-1.2 Generate conjectures and exchange mathematical ideas.

K-1.3 Explain and justify answers to simple problems.

K-1.4 Analyze patterns by reasoning systematically.

K-1.5 Generalize mathematical concepts.

K-1.6 Use a variety of forms of mathematical communication.

K-1.7 Generalize connections among mathematics, the environment, and other subjects.

K-1.8 Use multiple informal representations to convey mathematical ideas.

SC.K-2 Numbers and Operations: The student will demonstrate through the mathematical processes an emerging sense of quantity and numeral relationships, sets, and place values.

K-2.1 Recall numbers, counting forward through 99 and backward from 10.

K-2.2 Translate between numeral and quantity through 31.

K-2.3 Compare sets of no more than 31 objects by using the terms more than, less than, and the same as.

K-2.4 Represent simple joining and separating situations through 10.

K-2.5 Understand that addition results in increase and subtraction results in decrease.

K-2.6 Analyze the magnitude of digits through 99 on the basis of their place values.

K-2.7 Represent the place value of each digit in a two-digit whole number.

K-2.8 Identify ordinal positions through 31st.

SC.K-3 Algebra: The student will demonstrate through the mathematical processes an emerging sense of repeating and growing patterns and classification based on attributes.

K-3.1 Identify simple growing patterns.

K-3.2 Analyze simple repeating and growing relationships to extend patterns.

K-3.3 Translate simple repeating and growing patterns into rules.

K-3.4 Classify objects according to one or more attributes such as color, size, shape, and thickness.

SC.K-4 Geometry: The student will demonstrate through the mathematical processes an emerging sense of two- and three-dimensional geometric shapes and relative positions in space.

K-4.1 Identify the two-dimensional shapes square, circle, triangle, and rectangle and the three-dimensional shapes cube, sphere, and cylinder.

K-4.2 Represent two-dimensional geometric shapes.

K-4.3 Use the positional words near, far, below, above, beside, next to, across from, and between to describe the location of an object.

K-4.4 Use the directional words left and right to describe movement.

SC.K-5 Measurement: The student will demonstrate through the mathematical processes an emerging sense of coin values and the measurement concepts of length, weight, time, and temperature.

K-5.1 Identify a penny, a nickel, a dime, a quarter, and a dollar and the value of each.

K-5.2 Compare the lengths of two objects, both directly and indirectly, to order objects according to length.

K-5.3 Use nonstandard units to explore the measurement concepts of length and weight.

K-5.4 Identify rulers, yardsticks, and tape measures as devices used to measure length; scales and balances as devices used to measure weight; calendars and analog and digital clocks as devices used to measure time; and digital and standard thermometers as devices used to measure temperature.

K-5.5 Understand which measure-length, weight, time, or temperature-is appropriate for a given situation.

K-5.6 Use analog and digital clocks to tell time to the hour.

K-5.7 Use a calendar to identify dates, days of the week, and months of the year.

K-5.8 Recall equivalencies associated with time: 7 days = 1 week and 12 months = 1 year.

SC.K-6 Data Analysis and Probability: The student will demonstrate through the mathematical processes an emerging sense of organizing and interpret data.

K-6.1 Organize data in graphic displays in the form of drawings and pictures.

K-6.2 Interpret data in graphic displays in the form of drawings and pictures.

SC.1-1 Mathematical Processes: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

1-1.1 Apply substantive mathematical problem-solving strategies.

1-1.2 Generate conjectures and exchange mathematical ideas.

1-1.3 Explain and justify answers to simple problems.

1-1.4 Analyze patterns by reasoning systematically.

1-1.5 Generalize mathematical concepts.

1-1.6 Use a variety of forms of mathematical communication.

1-1.7 Generalize connections among mathematics, the environment, and other subjects.

1-1.8 Use multiple informal representations to convey mathematical ideas.

SC.1-2 Number and Operations: The student will demonstrate through the mathematical processes a sense of quantity and numeral relationships; the relationships among addition, subtraction, and related basic facts; and the connections among numeric, oral, and written-word forms of whole numbers.

1-2.1 Translate between numeral and quantity through 100.

1-2.2 Use estimation to determine the approximate number of objects in a set of 20 to 100 objects.

1-2.3 Represent quantities in word form through ten.

1-2.4 Recognize whole-number words that correspond to numerals through twenty.

1-2.5 Compare whole-number quantities through 100 by using the terms is greater than, is less than, and is equal to.

1-2.6 Recall basic addition facts through 9 + 9 and corresponding subtraction facts.

1-2.7 Summarize the inverse relationship between addition and subtraction.

1-2.8 Generate strategies to add and subtract without regrouping through two-digit numbers.

1-2.9 Analyze the magnitude of digits through 999 on the basis of their place values.

SC.1-3 Algebra: The student will demonstrate through the mathematical processes a sense of numeric patterns, the relationship between addition and subtraction, and change over time.

1-3.1 Analyze numeric patterns in addition and subtraction to develop strategies for acquiring basic facts.

1-3.2 Translate patterns into rules for simple addition and subtraction.

1-3.3 Illustrate the commutative property based on basic facts.

1-3.4 Analyze numeric relationships to complete and extend simple patterns.

1-3.5 Classify a number as odd or even.

1-3.6 Classify change over time as quantitative or qualitative.

SC.1-4 Geometry: The student will demonstrate through the mathematical processes a sense of two- and three-dimensional geometric shapes, symmetry, and relative positions and directions in space.

1-4.1 Identify the three-dimensional geometric shapes prism, pyramid, and cone.

1-4.2 Analyze the two-dimensional shapes circle, square, triangle, and rectangle.

1-4.3 Classify two-dimensional shapes as polygons or non-polygons.

1-4.4 Identify a line of symmetry.

1-4.5 Use the positional and directional terms north, south, east, and west to describe location and movement.

SC.1-5 Measurement: The student will demonstrate through the mathematical processes a sense of the value of combinations of coins and the measurement of length, weight, time, and temperature.

1-5.1 Use a counting procedure to determine the value of a collection of pennies, nickels, dimes, and quarters totaling less than a dollar.

1-5.2 Represent a nickel, a dime, a quarter, a half-dollar, and a dollar in combinations of coins.

1-5.3 Represent money by using the cent and dollar notations.

1-5.4 Use whole-inch units to measure the length of an object.

1-5.5 Generate common referents for whole inches.

1-5.6 Use common referents to make estimates in whole inches.

1-5.7 Use nonstandard units to measure the weight of objects.

1-5.8 Use analog and digital clocks to tell and record time to the half hour.

1-5.9 Illustrate past and future dates on a calendar.

1-5.10 Represent dates in standard form (June 1, 2007, for example) and numeric form (6-1-2007, for example).

1-5.11 Use Celsius and Fahrenheit thermometers to measure temperature.

SC.1-6 Data Analysis and Probability: The student will demonstrate through the mathematical processes a sense of collecting, organizing, and interpreting data and of making predictions on the basis of data.

1-6.1 Use survey questions to collect data.

1-6.2 Organize data in picture graphs, object graphs, bar graphs, and tables.

1-6.3 Interpret data in picture graphs, object graphs, bar graphs, and tables by using the comparative terms more, less, greater, fewer, greater than, and less than.

1-6.4 Predict on the basis of data whether events are likely or unlikely to occur.

SC.2-1 Mathematical Processes: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

2-1.1 Apply substantive mathematical problem-solving strategies.

2-1.2 Generate conjectures and exchange mathematical ideas.

2-1.3 Explain and justify answers to simple problems.

2-1.4 Analyze patterns by reasoning systematically.

2-1.5 Generalize mathematical concepts.

2-1.6 Use a variety of forms of mathematical communication.

2-1.7 Generalize connections among mathematics, the environment, and other subjects.

2-1.8 Use multiple informal representations to convey mathematical ideas.

SC.2-2 Numbers and Operations: The student will demonstrate through the mathematical processes an understanding of the base-ten numeration system; place values; and accurate, efficient, and generalizable methods of adding and subtracting whole numbers.

2-2.1 Generate estimation strategies to determine the approximate number of objects in a set of no more than 1,000 objects.

2-2.2 Represent quantities in word form through twenty.

2-2.3 Represent multiples of ten in word form through ninety.

2-2.4 Compare whole-number quantities through 999 by using the terms is less than, is greater than, and is equal to and the symbols <, >, and =.

2-2.5 Interpret models of equal grouping (multiplication) as repeated addition and arrays.

2-2.6 Interpret models of sharing equally (division) in as repeated subtraction and arrays.

2-2.7 Generate strategies to add and subtract pairs of two-digit whole numbers with regrouping.

2-2.8 Generate addition and subtraction strategies to find missing addends and subtrahends in number combinations through 20.

2-2.9 Generate strategies to round numbers through 90 to the nearest 10.

2-2.10 Analyze the magnitude of digits through 9,999 on the basis of their place values.

SC.2-3 Algebra: The student will demonstrate through the mathematical processes an understanding of numeric patterns and quantitative and qualitative change.

2-3.1 Analyze numeric patterns in skip counting that uses the numerals 1 through 10.

2-3.2 Translate patterns into rules for simple multiples.

2-3.3 Analyze relationships to complete and extend growing and repeating patterns involving numbers, symbols, and objects.

2-3.4 Identify quantitative and qualitative change over time.

2-3.5 Analyze quantitative and qualitative change over time.

SC.2-4 Geometry: The student will demonstrate through the mathematical processes an understanding of basic spatial reasoning and the connection between the identification of basic attributes and the classification of three-dimensional shapes.

2-4.1 Analyze the three-dimensional shapes spheres, cubes, cylinders, prisms, pyramids, and cones according to the number and shape of the faces, edges, corners, and bases of each.

2-4.2 Identify multiple lines of symmetry.

2-4.3 Predict the results of combining and subdividing polygons and circles.

SC.2-5 Measurement: The student will demonstrate through the mathematical processes an understanding of the value of combinations of coins and bills and the measurement of length, weight, time, and temperature.

2-5.1 Use a counting procedure to determine the value of a collection of coins and bills.

2-5.2 Use coins to make change up to one dollar.

2-5.3 Use appropriate tools to measure objects to the nearest whole unit: measuring length in centimeters, feet, and yards; measuring liquid volume in cups, quarts, and gallons; measuring weight in ounces and pounds; and measuring temperature on Celsius and Fahrenheit thermometers.

2-5.4 Generate common measurement referents for feet, yards, and centimeters.

2-5.5 Use common measurement referents to make estimates in feet, yards, and centimeters.

2-5.6 Predict whether the measurement will be greater or smaller when different units are used to measure the same object.

2-5.7 Use analog and digital clocks to tell and record time to the nearest quarter hour and to the nearest five-minute interval.

2-5.8 Match a.m. and p.m. to familiar situations.

2-5.9 Recall equivalencies associated with length and time: 12 inches = 1 foot, 3 feet = 1 yard, 60 minutes = 1 hour, and 24 hours = 1 day.

SC.2-6 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of creating questions to collect data, organizing data, describing trends of a data set, and making predictions based on data.

2-6.1 Create survey questions to collect data.

2-6.2 Organize data in charts, pictographs, and tables.

2-6.3 Infer trends in a data set as increasing, decreasing, or random.

2-6.4 Predict on the basis of data whether events are more likely or less likely to occur.

SC.3-1 Mathematical Processes: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

3-1.1 Analyze information to solve increasingly more sophisticated problems.

3-1.2 Construct arguments that lead to conclusions about general mathematical properties and relationships.

3-1.3 Explain and justify answers on the basis of mathematical properties, structures, and relationships.

3-1.4 Generate descriptions and mathematical statements about relationships between and among classes of objects.

3-1.5 Use correct, complete, and clearly written and oral mathematical language to pose questions, communicate ideas, and extend problem situations.

3-1.6 Generalize connections between new mathematical ideas and related concepts and subjects that have been previously considered.

3-1.7 Use flexibility in mathematical representations.

3-1.8 Recognize the limitations of various forms of mathematical representations.

SC.3-2 Numbers and Operations: The student will demonstrate through the mathematical processes an understanding of the representation of whole numbers and fractional parts; the addition and subtraction of whole numbers; accurate, efficient, and generalizable methods of multiplying whole numbers; and the relationships among multiplication, division, and related basic facts.

3-2.1 Compare whole-number quantities through 999,999 by using the terms is less than, is greater than, and is equal to and the symbols <, >, and =.

3-2.2 Represent in word form whole numbers through nine hundred ninety-nine thousand.

3-2.3 Apply an algorithm to add and subtract whole numbers fluently.

3-2.4 Apply procedures to round any whole number to the nearest 10, 100, or 1,000.

3-2.5 Understand fractions as parts of a whole.

3-2.6 Represent fractions that are greater than or equal to 1.

3-2.7 Recall basic multiplication facts through 12 x 12 and the corresponding division facts.

3-2.8 Compare the inverse relationship between multiplication and division.

3-2.9 Analyze the effect that adding, subtracting, or multiplying odd and/or even numbers has on the outcome.

3-2.10 Generate strategies to multiply whole numbers by using one single-digit factor and one multi-digit factor.

3-2.11 Use basic number combinations to compute related multiplication problems that involve multiples of 10.

3-2.12 Analyze the magnitude of digits through 999,999 on the basis of their place value.

SC.3-3 Algebra: The student will demonstrate through the mathematical processes an understanding of numeric patterns, symbols as representations of unknown quantity, and situations showing increase over time.

3-3.1 Create numeric patterns that involve whole-Number and Operations.

3-3.2 Apply procedures to find missing numbers in numeric patterns that involve whole-Number and Operations.

3-3.3 Use symbols to represent an unknown quantity in a simple addition, subtraction, or multiplication equation.

3-3.4 Illustrate situations that show change over time as increasing.

SC.3-4 Geometry: The student will demonstrate through the mathematical processes an understanding of the connection between the identification of basic attributes and the classification of two-dimensional shapes.

3-4.1 Identify the specific attributes of circles: center, radius, circumference, and diameter.

3-4.2 Classify polygons as either triangles, quadrilaterals, pentagons, hexagons, or octagons according to the number of their sides.

3-4.3 Classify lines and line segments as either parallel, perpendicular, or intersecting.

3-4.4 Classify angles as either right, acute, or obtuse.

3-4.5 Classify triangles by the length of their sides as either scalene, isosceles, or equilateral and by the size of their angles as either acute, obtuse, or right.

3-4.6 Exemplify points, lines, line segments, rays, and angles.

3-4.7 Analyze the results of combining and subdividing circles, triangles, quadrilaterals, pentagons, hexagons, and octagons.

3-4.8 Predict the results of one transformation-either slide, flip, or turn-of a geometric shape.

3-5.1 Use the fewest possible number of coins when making change.

3-5.2 Use appropriate tools to measure objects to the nearest unit: measuring length in meters and half inches; measuring liquid volume in fluid ounces, pints, and liters; and measuring mass in grams.

3-5.3 Recognize the relationship between meters and yards, kilometers and miles, liters and quarts, and kilograms and pounds.

3-5.4 Use common referents to make comparisons and estimates associated with length, liquid volume, and mass and weight: meters compared to yards, kilometers to miles, liters to quarts, and kilograms to pounds.

3-5.5 Generate strategies to determine the perimeters of polygons.

3-5.6 Use analog and digital clocks to tell time to the nearest minute.

3-5.7 Recall equivalencies associated with time and length: 60 seconds = 1 minute and 36 inches = 1 yard.

SC.3-6 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of organizing, interpreting, analyzing and making predictions about data, the benefits of multiple representations of a data set, and the basic concepts of probability.

3-6.1 Apply a procedure to find the range of a data set.

3-6.2 Organize data in tables, bar graphs, and dot plots.

3-6.3 Interpret data in tables, bar graphs, pictographs, and dot plots.

3-6.4 Analyze dot plots and bar graphs to make predictions about populations.

3-6.5 Compare the benefits of using tables, bar graphs, and dot plots as representations of a given data set.

3-6.6 Predict on the basis of data whether events are likely, unlikely, certain, or impossible to occur.

3-6.7 Understand when the probability of an event is 0 or 1.

SC.4-1 Mathematical Processes: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

4-1.1 Analyze information to solve increasingly more sophisticated problems.

4-1.2 Construct arguments that lead to conclusions about general mathematical properties and relationships.

4-1.3 Explain and justify answers to problems on the basis of mathematical properties, structures, and relationships on mathematical properties, structures, and relationships.

4-1.4 Generate descriptions and mathematical statements about relationships between and among classes of objects.

4-1.5 Use correct, complete, and clearly written and oral mathematical language to pose questions, communicate ideas, and extend problem situations.

4-1.6 Generalize connections between new mathematical ideas and related concepts and subjects that have been previously considered.

4-1.7 Use flexibility in mathematical representations.

4-1.8 Recognize the limitations of various forms of mathematical representations.

SC.4-2 Number and Operations: The student will demonstrate through the mathematical processes an understanding of decimal notation as an extension of the place-value system; the relationship between fractions and decimals; the multiplication of whole numbers; and accurate, efficient, and generalizable methods of dividing whole numbers, adding decimals, and subtracting decimals.

4-2.1 Recognize the period in the place-value structure of whole numbers: units, thousands, millions, and billions.

4-2.2 Apply divisibility rules for 2, 5, and 10.

4-2.3 Apply an algorithm to multiply whole numbers fluently.

4-2.4 Explain the effect on the product when one of the factors is changed.

4-2.5 Generate strategies to divide whole numbers by single-digit divisors.

4-2.6 Analyze the magnitude of digits through hundredths on the basis of their place value.

4-2.7 Compare decimals through hundredths by using the terms is less than, is greater than, and is equal to and the symbols <, >, and =.

4-2.8 Apply strategies and procedures to find equivalent forms of fractions.

4-2.9 Compare the relative size of fractions to the benchmarks 0, 1/2, and 1.

4-2.10 Identify common the fraction/decimal equivalents 1/2 =.5, 1/4 =.25, 3/4 =.75, 1/3 is approximately .33, 2/3 is approximately .67, multiples of 1/10, and multiples of 1/100.

4-2.11 Represent improper fractions, mixed numbers, and decimals.

4-2.12 Generate strategies to add and subtract decimals through hundredths.

SC.4-3 Algebra: The student will demonstrate through the mathematical processes an understanding of numeric and nonnumeric patterns, the representation of simple mathematical relationships, and the application of procedures to find the value of an unknown.

4-3.1 Analyze numeric, nonnumeric, and repeating patterns involving all operations and decimal patterns through hundredths.

4-3.2 Generalize a rule for numeric, nonnumeric, and repeating patterns involving all operations.

4-3.3 Use a rule to complete a sequence or a table.

4-3.4 Translate among, letters, symbols, and words to represent quantities in simple mathematical expressions or equations.

4-3.5 Apply procedures to find the value of an unknown letter or symbol in a whole-number equation.

4-3.6 Illustrate situations that show change over time as either increasing, decreasing, or varying.

SC.4-4 Geometry: The student will demonstrate through the mathematical processes an understanding of the relationship between two- and three-dimensional shapes, the use of transformations to determine congruency, and the representation of location and movement within the first quadrant of a coordinate system.

4-4.1 Analyze the quadrilaterals squares, rectangles, trapezoids, rhombuses, and parallelograms according to their properties.

4-4.2 Analyze the relationship between three-dimensional geometric shapes in the form of cubes, rectangular prisms, and cylinders and their two-dimensional nets.

4-4.3 Predict the results of multiple transformations of the same type-translation, reflection, or rotation-on a two-dimensional geometric shape.

4-4.4 Represent the two-dimensional shapes trapezoids, rhombuses, and parallelograms and the three-dimensional shapes cubes, rectangular prisms, and cylinders.

4-4.5 Use transformation(s) to prove congruency.

4-4.6 Represent points, lines, line segments, rays, angles, and polygons.

4-4.7 Represent with ordered pairs of whole numbers the location of points in the first quadrant of a coordinate grid.

4-4.8 Illustrate possible paths from one point to another along vertical and horizontal grid lines in the first quadrant of the coordinate plane.

SC.4-5 Measurement: The student will demonstrate through the mathematical processes an understanding of elapsed time; conversions within the U.S. Customary System; and accurate, efficient, and generalizable methods of determining area.

4-5.1 Use appropriate tools to measure objects to the nearest unit: measuring length in quarter inches, centimeters, and millimeters; measuring liquid volume in cups, quarts, and liters; and measuring weight and mass in pounds, milligrams, and kilograms.

4-5.2 Compare angle measures with referent angles of 45 degrees, 90 degrees, and 180 degrees to estimate angle measures.

4-5.3 Use equivalencies to convert units of measure within the U.S. Customary System: converting length in inches, feet, yards, and miles; converting weight in ounces, pounds, and tons; converting liquid volume in cups, pints, quarts, and gallons; and converting time in years, months, weeks, days, hours, minutes, and seconds.

4-5.4 Analyze the perimeter of a polygon.

4-5.5 Generate strategies to determine the area of rectangles and triangles.

4-5.6 Apply strategies and procedures to determine the amount of elapsed time in hours and minutes within a 12-hour period, either a.m. or p.m.

4-5.7 Use Celsius and Fahrenheit thermometers to determine temperature changes during time intervals.

4-5.8 Recall equivalencies associated with liquid volume, time, weight, and length: 8 liquid ounces = 1 cup, 2 cups = 1 pint, 2 pints = 1 quart, 4 quarts = 1 gallon; 365 days = 1 year, 52 weeks = 1 year; 16 ounces = 1 pound, 2,000 pounds = 1 ton; and 5,280 feet = 1 mile.

4-5.9 Exemplify situations in which highly accurate measurements are required.

SC.4-6 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of the impact of data-collection methods, the appropriate graph for categorical or numerical data, and the analysis of possible outcomes for a simple event.

4-6.1 Compare how data-collection methods impact survey results.

4-6.2 Interpret data in tables, line graphs, bar graphs, and double bar graphs whose scale increments are greater than or equal to 1.

4-6.3 Organize data in tables, line graphs, and bar graphs whose scale increments are greater than or equal to 1.

4-6.4 Distinguish between categorical and numerical data.

4-6.5 Match categorical and numerical data to appropriate graphs.

4-6.6 Predict on the basis of data whether events are likely, unlikely, certain, impossible, or equally likely to occur.

4-6.7 Analyze possible outcomes for a simple event.

SC.5-1 Mathematical Processes: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

5-1.1 Analyze information to solve increasingly more sophisticated problems.

5-1.2 Construct arguments that lead to conclusions about general mathematical properties and relationships.

5-1.3 Explain and justify answers based on mathematical properties, structures, and relationships.

5-1.4 Generate descriptions and mathematical statements about relationships between and among classes of objects.

5-1.5 Use correct, clear, and complete oral and written mathematical language to pose questions, communicate ideas, and extend problem situations.

5-1.6 Generalize connections between new mathematical ideas and related concepts and subjects that have been previously considered.

5-1.7 Use flexibility in mathematical representations.

5-1.8 Recognize the limitations of various forms of mathematical representations.

SC.5-2 Number and Operations: The student will demonstrate through the mathematical processes an understanding of the place value system; the division of whole numbers; the addition and subtraction of decimals; the relationships among whole numbers, fractions, and decimals; and accurate, efficient, and generalizable methods of adding and subtracting fractions.

5-2.1 Analyze the magnitude of a digit on the basis of its place value, using whole numbers and decimal numbers through thousandths.

5-2.2 Apply an algorithm to divide whole numbers fluently.

5-2.3 Understand the relationship among the divisor, dividend, and quotient.

5-2.4 Compare whole numbers, decimals, and fractions by using the symbols <, >, and =.

5-2.5 Apply an algorithm to add and subtract decimals through thousandths.

5-2.6 Classify numbers as prime, composite, or neither.

5-2.7 Generate strategies to find the greatest common factor and the least common multiple of two whole numbers.

5-2.8 Generate strategies to add and subtract fractions with like and unlike denominators.

5-2.9 Apply divisibility rules for 3, 6, and 9.

SC.5-3 Algebra: The student will demonstrate through the mathematical processes an understanding of the use of patterns, relations, functions, models, structures, and algebraic symbols to represent quantitative relationships and will analyze change in various contexts.

5-3.1 Represent numeric, algebraic, and geometric patterns in words, symbols, algebraic expressions, and algebraic equations.

5-3.2 Analyze patterns and functions with words, tables, and graphs.

5-3.3 Match tables, graphs, expressions, equations, and verbal descriptions of the same problem situation.

5-3.4 Identify applications of commutative, associative, and distributive properties with whole numbers.

5-3.5 Analyze situations that show change over time.

SC.5-4 Geometry: The student will demonstrate through the mathematical processes an understanding of congruency, spatial relationships, and relationships among the properties of quadrilaterals.

5-4.1 Apply the relationships of quadrilaterals to make logical arguments about their properties.

5-4.2 Compare the angles, side lengths, and perimeters of congruent shapes.

5-4.3 Classify shapes as congruent.

5-4.4 Translate between two-dimensional representations and three-dimensional objects.

5-4.5 Predict the results of multiple transformations on a geometric shape when combinations of translation, reflection, and rotation are used.

5-4.6 Analyze shapes to determine line symmetry and/or rotational symmetry.

SC.5-5 Measurement: The student will demonstrate through the mathematical processes an understanding of the units and systems of measurement and the application of tools and formulas to determine measurements.

5-5.1 Use appropriate tools and units to measure objects to the precision of one-eighth inch.

5-5.2 Use a protractor to measure angles from 0 to 180 degrees.

5-5.3 Use equivalencies to convert units of measure within the metric system: converting length in millimeters, centimeters, meters, and kilometers; converting liquid volume in milliliters, centiliters, liters, and kiloliters; and converting mass in milligrams, centigrams, grams, and kilograms.

5-5.4 Apply formulas to determine the perimeters and areas of triangles, rectangles, and parallelograms.

5-5.5 Apply strategies and formulas to determine the volume of rectangular prisms.

5-5.6 Apply procedures to determine the amount of elapsed time in hours, minutes, and seconds within a 24-hour period.

5-5.7 Understand the relationship between the Celsius and Fahrenheit temperature scales.

5-5.8 Recall equivalencies associated with length, liquid volume, and mass: 10 millimeters = 1 centimeter, 100 centimeters = 1 meter, 1000 meters = 1 kilometer; 10 milliliters = 1 centiliter, 100 centiliters = 1 liter, 1000 liters = 1 kiloliter; and 10 milligrams = 1 centigram, 100 centigrams = 1 gram, 1000 grams = 1 kilogram.

SC.5-6 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of investigation design, the effect of data-collection methods on a data set, the interpretation and application of the measures of central tendency, and the application of basic concepts of probability.

5-6.1 Design a mathematical investigation to address a question.

5-6.2 Analyze how data-collection methods affect the nature of the data set.

5-6.3 Apply procedures to calculate the measures of central tendency (mean, median, and mode).

5-6.4 Interpret the meaning and application of the measures of central tendency.

5-6.5 Represent the probability of a single-stage event in words and fractions.

5-6.6 Conclude why the sum of the probabilities of the outcomes of an experiment must equal 1.

SC.6-1 Mathematical Processes: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

6-1.1 Generate and solve complex abstract problems that involve modeling physical, social, and/or mathematical phenomena.

6-1.2 Evaluate conjectures and pose follow-up questions to prove or disprove conjectures.

6-1.3 Use inductive and deductive reasoning to formulate mathematical arguments.

6-1.4 Understand equivalent symbolic expressions as distinct symbolic forms that represent the same relationship.

6-1.5 Generalize mathematical statements based on inductive and deductive reasoning.

6-1.6 Use correct and clearly written or spoken words, variables, and notations to communicate about significant mathematical tasks.

6-1.7 Generalize connections among a variety of representational forms and real-world situations.

6-1.8 Use standard and nonstandard representations to convey and support mathematical relationships.

SC.6-2 Number and Operations: The student will demonstrate through the mathematical processes an understanding of the concepts of whole-number percentages, integers, and ratio and rate; the addition and subtraction of fractions; accurate, efficient, and generalizable methods of multiplying and dividing fractions and decimals; and the use of exponential notation to represent whole numbers.

6-2.1 Understand whole-number percentages through 100.

6-2.2 Understand integers.

6-2.3 Compare rational numbers and whole-number percentages through 100 by using the symbols less than or equal to, greater than or equal to, <, >, and =.

6-2.4 Apply an algorithm to add and subtract fractions.

6-2.5 Generate strategies to multiply and divide fractions and decimals.

6-2.6 Understand the relationship between ratio/rate and multiplication/division.

6-2.7 Apply strategies and procedures to determine values of powers of 10, up to 10to the 6th.

6-2.8 Represent the prime factorization of numbers by using exponents.

6-2.9 Represent whole numbers in exponential form.

SC.6-3 Algebra: The student will demonstrate through the mathematical processes an understanding of writing, interpreting, and using mathematical expressions, equations, and inequalities.

6-3.1 Analyze numeric and algebraic patterns and pattern relationships.

6-3.2 Apply order of operations to simplify whole-number expressions.

6-3.3 Represent algebraic relationships with variables in expressions, simple equations, and simple inequalities.

6-3.4 Use the commutative, associative, and distributive properties to show that two expressions are equivalent.

6-3.5 Use inverse operations to solve one-step equations that have whole-number solutions and variables with whole-number coefficients.

SC.6-4 Geometry: The student will demonstrate through the mathematical processes an understanding of shape, location, and movement within a coordinate system; similarity, complementary, and supplementary angles; and the relationship between line and rotational symmetry.

6-4.1 Represent with ordered pairs of integers the location of points in a coordinate grid.

6-4.2 Apply strategies and procedures to find the coordinates of the missing vertex of a square, rectangle, or right triangle when given the coordinates of the polygon's other vertices.

6-4.3 Generalize the relationship between line symmetry and rotational symmetry for two-dimensional shapes.

6-4.4 Construct two-dimensional shapes with line or rotational symmetry.

6-4.5 Identify the transformation(s) used to move a polygon from one location to another in the coordinate plane.

6-4.6 Explain how transformations affect the location of the original polygon in the coordinate plane.

6-4.7 Compare the angles, side lengths, and perimeters of similar shapes.

6-4.8 Classify shapes as similar.

6-4.9 Classify pairs of angles as either complementary or supplementary.

SC.6-5 Measurement: The student will demonstrate through the mathematical processes an understanding of surface area; the perimeter and area of irregular shapes; the relationships among the circumference, diameter, and radius of a circle; the use of proportions to determine unit rates; and the use of scale to determine distance.

6-5.1 Explain the relationships among the circumference, diameter, and radius of a circle.

6-5.2 Apply strategies and formulas with an approximation of pi (3.14, or 22/7) to find the circumference and area of a circle.

6-5.3 Generate strategies to determine the surface area of a rectangular prism and a cylinder.

6-5.4 Apply strategies and procedures to estimate the perimeters and areas of irregular shapes.

6-5.5 Apply strategies and procedures of combining and subdividing to find the perimeters and areas of irregular shapes.

6-5.6 Use proportions to determine unit rates.

6-5.7 Use a scale to determine distance.

SC.6-6 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of the relationships within one population or sample.

6-6.1 Predict the characteristics of one population based on the analysis of sample data.

6-6.2 Organize data in frequency tables, histograms, or stem-and-leaf plots as appropriate.

6-6.3 Analyze which measure of central tendency (mean, median, or mode) is the most appropriate for a given purpose.

6-6.4 Use theoretical probability to determine the sample space and probability for one- and two-stage events such as tree diagrams, models, lists, charts, and pictures.

6-6.5 Apply procedures to calculate the probability of complementary events.

SC.7-1 Mathematical Processes: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

7-1.1 Generate and solve complex abstract problems that involve modeling physical, social, or mathematical phenomena.

7-1.2 Evaluate conjectures and pose follow-up questions to prove or disprove conjectures.

7-1.3 Use inductive and deductive reasoning to formulate mathematical arguments.

7-1.4 Understand equivalent symbolic expressions as distinct symbolic forms that represent the same relationship.

7-1.5 Generalize mathematical statements based on inductive and deductive reasoning.

7-1.6 Use correct and clearly written or spoken words, variables, and notation to communicate about significant mathematical tasks.

7-1.7 Generalize connections among a variety of representational forms and real-world situations.

7-1.8 Use standard and nonstandard representations to convey and support mathematical relationships.

SC.7-2 Number and Operations: The student will demonstrate through the mathematical processes an understanding of the representation of rational numbers, percentages, and square roots of perfect squares; the application of ratios, rates, and proportions to solve problems; accurate, efficient, and generalizable methods for operations with integers; the multiplication and division of fractions and decimals; and the inverse relationship between squaring and finding the square roots of perfect squares.

7-2.1 Understand fractional percentages and percentages greater than one hundred.

7-2.2 Represent the location of rational numbers and square roots of perfect squares on a number line.

7-2.3 Compare rational numbers, percentages, and square roots of perfect squares by using the symbols less than or equal to, greater than or equal to, <, >, and =.

7-2.4 Understand the meaning of absolute value.

7-2.5 Apply ratios, rates, and proportions to discounts, taxes, tips, interest, unit costs, and similar shapes.

7-2.6 Translate between standard form and exponential form.

7-2.7 Translate between standard form and scientific notation.

7-2.8 Generate strategies to add, subtract, multiply, and divide integers.

7-2.9 Apply an algorithm to multiply and divide fractions and decimals.

7-2.10 Understand the inverse relationship between squaring and finding the square roots of perfect squares.

SC.7-3 Algebra: The student will demonstrate through the mathematical processes an understanding of proportional relationships.

7-3.1 Analyze geometric patterns and pattern relationships.

7-3.2 Analyze tables and graphs to describe the rate of change between and among quantities.

7-3.3 Understand slope as a constant rate of change.

7-3.4 Use inverse operations to solve two-step equations and two-step inequalities.

7-3.5 Represent on a number line the solution of a two-step inequality.

7-3.6 Represent proportional relationships with graphs, tables, and equations.

7-3.7 Classify relationships as either directly proportional, inversely proportional, or nonproportional.

SC.7-4 Geometry: The student will demonstrate through the mathematical processes an understanding of proportional reasoning, tessellations, the use of geometric properties to make deductive arguments. the results of the intersection of geometric shapes in a plane, and the relationships among angles formed when a transversal intersects two parallel lines.

7-4.1 Analyze geometric properties and the relationships among the properties of triangles, congruence, similarity, and transformations to make deductive arguments.

7-4.2 Explain the results of the intersection of two or more geometric shapes in a plane.

7-4.3 Illustrate the cross section of a solid.

7-4.4 Translate between two- and three-dimensional representations of compound figures.

7-4.5 Analyze the congruent and supplementary relationships-specifically, alternate interior, alternate exterior, corresponding, and adjacent-of the angles formed by parallel lines and a transversal.

7-4.6 Compare the areas of similar shapes and the areas of congruent shapes.

7-4.7 Explain the proportional relationship among attributes of similar shapes.

7-4.8 Apply proportional reasoning to find missing attributes of similar shapes.

7-4.9 Create tessellations with transformations.

7-4.10 Explain the relationship of the angle measurements among shapes that tessellate.

SC.7-5 Measurement: The student will demonstrate through the mathematical processes an understanding of how to use ratio and proportion to solve problems involving scale factors and rates and how to use one-step unit analysis to convert between and within the U.S. Customary System and the metric system.

7-5.1 Use ratio and proportion to solve problems involving scale factors and rates.

7-5.2 Apply strategies and formulas to determine the surface area and volume of the three-dimensional shapes prism, pyramid, and cylinder.

7-5.3 Generate strategies to determine the perimeters and areas of trapezoids.

7-5.4 Recall equivalencies associated with length, mass and weight, and liquid volume: 1 square yard = 9 square feet, 1 cubic meter = 1 million cubic centimeters, 1 kilometer = 5/8 mile, 1 inch = 2.54 centimeters; 2.2 kilograms = 1 pound; and 1.06 quarts = 1 liter.

7-5.5 Use one-step unit analysis to convert between and within the U.S. Customary System and the metric system.

SC.7-6 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of the relationships between two populations or samples.

7-6.1 Predict the characteristics of two populations based on the analysis of sample data.

7-6.2 Organize data in box plots or circle graphs as appropriate.

7-6.3 Apply procedures to calculate the interquartile range.

7-6.4 Interpret the interquartile range for data.

7-6.5 Apply procedures to calculate the probability of mutually exclusive simple or compound events.

7-6.6 Interpret the probability of mutually exclusive simple or compound events.

7-6.7 Differentiate between experimental and theoretical probability of the same event.

7-6.8 Use the fundamental counting principle to determine the number of possible outcomes for a multistage event.

SC.8-1 Mathematical Processes: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

8-1.1 Generate and solve complex abstract problems that involve modeling physical, social, or mathematical phenomena.

8-1.2 Evaluate conjectures and pose follow-up questions to prove or disprove conjectures.

8-1.3 Use inductive and deductive reasoning to formulate mathematical arguments.

8-1.4 Understand equivalent symbolic expressions as distinct symbolic forms that represent the same relationship.

8-1.5 Generalize mathematical statements based on inductive and deductive reasoning.

8-1.6 Use correct and clearly written or spoken words, variables, and notations to communicate about significant mathematical tasks.

8-1.7 Generalize connections among a variety of representational forms and real-world situations.

8-1.8 Use standard and nonstandard representations to convey and support mathematical relationships.

SC.8-2 Number and Operations: The student will demonstrate through the mathematical processes an understanding of operations with integers, the effects of multiplying and dividing with rational numbers, the comparative magnitude of rational and irrational numbers, the approximation of cube and square roots, and the application of proportional reasoning.

8-2.1 Apply an algorithm to add, subtract, multiply, and divide integers.

8-2.2 Understand the effect of multiplying and dividing a rational number by another rational number.

8-2.3 Represent the approximate location of irrational numbers on a number line.

8-2.4 Compare rational and irrational numbers by using the symbols less than or equal to, greater than or equal to, <, >, and =.

8-2.5 Apply the concept of absolute value.

8-2.6 Apply strategies and procedures to approximate between two whole numbers the square roots or cube roots of numbers less than 1,000.

8-2.7 Apply ratios, rates, and proportions.

SC.8-3 Algebra: The student will demonstrate through the mathematical processes an understanding of equations, inequalities, and linear functions.

8-3.1 Translate among verbal, graphic, tabular, and algebraic representations of linear functions.

8-3.2 Represent algebraic relationships with equations and inequalities.

8-3.3 Use commutative, associative, and distributive properties to examine the equivalence of a variety of algebraic expressions.

8-3.4 Apply procedures to solve multi-step equations.

8-3.5 Classify relationships between two variables in graphs, tables, and/or equations as either linear or nonlinear.

8-3.6 Identify the coordinates of the x- and y-intercepts of a linear equation from a graph, equation, and/or table.

8-3.7 Identify the slope of a linear equation from a graph, equation, and/or table.

SC.8-4 Geometry: The student will demonstrate through the mathematical processes an understanding of the Pythagorean theorem; the use of ordered pairs, equations, intercepts, and intersections to locate points and lines in a coordinate plane; and the effect of a dilation in a coordinate plane.

8-4.1 Apply the Pythagorean theorem.

8-4.2 Use ordered pairs, equations, intercepts, and intersections to locate points and lines in a coordinate plane.

8-4.3 Apply a dilation to a square, rectangle, or right triangle in a coordinate plane.

8-4.4 Analyze the effect of a dilation on a square, rectangle, or right triangle in a coordinate plane.

SC.8-5 Measurement: The student will demonstrate through the mathematical processes an understanding of the proportionality of similar figures; the necessary levels of accuracy and precision in measurement; the use of formulas to determine circumference, perimeter, area, and volume; and the use of conversions within and between the U.S. Customary System and the metric system.

8-5.1 Use proportional reasoning and the properties of similar shapes to determine the length of a missing side.

8-5.2 Explain the effect on the area of two-dimensional shapes and on the volume of three-dimensional shapes when one or more of the dimensions are changed.

8-5.3 Apply strategies and formulas to determine the volume of the three-dimensional shapes cone and sphere.

8-5.4 Apply formulas to determine the exact (pi) circumference and area of a circle.

8-5.5 Apply formulas to determine the perimeters and areas of trapezoids.

8-5.6 Analyze a variety of measurement situations to determine the necessary level of accuracy and precision.

8-5.7 Use multi-step unit analysis to convert between and within U.S. Customary System and the metric system.

SC.8-6 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of the relationships between two variables within one population or sample.

8-6.1 Generalize the relationship between two sets of data by using scatterplots and lines of best fit.

8-6.2 Organize data in matrices or scatterplots as appropriate.

8-6.3 Use theoretical and experimental probability to make inferences and convincing arguments about an event or events.

8-6.4 Apply procedures to calculate the probability of two dependent events.

8-6.5 Interpret the probability for two dependent events.

8-6.6 Apply procedures to compute the odds of a given event.

8-6.7 Analyze probability using area models.

8-6.8 Interpret graphic and tabular data representations by using range and the measures of central tendency (mean, median, and mode).

SC.EA-1 Elementary Algebra: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

EA-1.1 Communicate a knowledge of algebraic relationships by using mathematical terminology appropriately.

EA-1.2 Connect algebra with other branches of mathematics.

EA-1.3 Apply algebraic methods to solve problems in real-world contexts.

EA-1.4 Judge the reasonableness of mathematical solutions.

EA-1.5 Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

EA-1.6 Understand how algebraic relationships can be represented in concrete models, pictorial models, and diagrams.

EA-1.7 Understand how to represent algebraic relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

SC.EA-2 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of the real number system and operations involving exponents, matrices, and algebraic expressions.

EA-2.1 Exemplify elements of the real number system (including integers, rational numbers, and irrational numbers).

EA-2.2 Apply the laws of exponents and roots to solve problems.

EA-2.3 Carry out a procedure to perform operations (including multiplication and division) with numbers written in scientific notation.

EA-2.4 Use dimensional analysis to convert units of measure within a system.

EA-2.5 Carry out a procedure using the properties of real numbers (including commutative, associative, and distributive) to simplify expressions.

EA-2.6 Carry out a procedure to evaluate an expression by substituting a value for the variable.

EA-2.7 Carry out a procedure (including addition, subtraction, multiplication, and division by a monomial) to simplify polynomial expressions.

EA-2.8 Carry out a procedure to factor binomials, trinomials, and polynomials by using various techniques (including the greatest common factor, the difference between two squares, and quadratic trinomials).

EA-2.9 Carry out a procedure to perform operations with matrices (including addition, subtraction, and scalar multiplication).

EA-2.10 Represent applied problems by using matrices.

SC.EA-3 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of relationships and functions.

EA-3.1 Classify a relationship as being either a function or not a function when given data as a table, set of ordered pairs, or graph.

EA-3.2 Use function notation to represent functional relationships.

EA-3.3 Carry out a procedure to evaluate a function for a given element in the domain.

EA-3.4 Analyze the graph of a continuous function to determine the domain and range of the function.

EA-3.5 Carry out a procedure to graph parent functions (including y = x, y = x^2, y = square root of x, y = |x|, and y = 1/x).

EA-3.6 Classify a variation as either direct or inverse.

EA-3.7 Carry out a procedure to solve literal equations for a specified variable.

EA-3.8 Apply proportional reasoning to solve problems.

SC.EA-4 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of the procedures for writing and solving linear equations and inequalities.

EA-4.1 Carry out a procedure to write an equation of a line with a given slope and a y-intercept.

EA-4.2 Carry out a procedure to write an equation of a line with a given slope passing through a given point.

EA-4.3 Carry out a procedure to write an equation of a line passing through two given points.

EA-4.4 Use a procedure to write an equation of a trend line from a given scatterplot.

EA-4.5 Analyze a scatterplot to make predictions.

EA-4.6 Represent linear equations in multiple forms (including point-slope, slope-intercept, and standard).

EA-4.7 Carry out procedures to solve linear equations for one variable algebraically.

EA-4.8 Carry out procedures to solve linear inequalities for one variable algebraically and then to graph the solution.

EA-4.9 Carry out a procedure to solve systems of two linear equations graphically.

EA-4.10 Carry out a procedure to solve systems of two linear equations algebraically.

SC.EA-5 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of the graphs and characteristics of linear equations and inequalities.

EA-5.1 Carry out a procedure to graph a line when given the equation of the line.

EA-5.2 Analyze the effects of changes in the slope, m, and the y-intercept, b, on the graph of y = mx + b.

EA-5.3 Carry out a procedure to graph the line with a given slope and a y-intercept.

EA-5.4 Carry out a procedure to graph the line with a given slope passing through a given point.

EA-5.5 Carry out a procedure to determine the x-intercept and y-intercept of lines from data given tabularly, graphically, symbolically, and verbally.

EA-5.6 Carry out a procedure to determine the slope of a line from data given tabularly, graphically, symbolically, and verbally.

EA-5.7 Apply the concept of slope as a rate of change to solve problems.

EA-5.8 Analyze the equations of two lines to determine whether the lines are perpendicular or parallel.

EA-5.9 Analyze given information to write a linear function that models a given problem situation.

EA-5.10 Analyze given information to determine the domain and range of a linear function in a problem situation.

EA-5.11 Analyze given information to write a system of linear equations that models a given problem situation.

EA-5.12 Analyze given information to write a linear inequality in one variable that models a given problem situation.

SC.EA-6 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of quadratic relationships and functions.

EA-6.1 Analyze the effects of changing the leading coefficient a on the graph of y = ax^2.

EA-6.2 Analyze the effects of changing the constant c on the graph of y = x^2 + c.

EA-6.3 Analyze the graph of a quadratic function to determine its equation.

EA-6.4 Carry out a procedure to solve quadratic equations by factoring.

EA-6.5 Carry out a graphic procedure to approximate the solutions of quadratic equations.

EA-6.6 Analyze given information to determine the domain of a quadratic function in a problem situation.

SC.IA-1 Intermediate Algebra: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

IA-1.1 Communicate a knowledge of algebraic relationships by using mathematical terminology appropriately.

IA-1.2 Connect algebra with other branches of mathematics.

IA-1.3 Apply algebraic methods to solve problems in real-world contexts.

IA-1.4 Judge the reasonableness of mathematical solutions.

IA-1.5 Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

IA-1.6 Understand how algebraic relationships can be represented in concrete models, pictorial models, and diagrams.

IA-1.7 Understand how to represent algebraic relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

SC.IA-2 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of functions, systems of equations, and systems of linear inequalities.

IA-2.1 Carry out a procedure to solve a system of linear inequalities algebraically.

IA-2.2 Carry out a procedure to solve a system of linear inequalities graphically.

IA-2.3 Analyze a problem situation to determine a system of linear inequalities that models the problem situation.

IA-2.4 Use linear programming to solve contextual problems involving a system of linear inequalities.

IA-2.5 Carry out procedures to perform operations on polynomial functions (including f(x) + g(x), f(x) - g(x), f(x) x g(x), and f(x)/g(x)).

IA-2.6 Apply a procedure to write the equation of a composition of given functions.

IA-2.7 Carry out a procedure to graph translations of parent functions (including y = x, y = x^2, y = square root of x, y = |x|, and y = 1/x).

IA-2.8 Carry out a procedure to graph transformations of parent functions (including y = x, y = x^2, y = square root of x, y = |x|.

IA-2.9 Carry out a procedure to graph discontinuous functions (including piecewise and step functions).

IA-2.10 Carry out a procedure to determine the domain and range of discontinuous functions (including piecewise and step functions).

IA-2.11 Carry out a procedure to solve a system of equations (including two linear functions and one linear function with one quadratic function).

SC.IA-3 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of quadratic equations and the complex number system.

IA-3.1 Carry out a procedure to simplify expressions involving powers of i.

IA-3.2 Carry out a procedure to perform operations with complex numbers (including addition, subtraction, multiplication, and division).

IA-3.3 Carry out a procedure to solve quadratic equations algebraically (including factoring, completing the square, and applying the quadratic formula).

IA-3.4 Use the discriminant to determine the number and type of solutions of a quadratic equation.

IA-3.5 Analyze given information (including quadratic models) to solve contextual problems.

IA-3.6 Carry out a procedure to write an equation of a quadratic function when given its roots.

SC.IA-4 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of algebraic expressions and nonlinear functions.

IA-4.1 Carry out a procedure to perform operations (including multiplication, exponentiation, and division) with polynomial expressions.

IA-4.2 Carry out a procedure to determine specified points (including zeros, maximums, and minimums) of polynomial functions.

IA-4.3 Carry out a procedure to solve polynomial equations (including factoring by grouping, factoring the difference between two squares, factoring the sum of two cubes, and factoring the difference between two cubes).

IA-4.4 Analyze given information (including polynomial models) to solve contextual problems.

IA-4.5 Carry out a procedure to simplify algebraic expressions involving rational exponents.

IA-4.6 Carry out a procedure to simplify algebraic expressions involving logarithms.

IA-4.7 Carry out a procedure to perform operations with expressions involving rational exponents (including addition, subtraction, multiplication, division, and exponentiation).

IA-4.8 Carry out a procedure to perform operations with rational expressions (including addition, subtraction, multiplication, and division).

IA-4.9 Carry out a procedure to solve radical equations algebraically.

IA-4.10 Carry out a procedure to solve logarithmic equations algebraically.

IA-4.11 Carry out a procedure to solve logarithmic equations graphically.

IA-4.12 Carry out a procedure to solve rational equations algebraically.

IA-4.13 Carry out a procedure to graph logarithmic functions.

IA-4.14 Carry out a procedure to graph exponential functions.

SC.IA-5 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of conic sections.

IA-5.1 Carry out a procedure to graph the circle whose equation is the form x^2 + y^2 = r^2.

IA-5.2 Carry out a procedure to write an equation of a circle centered at the origin when given its radius.

IA-5.3 Carry out a procedure to graph the ellipse whose equation is the form x^2/a^2 + y^2/b^2 = 1.

IA-5.4 Carry out a procedure to write an equation of an ellipse centered at the origin when given information from among length of major axis, length of minor axis, and vertices.

IA-5.5 Carry out a procedure to graph the hyperbola whose equation is the form x^2/a^2 + y^2/b^2 = 1.

IA-5.6 Carry out a procedure to write an equation of a hyperbola centered at the origin with specified vertices.

IA-5.7 Match the equation of a conic section with its graph.

SC.IA-6 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of sequences and series.

IA-6.1 Categorize a sequence as arithmetic, geometric, or neither.

IA-6.2 Carry out a procedure to write a specified term of an arithmetic or geometric sequence when given the nth term of the sequence.

IA-6.3 Carry out a procedure to write a formula for the nth term of an arithmetic or geometric sequence when given at least four consecutive terms of the sequence.

IA-6.4 Carry out a procedure to write a formula for the nth term of an arithmetic or geometric sequence when given at least four terms of the sequence.

IA-6.5 Represent an arithmetic or geometric series by using sigma notation.

IA-6.6 Carry out a procedure to calculate the sum of an arithmetic or geometric series written in sigma notation.

IA-6.7 Carry out a procedure to determine consecutive terms of a sequence that is defined recursively.

IA-6.8 Carry out a procedure to define a sequence recursively when given four or more consecutive terms of the sequence.

IA-6.9 Translate between the explicit form and the recursive form of sequences.

SC.G-1 Geometry: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

G-1.1 Demonstrate an understanding of the axiomatic structure of geometry by using undefined terms, definitions, postulates, theorems, and corollaries.

G-1.2 Communicate knowledge of geometric relationships by using mathematical terminology appropriately.

G-1.3 Apply basic rules of logic to determine the validity of the converse, inverse, and contrapositive of a conditional statement.

G-1.4 Formulate and test conjectures by using a variety of tools such as concrete models, graphing calculators, spreadsheets, and dynamic geometry software.

G-1.5 Use inductive reasoning to formulate conjectures.

G-1.6 Use deductive reasoning to validate conjectures with formal and informal proofs, and give counterexamples to disprove a statement.

G-1.7 Understand the historical development of geometry.

G-1.8 Connect geometry with other branches of mathematics.

G-1.9 Demonstrate an understanding of how geometry applies to in real-world contexts (including architecture, construction, farming, and astronomy).

G-1.10 Demonstrate an understanding of geometric relationships (including constructions through investigations by using a variety of tools such as straightedge, compass, Patty Paper, dynamic geometry software, and handheld computing devices).

SC.G-2 Geometry: The student will demonstrate through the mathematical processes an understanding of the properties of basic geometric figures and the relationships between and among them.

G-2.1 Infer missing elements of visual or numerical geometric patterns (including triangular and rectangular numbers and the number of diagonals in polygons).

G-2.2 Apply properties of parallel lines, intersecting lines, and parallel lines cut by a transversal to solve problems.

G-2.3 Use the congruence of line segments and angles to solve problems.

G-2.4 Use direct measurement to determine the length of a segment, degree of an angle, and distance from a point to a line.

G-2.5 Carry out a procedure to create geometric constructions (including the midpoint of a line segment, the angle bisector, the perpendicular bisector of a line segment, the line through a given point that is parallel to a given line, and the line through a given point that is perpendicular to a given line).

G-2.6 Use scale factors to solve problems involving scale drawings and models.

G-2.7 Use geometric probability to solve problems.

SC.G-3 Geometry: The student will demonstrate through the mathematical processes an understanding of the properties and special segments of triangles and the relationships between and among triangles.

G-3.1 Carry out a procedure to compute the perimeter of a triangle.

G-3.2 Carry out a procedure to compute the area of a triangle.

G-3.3 Analyze how changes in dimensions affect the perimeter or area of triangles.

G-3.4 Apply properties of isosceles and equilateral triangles to solve problems.

G-3.5 Use interior angles, exterior angles, medians, angle bisectors, altitudes, and perpendicular bisectors to solve problems.

G-3.6 Apply the triangle sum theorem to solve problems.

G-3.7 Apply the triangle inequality theorem to solve problems.

G-3.8 Apply congruence and similarity relationships among triangles to solve problems.

G-3.9 Apply theorems to prove that triangles are either similar or congruent.

G-3.10 Use the Pythagorean theorem and its converse to solve problems.

G-3.11 Use the properties of 45-45-90 and 30-60-90 triangles to solve problems.

G-3.12 Use trigonometric ratios (including sine, cosine, and tangent) to solve problems involving right triangles.

SC.G-4 Geometry: The student will demonstrate through the mathematical processes an understanding of the properties of quadrilaterals and other polygons and the relationships between and among them.

G-4.1 Carry out a procedure to compute the perimeter of quadrilaterals, regular polygons, and composite figures.

G-4.2 Carry out a procedure to find the area of quadrilaterals, regular polygons, and composite figures.

G-4.3 Apply procedures to compute measures of interior and exterior angles of polygons.

G-4.4 Analyze how changes in dimensions affect the perimeter or area of quadrilaterals and regular polygons.

G-4.5 Apply the properties and attributes of quadrilaterals and regular polygons and their component parts to solve problems.

G-4.6 Apply congruence and similarity relationships among shapes (including quadrilaterals and polygons) to solve problems.

SC.G-5 Geometry: The student will demonstrate through the mathematical processes an understanding of the properties of circles, the lines that intersect them, and the use of their special segments.

G-5.1 Carry out a procedure to compute the circumference of circles.

G-5.2 Carry out a procedure to compute the area of circles.

G-5.3 Analyze how a change in the radius affects the circumference or area of a circle.

G-5.4 Carry out a procedure to compute the length of an arc or the area of a sector of a circle.

G-5.5 Apply the properties of the component parts of a circle (including radii, diameters, chords, sectors, arcs, and segments) to solve problems.

G-5.6 Apply the properties of lines that intersect circles (including two secants, two tangents, and a secant and a tangent) to solve problems.

G-5.7 Apply the properties of central angles, inscribed angles, and arcs of circles to solve problems.

SC.G-6 Geometry: The student will demonstrate through the mathematical processes an understanding of transformations, coordinate geometry, and vectors.

G-6.1 Use the distance formula to solve problems.

G-6.2 Use the midpoint formula to solve problems.

G-6.3 Apply transformations-translation, reflection, rotation, and dilation-to figures in the coordinate plane by using sketches and coordinates.

G-6.4 Apply transformations (including translation and dilation) to figures in the coordinate plane by using matrices.

G-6.5 Carry out a procedure to represent the sum of two vectors geometrically by using the parallelogram method.

G-6.6 Carry out a procedure to determine the magnitude and direction of the resultant of two vectors by using a scale drawing and direct measurement.

G-6.7 Carry out a procedure to compute the magnitude of the resultant of two perpendicular vectors by using the Pythagorean theorem.

G-6.8 Carry out a procedure to determine the direction of the resultant of two perpendicular vectors by using a scale drawing and direct measurement.

SC.G-7 Geometry: The student will demonstrate through the mathematical processes an understanding of the surface area and volume of three-dimensional objects.

G-7.1 Carry out a procedure to compute the surface area of three-dimensional objects (including cones, cylinders, pyramids, prisms, spheres, and hemispheres).

G-7.2 Carry out a procedure to compute the volume of three-dimensional objects (including cones, cylinders, pyramids, prisms, spheres, hemispheres, and composite objects).

G-7.3 Analyze how changes in dimensions affect the volume of objects (including cylinders, prisms, and spheres).

G-7.4 Apply congruence and similarity relationships among geometric objects to solve problems.

G-7.5 Apply a procedure to draw a top view, front view, and side view of a three-dimensional object.

G-7.6 Apply a procedure to draw an isometric view of a three-dimensional object.

SC.PC-1 Precalculus: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

PC-1.1 Communicate knowledge of algebraic and trigonometric relationships by using mathematical terminology appropriately.

PC-1.2 Connect algebra and trigonometry with other branches of mathematics.

PC-1.3 Apply algebraic methods to solve problems in real-world contexts.

PC-1.4 Judge the reasonableness of mathematical solutions.

PC-1.5 Demonstrate an understanding of algebraic and trigonometric relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

PC-1.6 Understand how algebraic and trigonometric relationships can be represented in concrete models, pictorial models, and diagrams.

PC-1.7 Understand how to represent algebraic and trigonometric relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

SC.PC-2 Precalculus: The student will demonstrate through the mathematical processes an understanding of the characteristics and behaviors of functions and the effect of operations on functions.

PC-2.1 Carry out a procedure to graph parent functions (including y = x^n, y = log base a(x), y = log base n (x), y = 1/x, y = e^x, y = a^x, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

PC-2.2 Carry out a procedure to graph transformations (including -f(x), a x f(x), f(x) + d, f(x-c), f(-x), f(bx), |f(x)|, and f(|x|)) of parent functions and combinations of transformations.

PC-2.3 Analyze a graph to describe the transformation (including -f(x), a x f(x), f(x) + d, f(x-c), f(-x), f(bx), |f(x)|, and f(|x|)) of parent functions.

PC-2.4 Carry out procedures to algebraically solve equations involving parent functions or transformations of parent functions (including y = x^n, y = log base a(x), y = log base n (x), y = 1/x, y = e^x, y = a^x, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

PC-2.5 Analyze graphs, tables, and equations to determine the domain and range of parent functions or transformations of parent functions (including y = x^n, y = log base a(x), y = log base n (x), y = 1/x, y = e^x, y = a^x, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

PC-2.6 Analyze a function or the symmetry of its graph to determine whether the function is even, odd, or neither.

PC-2.7 Recognize and use connections among significant points of a function (including roots, maximum points, and minimum points), the graph of a function, and the algebraic representation of a function.

PC-2.8 Carry out a procedure to determine whether the inverse of a function exists.

PC-2.9 Carry out a procedure to write a rule for the inverse of a function, if it exists.

SC.PC-3 Precalculus: The student will demonstrate through the mathematical processes an understanding of the behaviors of polynomial and rational functions.

PC-3.1 Carry out a procedure to graph quadratic and higher-order polynomial functions by analyzing intercepts and end behavior.

PC-3.2 Apply the rational root theorem to determine a set of possible rational roots of a polynomial equation.

PC-3.3 Carry out a procedure to calculate the zeros of polynomial functions when given a set of possible zeros.

PC-3.4 Carry out procedures to determine characteristics of rational functions (including domain, range, intercepts, asymptotes, and discontinuities).

PC-3.5 Analyze given information to write a polynomial function that models a given problem situation.

PC-3.6 Carry out a procedure to solve polynomial equations algebraically.

PC-3.7 Carry out a procedure to solve polynomial equations graphically.

PC-3.8 Carry out a procedure to solve rational equations algebraically.

PC-3.9 Carry out a procedure to solve rational equations graphically.

PC-3.10 Carry out a procedure to solve polynomial inequalities algebraically.

PC-3.11 Carry out a procedure to solve polynomial inequalities graphically.

SC.PC-4 Precalculus: The student will demonstrate through the mathematical processes an understanding of the behaviors of exponential and logarithmic functions.

PC-4.1 Carry out a procedure to graph exponential functions by analyzing intercepts and end behavior.

PC-4.2 Carry out a procedure to graph logarithmic functions by analyzing intercepts and end behavior.

PC-4.3 Carry out procedures to determine characteristics of exponential functions (including domain, range, intercepts, and asymptotes).

PC-4.4 Carry out procedures to determine characteristics of logarithmic functions (including domain, range, intercepts, and asymptotes).

PC-4.5 Apply the laws of exponents to solve problems involving rational exponents.

PC-4.6 Analyze given information to write an exponential function that models a given problem situation.

PC-4.7 Apply the laws of logarithms to solve problems.

PC-4.8 Carry out a procedure to solve exponential equations algebraically.

PC-4.9 Carry out a procedure to solve exponential equations graphically.

PC-4.10 Carry out a procedure to solve logarithmic equations algebraically.

PC-4.11 Carry out a procedure to solve logarithmic equations graphically.

SC.PC-5 Precalculus: The student will demonstrate through the mathematical processes an understanding of the behaviors of trigonometric functions.

PC-5.1 Understand how angles are measured in either degrees or radians.

PC-5.2 Carry out a procedure to convert between degree and radian measures.

PC-5.3 Carry out a procedure to plot points in the polar coordinate system.

PC-5.4 Carry out a procedure to graph trigonometric functions by analyzing intercepts, periodic behavior, and graphs of reciprocal functions.

PC-5.5 Carry out procedures to determine the characteristics of trigonometric functions (including domain, range, intercepts, and asymptotes).

PC-5.6 Apply a procedure to evaluate trigonometric expressions.

PC-5.7 Analyze given information to write a trigonometric function that models a given problem situation involving periodic phenomena.

PC-5.8 Analyze given information to write a trigonometric equation that models a given problem situation involving right triangles.

PC-5.9 Carry out a procedure to calculate the area of a triangle when given the lengths of two sides and the measure of the included angle.

PC-5.10 Carry out a procedure to solve trigonometric equations algebraically.

PC-5.11 Carry out a procedure to solve trigonometric equations graphically.

PC-5.12 Apply the laws of sines and cosines to solve problems.

PC-5.13 Apply a procedure to graph the inverse functions of sine, cosine, and tangent.

PC-5.14 Apply trigonometric relationships (including reciprocal identities; Pythagorean identities; even and odd identities; addition and subtraction formulas of sine, cosine, and tangent; and double angle formulas) to verify other trigonometric identities.

PC-5.15 Carry out a procedure to compute the slope of a line when given the angle of inclination of the line.

SC.PC-6 Precalculus: The student will demonstrate through the mathematical processes an understanding of the behavior of conic sections both geometrically and algebraically.

PC-6.1 Carry out a procedure to graph the circle whose equation is the form (x - h)^2 + (y - k)^2 = r^2.

PC-6.2 Analyze given information about the center and the radius or the center and the diameter to write an equation of a circle.

PC-6.3 Apply a procedure to calculate the coordinates of points where a line intersects a circle.

PC-6.4 Carry out a procedure to graph the ellipse whose equation is the form (x -h)^2/a^2 + (y - k)^2/b^2 = 1.

PC-6.5 Carry out a procedure to graph the hyperbola whose equation is the form (x -h)^2/a^2 + (y - k)^2/b^2 = 1.

PC-6.6 Carry out a procedure to graph the parabola whose equation is the form y - k = a(x - h)^2.

SC.DA-1 Data Analysis and Probability: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

DA-1.1 Execute procedures to conduct simple probability experiments and collect data by using manipulatives (including spinners, dice, cards, and coins).

DA-1.2 Execute procedures to find measures of probability and statistics by using tools such as handheld computing devices, spreadsheets, and statistical software.

DA-1.3 Execute procedures to conduct a simulation by using random number tables and/or technology (including handheld computing devices and computers).

DA-1.4 Design and conduct a statistical research project and produce a report that summarizes the findings.

DA-1.5 Apply the principles of probability and statistics to solve problems in real-world contexts.

DA-1.6 Communicate a knowledge of data analysis and probability by using mathematical terminology appropriately.

DA-1.7 Judge the reasonableness of mathematical solutions on the basis of the source of the data, the design of the study, the way the data are displayed, and the way the data are analyzed.

DA-1.8 Compare data sets by using graphs and summary statistics.

SC.DA-2 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of the design of a statistical study.

DA-2.1 Classify a data-collection procedure as a survey, an observational study, or a controlled experiment.

DA-2.2 Compare various random sampling techniques (including simple, stratified, cluster, and systematic).

DA-2.3 Analyze a data-collection procedure to classify the technique used as either simple cluster, systematic, or convenience sampling.

DA-2.4 Critique data-collection methods and describe how bias can be controlled.

DA-2.5 Judge which of two or more possible experimental designs will best answer a given research question.

DA-2.6 Generate a research question and design a statistical study to answer a given research question.

SC.DA-3 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of the methodology for collecting, organizing, displaying, and interpreting data.

DA-3.1 Use manipulatives, random number tables, and technology to collect data and conduct experiments and simulations.

DA-3.2 Organize and interpret data by using pictographs, bar graphs, pie charts, dot plots, histograms, time-series plots, stem-and-leaf plots, box-and-whiskers plots, and scatterplots.

DA-3.3 Select appropriate graphic display(s) from among pictographs, bar graphs, pie charts, dot plots, histograms, time-series plots, stem-and-leaf plots, box-and-whiskers plots, and scatterplots when given a data set or problem situation.

DA-3.4 Represent frequency distributions by using displays such as categorical frequency distributions/Pareto charts, histograms, frequency polygons, and cumulative frequency distributions/ogives.

DA-3.5 Classify a scatterplot by shape (including linear, quadratic, and exponential).

DA-3.6 Classify graphically and analytically the correlation between two variables as either positive, negative, or zero.

DA-3.7 Carry out a procedure to determine an equation of a trend line for a scatterplot exhibiting a linear pattern by using visual approximation.

DA-3.8 Carry out a procedure using technology to determine a line of best fit for a scatterplot exhibiting a linear pattern.

DA-3.9 Explain the meaning of the correlation coefficient r.

DA-3.10 Use interpolation or extrapolation to predict values based on the relationship between two variables.

SC.DA-4 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of basic statistical methods of analyzing data.

DA-4.1 Classify a variable as either a statistic or a parameter.

DA-4.2 Compare descriptive and inferential statistics.

DA-4.3 Classify a variable as either discrete or continuous and as either categorical or quantitative.

DA-4.4 Use procedures and/or technology to find measures of central tendency (mean, median, and mode) for given data.

DA-4.5 Predict the effect of transformations of data on measures of central tendency, variability, and the shape of the distribution.

DA-4.6 Use procedures and/or technology to find measures of spread (range, variance, standard deviation, and interquartile range) and outliers for given data.

DA-4.7 Use procedures and/or technology to find measures of position (including median, quartiles, percentiles, and standard scores) for given data.

DA-4.8 Classify a distribution as either symmetric, positively skewed, or negatively skewed.

DA-4.9 Explain the significance of the shape of a distribution.

DA-4.10 Use a knowledge of the empirical rule to solve problems involving data that are distributed normally.

DA-4.11 Use control charts to determine whether a process is in control.

SC.DA-5 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of the basic concepts of probability.

DA-5.1 Construct a sample space for an experiment and represent it as a list, chart, picture, or tree diagram.

DA-5.2 Use counting techniques to determine the number of possible outcomes for an event.

DA-5.3 Classify events as either dependent or independent.

DA-5.4 Categorize two events either as mutually exclusive or as not mutually exclusive of one another.

DA-5.5 Use the concept of complementary sets to compute probabilities.

DA-5.6 Use the binomial probability distribution to solve problems.

DA-5.7 Carry out a procedure to compute simple probabilities and compound probabilities (including conditional probabilities).

DA-5.8 Use a procedure to find geometric probability in real-world contexts.

DA-5.9 Compare theoretical and experimental probabilities.

DA-5.10 Construct and compare theoretical and experimental probability distributions.

DA-5.11 Use procedures to find the expected value of discrete random variables and construct meaning within contexts.

DA-5.12 Understand the law of large numbers.

DA-5.13 Carry out a procedure to compute conditional probability by using two-way tables.

SC.EA-1 Elementary Algebra: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

EA-1.1 Communicate a knowledge of algebraic relationships by using mathematical terminology appropriately.

EA-1.2 Connect algebra with other branches of mathematics.

EA-1.3 Apply algebraic methods to solve problems in real-world contexts.

EA-1.4 Judge the reasonableness of mathematical solutions.

EA-1.5 Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

EA-1.6 Understand how algebraic relationships can be represented in concrete models, pictorial models, and diagrams.

EA-1.7 Understand how to represent algebraic relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

SC.EA-2 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of the real number system and operations involving exponents, matrices, and algebraic expressions.

EA-2.1 Exemplify elements of the real number system (including integers, rational numbers, and irrational numbers).

EA-2.2 Apply the laws of exponents and roots to solve problems.

EA-2.3 Carry out a procedure to perform operations (including multiplication and division) with numbers written in scientific notation.

EA-2.4 Use dimensional analysis to convert units of measure within a system.

EA-2.5 Carry out a procedure using the properties of real numbers (including commutative, associative, and distributive) to simplify expressions.

EA-2.6 Carry out a procedure to evaluate an expression by substituting a value for the variable.

EA-2.7 Carry out a procedure (including addition, subtraction, multiplication, and division by a monomial) to simplify polynomial expressions.

EA-2.8 Carry out a procedure to factor binomials, trinomials, and polynomials by using various techniques (including the greatest common factor, the difference between two squares, and quadratic trinomials).

EA-2.9 Carry out a procedure to perform operations with matrices (including addition, subtraction, and scalar multiplication).

EA-2.10 Represent applied problems by using matrices.

SC.EA-3 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of relationships and functions.

EA-3.1 Classify a relationship as being either a function or not a function when given data as a table, set of ordered pairs, or graph.

EA-3.2 Use function notation to represent functional relationships.

EA-3.3 Carry out a procedure to evaluate a function for a given element in the domain.

EA-3.4 Analyze the graph of a continuous function to determine the domain and range of the function.

EA-3.5 Carry out a procedure to graph parent functions (including y = x, y = x^2, y = square root of x, y = |x|, and y = 1/x).

EA-3.6 Classify a variation as either direct or inverse.

EA-3.7 Carry out a procedure to solve literal equations for a specified variable.

EA-3.8 Apply proportional reasoning to solve problems.

SC.EA-4 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of the procedures for writing and solving linear equations and inequalities.

EA-4.1 Carry out a procedure to write an equation of a line with a given slope and a y-intercept.

EA-4.2 Carry out a procedure to write an equation of a line with a given slope passing through a given point.

EA-4.3 Carry out a procedure to write an equation of a line passing through two given points.

EA-4.4 Use a procedure to write an equation of a trend line from a given scatterplot.

EA-4.5 Analyze a scatterplot to make predictions.

EA-4.6 Represent linear equations in multiple forms (including point-slope, slope-intercept, and standard).

EA-4.7 Carry out procedures to solve linear equations for one variable algebraically.

EA-4.8 Carry out procedures to solve linear inequalities for one variable algebraically and then to graph the solution.

EA-4.9 Carry out a procedure to solve systems of two linear equations graphically.

EA-4.10 Carry out a procedure to solve systems of two linear equations algebraically.

SC.EA-5 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of the graphs and characteristics of linear equations and inequalities.

EA-5.1 Carry out a procedure to graph a line when given the equation of the line.

EA-5.2 Analyze the effects of changes in the slope, m, and the y-intercept, b, on the graph of y = mx + b.

EA-5.3 Carry out a procedure to graph the line with a given slope and a y-intercept.

EA-5.4 Carry out a procedure to graph the line with a given slope passing through a given point.

EA-5.5 Carry out a procedure to determine the x-intercept and y-intercept of lines from data given tabularly, graphically, symbolically, and verbally.

EA-5.6 Carry out a procedure to determine the slope of a line from data given tabularly, graphically, symbolically, and verbally.

EA-5.7 Apply the concept of slope as a rate of change to solve problems.

EA-5.8 Analyze the equations of two lines to determine whether the lines are perpendicular or parallel.

EA-5.9 Analyze given information to write a linear function that models a given problem situation.

EA-5.10 Analyze given information to determine the domain and range of a linear function in a problem situation.

EA-5.11 Analyze given information to write a system of linear equations that models a given problem situation.

EA-5.12 Analyze given information to write a linear inequality in one variable that models a given problem situation.

SC.EA-6 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of quadratic relationships and functions.

EA-6.1 Analyze the effects of changing the leading coefficient a on the graph of y = ax^2.

EA-6.2 Analyze the effects of changing the constant c on the graph of y = x^2 + c.

EA-6.3 Analyze the graph of a quadratic function to determine its equation.

EA-6.4 Carry out a procedure to solve quadratic equations by factoring.

EA-6.5 Carry out a graphic procedure to approximate the solutions of quadratic equations.

EA-6.6 Analyze given information to determine the domain of a quadratic function in a problem situation.

SC.IA-1 Intermediate Algebra: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

IA-1.1 Communicate a knowledge of algebraic relationships by using mathematical terminology appropriately.

IA-1.2 Connect algebra with other branches of mathematics.

IA-1.3 Apply algebraic methods to solve problems in real-world contexts.

IA-1.4 Judge the reasonableness of mathematical solutions.

IA-1.5 Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

IA-1.6 Understand how algebraic relationships can be represented in concrete models, pictorial models, and diagrams.

IA-1.7 Understand how to represent algebraic relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

SC.IA-2 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of functions, systems of equations, and systems of linear inequalities.

IA-2.1 Carry out a procedure to solve a system of linear inequalities algebraically.

IA-2.2 Carry out a procedure to solve a system of linear inequalities graphically.

IA-2.3 Analyze a problem situation to determine a system of linear inequalities that models the problem situation.

IA-2.4 Use linear programming to solve contextual problems involving a system of linear inequalities.

IA-2.5 Carry out procedures to perform operations on polynomial functions (including f(x) + g(x), f(x) - g(x), f(x) x g(x), and f(x)/g(x)).

IA-2.6 Apply a procedure to write the equation of a composition of given functions.

IA-2.7 Carry out a procedure to graph translations of parent functions (including y = x, y = x^2, y = square root of x, y = |x|, and y = 1/x).

IA-2.8 Carry out a procedure to graph transformations of parent functions (including y = x, y = x^2, y = square root of x, y = |x|.

IA-2.9 Carry out a procedure to graph discontinuous functions (including piecewise and step functions).

IA-2.10 Carry out a procedure to determine the domain and range of discontinuous functions (including piecewise and step functions).

IA-2.11 Carry out a procedure to solve a system of equations (including two linear functions and one linear function with one quadratic function).

SC.IA-3 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of quadratic equations and the complex number system.

IA-3.1 Carry out a procedure to simplify expressions involving powers of i.

IA-3.2 Carry out a procedure to perform operations with complex numbers (including addition, subtraction, multiplication, and division).

IA-3.3 Carry out a procedure to solve quadratic equations algebraically (including factoring, completing the square, and applying the quadratic formula).

IA-3.4 Use the discriminant to determine the number and type of solutions of a quadratic equation.

IA-3.5 Analyze given information (including quadratic models) to solve contextual problems.

IA-3.6 Carry out a procedure to write an equation of a quadratic function when given its roots.

SC.IA-4 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of algebraic expressions and nonlinear functions.

IA-4.1 Carry out a procedure to perform operations (including multiplication, exponentiation, and division) with polynomial expressions.

IA-4.2 Carry out a procedure to determine specified points (including zeros, maximums, and minimums) of polynomial functions.

IA-4.3 Carry out a procedure to solve polynomial equations (including factoring by grouping, factoring the difference between two squares, factoring the sum of two cubes, and factoring the difference between two cubes).

IA-4.4 Analyze given information (including polynomial models) to solve contextual problems.

IA-4.5 Carry out a procedure to simplify algebraic expressions involving rational exponents.

IA-4.6 Carry out a procedure to simplify algebraic expressions involving logarithms.

IA-4.7 Carry out a procedure to perform operations with expressions involving rational exponents (including addition, subtraction, multiplication, division, and exponentiation).

IA-4.8 Carry out a procedure to perform operations with rational expressions (including addition, subtraction, multiplication, and division).

IA-4.9 Carry out a procedure to solve radical equations algebraically.

IA-4.10 Carry out a procedure to solve logarithmic equations algebraically.

IA-4.11 Carry out a procedure to solve logarithmic equations graphically.

IA-4.12 Carry out a procedure to solve rational equations algebraically.

IA-4.13 Carry out a procedure to graph logarithmic functions.

IA-4.14 Carry out a procedure to graph exponential functions.

SC.IA-5 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of conic sections.

IA-5.1 Carry out a procedure to graph the circle whose equation is the form x^2 + y^2 = r^2.

IA-5.2 Carry out a procedure to write an equation of a circle centered at the origin when given its radius.

IA-5.3 Carry out a procedure to graph the ellipse whose equation is the form x^2/a^2 + y^2/b^2 = 1.

IA-5.4 Carry out a procedure to write an equation of an ellipse centered at the origin when given information from among length of major axis, length of minor axis, and vertices.

IA-5.5 Carry out a procedure to graph the hyperbola whose equation is the form x^2/a^2 + y^2/b^2 = 1.

IA-5.6 Carry out a procedure to write an equation of a hyperbola centered at the origin with specified vertices.

IA-5.7 Match the equation of a conic section with its graph.

SC.IA-6 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of sequences and series.

IA-6.1 Categorize a sequence as arithmetic, geometric, or neither.

IA-6.2 Carry out a procedure to write a specified term of an arithmetic or geometric sequence when given the nth term of the sequence.

IA-6.3 Carry out a procedure to write a formula for the nth term of an arithmetic or geometric sequence when given at least four consecutive terms of the sequence.

IA-6.4 Carry out a procedure to write a formula for the nth term of an arithmetic or geometric sequence when given at least four terms of the sequence.

IA-6.5 Represent an arithmetic or geometric series by using sigma notation.

IA-6.6 Carry out a procedure to calculate the sum of an arithmetic or geometric series written in sigma notation.

IA-6.7 Carry out a procedure to determine consecutive terms of a sequence that is defined recursively.

IA-6.8 Carry out a procedure to define a sequence recursively when given four or more consecutive terms of the sequence.

IA-6.9 Translate between the explicit form and the recursive form of sequences.

SC.G-1 Geometry: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

G-1.1 Demonstrate an understanding of the axiomatic structure of geometry by using undefined terms, definitions, postulates, theorems, and corollaries.

G-1.2 Communicate knowledge of geometric relationships by using mathematical terminology appropriately.

G-1.3 Apply basic rules of logic to determine the validity of the converse, inverse, and contrapositive of a conditional statement.

G-1.4 Formulate and test conjectures by using a variety of tools such as concrete models, graphing calculators, spreadsheets, and dynamic geometry software.

G-1.5 Use inductive reasoning to formulate conjectures.

G-1.6 Use deductive reasoning to validate conjectures with formal and informal proofs, and give counterexamples to disprove a statement.

G-1.7 Understand the historical development of geometry.

G-1.8 Connect geometry with other branches of mathematics.

G-1.9 Demonstrate an understanding of how geometry applies to in real-world contexts (including architecture, construction, farming, and astronomy).

G-1.10 Demonstrate an understanding of geometric relationships (including constructions through investigations by using a variety of tools such as straightedge, compass, Patty Paper, dynamic geometry software, and handheld computing devices).

SC.G-2 Geometry: The student will demonstrate through the mathematical processes an understanding of the properties of basic geometric figures and the relationships between and among them.

G-2.1 Infer missing elements of visual or numerical geometric patterns (including triangular and rectangular numbers and the number of diagonals in polygons).

G-2.2 Apply properties of parallel lines, intersecting lines, and parallel lines cut by a transversal to solve problems.

G-2.3 Use the congruence of line segments and angles to solve problems.

G-2.4 Use direct measurement to determine the length of a segment, degree of an angle, and distance from a point to a line.

G-2.5 Carry out a procedure to create geometric constructions (including the midpoint of a line segment, the angle bisector, the perpendicular bisector of a line segment, the line through a given point that is parallel to a given line, and the line through a given point that is perpendicular to a given line).

G-2.6 Use scale factors to solve problems involving scale drawings and models.

G-2.7 Use geometric probability to solve problems.

SC.G-3 Geometry: The student will demonstrate through the mathematical processes an understanding of the properties and special segments of triangles and the relationships between and among triangles.

G-3.1 Carry out a procedure to compute the perimeter of a triangle.

G-3.2 Carry out a procedure to compute the area of a triangle.

G-3.3 Analyze how changes in dimensions affect the perimeter or area of triangles.

G-3.4 Apply properties of isosceles and equilateral triangles to solve problems.

G-3.5 Use interior angles, exterior angles, medians, angle bisectors, altitudes, and perpendicular bisectors to solve problems.

G-3.6 Apply the triangle sum theorem to solve problems.

G-3.7 Apply the triangle inequality theorem to solve problems.

G-3.8 Apply congruence and similarity relationships among triangles to solve problems.

G-3.9 Apply theorems to prove that triangles are either similar or congruent.

G-3.10 Use the Pythagorean theorem and its converse to solve problems.

G-3.11 Use the properties of 45-45-90 and 30-60-90 triangles to solve problems.

G-3.12 Use trigonometric ratios (including sine, cosine, and tangent) to solve problems involving right triangles.

SC.G-4 Geometry: The student will demonstrate through the mathematical processes an understanding of the properties of quadrilaterals and other polygons and the relationships between and among them.

G-4.1 Carry out a procedure to compute the perimeter of quadrilaterals, regular polygons, and composite figures.

G-4.2 Carry out a procedure to find the area of quadrilaterals, regular polygons, and composite figures.

G-4.3 Apply procedures to compute measures of interior and exterior angles of polygons.

G-4.4 Analyze how changes in dimensions affect the perimeter or area of quadrilaterals and regular polygons.

G-4.5 Apply the properties and attributes of quadrilaterals and regular polygons and their component parts to solve problems.

G-4.6 Apply congruence and similarity relationships among shapes (including quadrilaterals and polygons) to solve problems.

SC.G-5 Geometry: The student will demonstrate through the mathematical processes an understanding of the properties of circles, the lines that intersect them, and the use of their special segments.

G-5.1 Carry out a procedure to compute the circumference of circles.

G-5.2 Carry out a procedure to compute the area of circles.

G-5.3 Analyze how a change in the radius affects the circumference or area of a circle.

G-5.4 Carry out a procedure to compute the length of an arc or the area of a sector of a circle.

G-5.5 Apply the properties of the component parts of a circle (including radii, diameters, chords, sectors, arcs, and segments) to solve problems.

G-5.6 Apply the properties of lines that intersect circles (including two secants, two tangents, and a secant and a tangent) to solve problems.

G-5.7 Apply the properties of central angles, inscribed angles, and arcs of circles to solve problems.

SC.G-6 Geometry: The student will demonstrate through the mathematical processes an understanding of transformations, coordinate geometry, and vectors.

G-6.1 Use the distance formula to solve problems.

G-6.2 Use the midpoint formula to solve problems.

G-6.3 Apply transformations-translation, reflection, rotation, and dilation-to figures in the coordinate plane by using sketches and coordinates.

G-6.4 Apply transformations (including translation and dilation) to figures in the coordinate plane by using matrices.

G-6.5 Carry out a procedure to represent the sum of two vectors geometrically by using the parallelogram method.

G-6.6 Carry out a procedure to determine the magnitude and direction of the resultant of two vectors by using a scale drawing and direct measurement.

G-6.7 Carry out a procedure to compute the magnitude of the resultant of two perpendicular vectors by using the Pythagorean theorem.

G-6.8 Carry out a procedure to determine the direction of the resultant of two perpendicular vectors by using a scale drawing and direct measurement.

SC.G-7 Geometry: The student will demonstrate through the mathematical processes an understanding of the surface area and volume of three-dimensional objects.

G-7.1 Carry out a procedure to compute the surface area of three-dimensional objects (including cones, cylinders, pyramids, prisms, spheres, and hemispheres).

G-7.2 Carry out a procedure to compute the volume of three-dimensional objects (including cones, cylinders, pyramids, prisms, spheres, hemispheres, and composite objects).

G-7.3 Analyze how changes in dimensions affect the volume of objects (including cylinders, prisms, and spheres).

G-7.4 Apply congruence and similarity relationships among geometric objects to solve problems.

G-7.5 Apply a procedure to draw a top view, front view, and side view of a three-dimensional object.

G-7.6 Apply a procedure to draw an isometric view of a three-dimensional object.

SC.PC-1 Precalculus: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

PC-1.1 Communicate knowledge of algebraic and trigonometric relationships by using mathematical terminology appropriately.

PC-1.2 Connect algebra and trigonometry with other branches of mathematics.

PC-1.3 Apply algebraic methods to solve problems in real-world contexts.

PC-1.4 Judge the reasonableness of mathematical solutions.

PC-1.5 Demonstrate an understanding of algebraic and trigonometric relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

PC-1.6 Understand how algebraic and trigonometric relationships can be represented in concrete models, pictorial models, and diagrams.

PC-1.7 Understand how to represent algebraic and trigonometric relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

SC.PC-2 Precalculus: The student will demonstrate through the mathematical processes an understanding of the characteristics and behaviors of functions and the effect of operations on functions.

PC-2.1 Carry out a procedure to graph parent functions (including y = x^n, y = log base a(x), y = log base n (x), y = 1/x, y = e^x, y = a^x, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

PC-2.2 Carry out a procedure to graph transformations (including -f(x), a x f(x), f(x) + d, f(x-c), f(-x), f(bx), |f(x)|, and f(|x|)) of parent functions and combinations of transformations.

PC-2.3 Analyze a graph to describe the transformation (including -f(x), a x f(x), f(x) + d, f(x-c), f(-x), f(bx), |f(x)|, and f(|x|)) of parent functions.

PC-2.4 Carry out procedures to algebraically solve equations involving parent functions or transformations of parent functions (including y = x^n, y = log base a(x), y = log base n (x), y = 1/x, y = e^x, y = a^x, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

PC-2.5 Analyze graphs, tables, and equations to determine the domain and range of parent functions or transformations of parent functions (including y = x^n, y = log base a(x), y = log base n (x), y = 1/x, y = e^x, y = a^x, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

PC-2.6 Analyze a function or the symmetry of its graph to determine whether the function is even, odd, or neither.

PC-2.7 Recognize and use connections among significant points of a function (including roots, maximum points, and minimum points), the graph of a function, and the algebraic representation of a function.

PC-2.8 Carry out a procedure to determine whether the inverse of a function exists.

PC-2.9 Carry out a procedure to write a rule for the inverse of a function, if it exists.

SC.PC-3 Precalculus: The student will demonstrate through the mathematical processes an understanding of the behaviors of polynomial and rational functions.

PC-3.1 Carry out a procedure to graph quadratic and higher-order polynomial functions by analyzing intercepts and end behavior.

PC-3.2 Apply the rational root theorem to determine a set of possible rational roots of a polynomial equation.

PC-3.3 Carry out a procedure to calculate the zeros of polynomial functions when given a set of possible zeros.

PC-3.4 Carry out procedures to determine characteristics of rational functions (including domain, range, intercepts, asymptotes, and discontinuities).

PC-3.5 Analyze given information to write a polynomial function that models a given problem situation.

PC-3.6 Carry out a procedure to solve polynomial equations algebraically.

PC-3.7 Carry out a procedure to solve polynomial equations graphically.

PC-3.8 Carry out a procedure to solve rational equations algebraically.

PC-3.9 Carry out a procedure to solve rational equations graphically.

PC-3.10 Carry out a procedure to solve polynomial inequalities algebraically.

PC-3.11 Carry out a procedure to solve polynomial inequalities graphically.

SC.PC-4 Precalculus: The student will demonstrate through the mathematical processes an understanding of the behaviors of exponential and logarithmic functions.

PC-4.1 Carry out a procedure to graph exponential functions by analyzing intercepts and end behavior.

PC-4.2 Carry out a procedure to graph logarithmic functions by analyzing intercepts and end behavior.

PC-4.3 Carry out procedures to determine characteristics of exponential functions (including domain, range, intercepts, and asymptotes).

PC-4.4 Carry out procedures to determine characteristics of logarithmic functions (including domain, range, intercepts, and asymptotes).

PC-4.5 Apply the laws of exponents to solve problems involving rational exponents.

PC-4.6 Analyze given information to write an exponential function that models a given problem situation.

PC-4.7 Apply the laws of logarithms to solve problems.

PC-4.8 Carry out a procedure to solve exponential equations algebraically.

PC-4.9 Carry out a procedure to solve exponential equations graphically.

PC-4.10 Carry out a procedure to solve logarithmic equations algebraically.

PC-4.11 Carry out a procedure to solve logarithmic equations graphically.

SC.PC-5 Precalculus: The student will demonstrate through the mathematical processes an understanding of the behaviors of trigonometric functions.

PC-5.1 Understand how angles are measured in either degrees or radians.

PC-5.2 Carry out a procedure to convert between degree and radian measures.

PC-5.3 Carry out a procedure to plot points in the polar coordinate system.

PC-5.4 Carry out a procedure to graph trigonometric functions by analyzing intercepts, periodic behavior, and graphs of reciprocal functions.

PC-5.5 Carry out procedures to determine the characteristics of trigonometric functions (including domain, range, intercepts, and asymptotes).

PC-5.6 Apply a procedure to evaluate trigonometric expressions.

PC-5.7 Analyze given information to write a trigonometric function that models a given problem situation involving periodic phenomena.

PC-5.8 Analyze given information to write a trigonometric equation that models a given problem situation involving right triangles.

PC-5.9 Carry out a procedure to calculate the area of a triangle when given the lengths of two sides and the measure of the included angle.

PC-5.10 Carry out a procedure to solve trigonometric equations algebraically.

PC-5.11 Carry out a procedure to solve trigonometric equations graphically.

PC-5.12 Apply the laws of sines and cosines to solve problems.

PC-5.13 Apply a procedure to graph the inverse functions of sine, cosine, and tangent.

PC-5.14 Apply trigonometric relationships (including reciprocal identities; Pythagorean identities; even and odd identities; addition and subtraction formulas of sine, cosine, and tangent; and double angle formulas) to verify other trigonometric identities.

PC-5.15 Carry out a procedure to compute the slope of a line when given the angle of inclination of the line.

SC.PC-6 Precalculus: The student will demonstrate through the mathematical processes an understanding of the behavior of conic sections both geometrically and algebraically.

PC-6.1 Carry out a procedure to graph the circle whose equation is the form (x - h)^2 + (y - k)^2 = r^2.

PC-6.2 Analyze given information about the center and the radius or the center and the diameter to write an equation of a circle.

PC-6.3 Apply a procedure to calculate the coordinates of points where a line intersects a circle.

PC-6.4 Carry out a procedure to graph the ellipse whose equation is the form (x -h)^2/a^2 + (y - k)^2/b^2 = 1.

PC-6.5 Carry out a procedure to graph the hyperbola whose equation is the form (x -h)^2/a^2 + (y - k)^2/b^2 = 1.

PC-6.6 Carry out a procedure to graph the parabola whose equation is the form y - k = a(x - h)^2.

SC.DA-1 Data Analysis and Probability: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

DA-1.1 Execute procedures to conduct simple probability experiments and collect data by using manipulatives (including spinners, dice, cards, and coins).

DA-1.2 Execute procedures to find measures of probability and statistics by using tools such as handheld computing devices, spreadsheets, and statistical software.

DA-1.3 Execute procedures to conduct a simulation by using random number tables and/or technology (including handheld computing devices and computers).

DA-1.4 Design and conduct a statistical research project and produce a report that summarizes the findings.

DA-1.5 Apply the principles of probability and statistics to solve problems in real-world contexts.

DA-1.6 Communicate a knowledge of data analysis and probability by using mathematical terminology appropriately.

DA-1.7 Judge the reasonableness of mathematical solutions on the basis of the source of the data, the design of the study, the way the data are displayed, and the way the data are analyzed.

DA-1.8 Compare data sets by using graphs and summary statistics.

SC.DA-2 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of the design of a statistical study.

DA-2.1 Classify a data-collection procedure as a survey, an observational study, or a controlled experiment.

DA-2.2 Compare various random sampling techniques (including simple, stratified, cluster, and systematic).

DA-2.3 Analyze a data-collection procedure to classify the technique used as either simple cluster, systematic, or convenience sampling.

DA-2.4 Critique data-collection methods and describe how bias can be controlled.

DA-2.5 Judge which of two or more possible experimental designs will best answer a given research question.

DA-2.6 Generate a research question and design a statistical study to answer a given research question.

SC.DA-3 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of the methodology for collecting, organizing, displaying, and interpreting data.

DA-3.1 Use manipulatives, random number tables, and technology to collect data and conduct experiments and simulations.

DA-3.2 Organize and interpret data by using pictographs, bar graphs, pie charts, dot plots, histograms, time-series plots, stem-and-leaf plots, box-and-whiskers plots, and scatterplots.

DA-3.3 Select appropriate graphic display(s) from among pictographs, bar graphs, pie charts, dot plots, histograms, time-series plots, stem-and-leaf plots, box-and-whiskers plots, and scatterplots when given a data set or problem situation.

DA-3.4 Represent frequency distributions by using displays such as categorical frequency distributions/Pareto charts, histograms, frequency polygons, and cumulative frequency distributions/ogives.

DA-3.5 Classify a scatterplot by shape (including linear, quadratic, and exponential).

DA-3.6 Classify graphically and analytically the correlation between two variables as either positive, negative, or zero.

DA-3.7 Carry out a procedure to determine an equation of a trend line for a scatterplot exhibiting a linear pattern by using visual approximation.

DA-3.8 Carry out a procedure using technology to determine a line of best fit for a scatterplot exhibiting a linear pattern.

DA-3.9 Explain the meaning of the correlation coefficient r.

DA-3.10 Use interpolation or extrapolation to predict values based on the relationship between two variables.

SC.DA-4 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of basic statistical methods of analyzing data.

DA-4.1 Classify a variable as either a statistic or a parameter.

DA-4.2 Compare descriptive and inferential statistics.

DA-4.3 Classify a variable as either discrete or continuous and as either categorical or quantitative.

DA-4.4 Use procedures and/or technology to find measures of central tendency (mean, median, and mode) for given data.

DA-4.5 Predict the effect of transformations of data on measures of central tendency, variability, and the shape of the distribution.

DA-4.6 Use procedures and/or technology to find measures of spread (range, variance, standard deviation, and interquartile range) and outliers for given data.

DA-4.7 Use procedures and/or technology to find measures of position (including median, quartiles, percentiles, and standard scores) for given data.

DA-4.8 Classify a distribution as either symmetric, positively skewed, or negatively skewed.

DA-4.9 Explain the significance of the shape of a distribution.

DA-4.10 Use a knowledge of the empirical rule to solve problems involving data that are distributed normally.

DA-4.11 Use control charts to determine whether a process is in control.

SC.DA-5 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of the basic concepts of probability.

DA-5.1 Construct a sample space for an experiment and represent it as a list, chart, picture, or tree diagram.

DA-5.2 Use counting techniques to determine the number of possible outcomes for an event.

DA-5.3 Classify events as either dependent or independent.

DA-5.4 Categorize two events either as mutually exclusive or as not mutually exclusive of one another.

DA-5.5 Use the concept of complementary sets to compute probabilities.

DA-5.6 Use the binomial probability distribution to solve problems.

DA-5.7 Carry out a procedure to compute simple probabilities and compound probabilities (including conditional probabilities).

DA-5.8 Use a procedure to find geometric probability in real-world contexts.

DA-5.9 Compare theoretical and experimental probabilities.

DA-5.10 Construct and compare theoretical and experimental probability distributions.

DA-5.11 Use procedures to find the expected value of discrete random variables and construct meaning within contexts.

DA-5.12 Understand the law of large numbers.

DA-5.13 Carry out a procedure to compute conditional probability by using two-way tables.

SC.EA-1 Elementary Algebra: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

EA-1.1 Communicate a knowledge of algebraic relationships by using mathematical terminology appropriately.

EA-1.2 Connect algebra with other branches of mathematics.

EA-1.3 Apply algebraic methods to solve problems in real-world contexts.

EA-1.4 Judge the reasonableness of mathematical solutions.

EA-1.5 Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

EA-1.6 Understand how algebraic relationships can be represented in concrete models, pictorial models, and diagrams.

EA-1.7 Understand how to represent algebraic relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

SC.EA-2 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of the real number system and operations involving exponents, matrices, and algebraic expressions.

EA-2.1 Exemplify elements of the real number system (including integers, rational numbers, and irrational numbers).

EA-2.2 Apply the laws of exponents and roots to solve problems.

EA-2.3 Carry out a procedure to perform operations (including multiplication and division) with numbers written in scientific notation.

EA-2.4 Use dimensional analysis to convert units of measure within a system.

EA-2.5 Carry out a procedure using the properties of real numbers (including commutative, associative, and distributive) to simplify expressions.

EA-2.6 Carry out a procedure to evaluate an expression by substituting a value for the variable.

EA-2.7 Carry out a procedure (including addition, subtraction, multiplication, and division by a monomial) to simplify polynomial expressions.

EA-2.8 Carry out a procedure to factor binomials, trinomials, and polynomials by using various techniques (including the greatest common factor, the difference between two squares, and quadratic trinomials).

EA-2.9 Carry out a procedure to perform operations with matrices (including addition, subtraction, and scalar multiplication).

EA-2.10 Represent applied problems by using matrices.

SC.EA-3 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of relationships and functions.

EA-3.1 Classify a relationship as being either a function or not a function when given data as a table, set of ordered pairs, or graph.

EA-3.2 Use function notation to represent functional relationships.

EA-3.3 Carry out a procedure to evaluate a function for a given element in the domain.

EA-3.4 Analyze the graph of a continuous function to determine the domain and range of the function.

EA-3.5 Carry out a procedure to graph parent functions (including y = x, y = x^2, y = square root of x, y = |x|, and y = 1/x).

EA-3.6 Classify a variation as either direct or inverse.

EA-3.7 Carry out a procedure to solve literal equations for a specified variable.

EA-3.8 Apply proportional reasoning to solve problems.

SC.EA-4 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of the procedures for writing and solving linear equations and inequalities.

EA-4.1 Carry out a procedure to write an equation of a line with a given slope and a y-intercept.

EA-4.2 Carry out a procedure to write an equation of a line with a given slope passing through a given point.

EA-4.3 Carry out a procedure to write an equation of a line passing through two given points.

EA-4.4 Use a procedure to write an equation of a trend line from a given scatterplot.

EA-4.5 Analyze a scatterplot to make predictions.

EA-4.6 Represent linear equations in multiple forms (including point-slope, slope-intercept, and standard).

EA-4.7 Carry out procedures to solve linear equations for one variable algebraically.

EA-4.8 Carry out procedures to solve linear inequalities for one variable algebraically and then to graph the solution.

EA-4.9 Carry out a procedure to solve systems of two linear equations graphically.

EA-4.10 Carry out a procedure to solve systems of two linear equations algebraically.

SC.EA-5 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of the graphs and characteristics of linear equations and inequalities.

EA-5.1 Carry out a procedure to graph a line when given the equation of the line.

EA-5.2 Analyze the effects of changes in the slope, m, and the y-intercept, b, on the graph of y = mx + b.

EA-5.3 Carry out a procedure to graph the line with a given slope and a y-intercept.

EA-5.4 Carry out a procedure to graph the line with a given slope passing through a given point.

EA-5.5 Carry out a procedure to determine the x-intercept and y-intercept of lines from data given tabularly, graphically, symbolically, and verbally.

EA-5.6 Carry out a procedure to determine the slope of a line from data given tabularly, graphically, symbolically, and verbally.

EA-5.7 Apply the concept of slope as a rate of change to solve problems.

EA-5.8 Analyze the equations of two lines to determine whether the lines are perpendicular or parallel.

EA-5.9 Analyze given information to write a linear function that models a given problem situation.

EA-5.10 Analyze given information to determine the domain and range of a linear function in a problem situation.

EA-5.11 Analyze given information to write a system of linear equations that models a given problem situation.

EA-5.12 Analyze given information to write a linear inequality in one variable that models a given problem situation.

SC.EA-6 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of quadratic relationships and functions.

EA-6.1 Analyze the effects of changing the leading coefficient a on the graph of y = ax^2.

EA-6.2 Analyze the effects of changing the constant c on the graph of y = x^2 + c.

EA-6.3 Analyze the graph of a quadratic function to determine its equation.

EA-6.4 Carry out a procedure to solve quadratic equations by factoring.

EA-6.5 Carry out a graphic procedure to approximate the solutions of quadratic equations.

EA-6.6 Analyze given information to determine the domain of a quadratic function in a problem situation.

SC.IA-1 Intermediate Algebra: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

IA-1.1 Communicate a knowledge of algebraic relationships by using mathematical terminology appropriately.

IA-1.2 Connect algebra with other branches of mathematics.

IA-1.3 Apply algebraic methods to solve problems in real-world contexts.

IA-1.4 Judge the reasonableness of mathematical solutions.

IA-1.5 Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

IA-1.6 Understand how algebraic relationships can be represented in concrete models, pictorial models, and diagrams.

IA-1.7 Understand how to represent algebraic relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

SC.IA-2 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of functions, systems of equations, and systems of linear inequalities.

IA-2.1 Carry out a procedure to solve a system of linear inequalities algebraically.

IA-2.2 Carry out a procedure to solve a system of linear inequalities graphically.

IA-2.3 Analyze a problem situation to determine a system of linear inequalities that models the problem situation.

IA-2.4 Use linear programming to solve contextual problems involving a system of linear inequalities.

IA-2.5 Carry out procedures to perform operations on polynomial functions (including f(x) + g(x), f(x) - g(x), f(x) x g(x), and f(x)/g(x)).

IA-2.6 Apply a procedure to write the equation of a composition of given functions.

IA-2.7 Carry out a procedure to graph translations of parent functions (including y = x, y = x^2, y = square root of x, y = |x|, and y = 1/x).

IA-2.8 Carry out a procedure to graph transformations of parent functions (including y = x, y = x^2, y = square root of x, y = |x|.

IA-2.9 Carry out a procedure to graph discontinuous functions (including piecewise and step functions).

IA-2.10 Carry out a procedure to determine the domain and range of discontinuous functions (including piecewise and step functions).

IA-2.11 Carry out a procedure to solve a system of equations (including two linear functions and one linear function with one quadratic function).

SC.IA-3 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of quadratic equations and the complex number system.

IA-3.1 Carry out a procedure to simplify expressions involving powers of i.

IA-3.2 Carry out a procedure to perform operations with complex numbers (including addition, subtraction, multiplication, and division).

IA-3.3 Carry out a procedure to solve quadratic equations algebraically (including factoring, completing the square, and applying the quadratic formula).

IA-3.4 Use the discriminant to determine the number and type of solutions of a quadratic equation.

IA-3.5 Analyze given information (including quadratic models) to solve contextual problems.

IA-3.6 Carry out a procedure to write an equation of a quadratic function when given its roots.

SC.IA-4 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of algebraic expressions and nonlinear functions.

IA-4.1 Carry out a procedure to perform operations (including multiplication, exponentiation, and division) with polynomial expressions.

IA-4.2 Carry out a procedure to determine specified points (including zeros, maximums, and minimums) of polynomial functions.

IA-4.3 Carry out a procedure to solve polynomial equations (including factoring by grouping, factoring the difference between two squares, factoring the sum of two cubes, and factoring the difference between two cubes).

IA-4.4 Analyze given information (including polynomial models) to solve contextual problems.

IA-4.5 Carry out a procedure to simplify algebraic expressions involving rational exponents.

IA-4.6 Carry out a procedure to simplify algebraic expressions involving logarithms.

IA-4.7 Carry out a procedure to perform operations with expressions involving rational exponents (including addition, subtraction, multiplication, division, and exponentiation).

IA-4.8 Carry out a procedure to perform operations with rational expressions (including addition, subtraction, multiplication, and division).

IA-4.9 Carry out a procedure to solve radical equations algebraically.

IA-4.10 Carry out a procedure to solve logarithmic equations algebraically.

IA-4.11 Carry out a procedure to solve logarithmic equations graphically.

IA-4.12 Carry out a procedure to solve rational equations algebraically.

IA-4.13 Carry out a procedure to graph logarithmic functions.

IA-4.14 Carry out a procedure to graph exponential functions.

SC.IA-5 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of conic sections.

IA-5.1 Carry out a procedure to graph the circle whose equation is the form x^2 + y^2 = r^2.

IA-5.2 Carry out a procedure to write an equation of a circle centered at the origin when given its radius.

IA-5.3 Carry out a procedure to graph the ellipse whose equation is the form x^2/a^2 + y^2/b^2 = 1.

IA-5.4 Carry out a procedure to write an equation of an ellipse centered at the origin when given information from among length of major axis, length of minor axis, and vertices.

IA-5.5 Carry out a procedure to graph the hyperbola whose equation is the form x^2/a^2 + y^2/b^2 = 1.

IA-5.6 Carry out a procedure to write an equation of a hyperbola centered at the origin with specified vertices.

IA-5.7 Match the equation of a conic section with its graph.

SC.IA-6 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of sequences and series.

IA-6.1 Categorize a sequence as arithmetic, geometric, or neither.

IA-6.2 Carry out a procedure to write a specified term of an arithmetic or geometric sequence when given the nth term of the sequence.

IA-6.3 Carry out a procedure to write a formula for the nth term of an arithmetic or geometric sequence when given at least four consecutive terms of the sequence.

IA-6.4 Carry out a procedure to write a formula for the nth term of an arithmetic or geometric sequence when given at least four terms of the sequence.

IA-6.5 Represent an arithmetic or geometric series by using sigma notation.

IA-6.6 Carry out a procedure to calculate the sum of an arithmetic or geometric series written in sigma notation.

IA-6.7 Carry out a procedure to determine consecutive terms of a sequence that is defined recursively.

IA-6.8 Carry out a procedure to define a sequence recursively when given four or more consecutive terms of the sequence.

IA-6.9 Translate between the explicit form and the recursive form of sequences.

SC.G-1 Geometry: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

G-1.1 Demonstrate an understanding of the axiomatic structure of geometry by using undefined terms, definitions, postulates, theorems, and corollaries.

G-1.2 Communicate knowledge of geometric relationships by using mathematical terminology appropriately.

G-1.3 Apply basic rules of logic to determine the validity of the converse, inverse, and contrapositive of a conditional statement.

G-1.4 Formulate and test conjectures by using a variety of tools such as concrete models, graphing calculators, spreadsheets, and dynamic geometry software.

G-1.5 Use inductive reasoning to formulate conjectures.

G-1.6 Use deductive reasoning to validate conjectures with formal and informal proofs, and give counterexamples to disprove a statement.

G-1.7 Understand the historical development of geometry.

G-1.8 Connect geometry with other branches of mathematics.

G-1.9 Demonstrate an understanding of how geometry applies to in real-world contexts (including architecture, construction, farming, and astronomy).

G-1.10 Demonstrate an understanding of geometric relationships (including constructions through investigations by using a variety of tools such as straightedge, compass, Patty Paper, dynamic geometry software, and handheld computing devices).

SC.G-2 Geometry: The student will demonstrate through the mathematical processes an understanding of the properties of basic geometric figures and the relationships between and among them.

G-2.1 Infer missing elements of visual or numerical geometric patterns (including triangular and rectangular numbers and the number of diagonals in polygons).

G-2.2 Apply properties of parallel lines, intersecting lines, and parallel lines cut by a transversal to solve problems.

G-2.3 Use the congruence of line segments and angles to solve problems.

G-2.4 Use direct measurement to determine the length of a segment, degree of an angle, and distance from a point to a line.

G-2.5 Carry out a procedure to create geometric constructions (including the midpoint of a line segment, the angle bisector, the perpendicular bisector of a line segment, the line through a given point that is parallel to a given line, and the line through a given point that is perpendicular to a given line).

G-2.6 Use scale factors to solve problems involving scale drawings and models.

G-2.7 Use geometric probability to solve problems.

SC.G-3 Geometry: The student will demonstrate through the mathematical processes an understanding of the properties and special segments of triangles and the relationships between and among triangles.

G-3.1 Carry out a procedure to compute the perimeter of a triangle.

G-3.2 Carry out a procedure to compute the area of a triangle.

G-3.3 Analyze how changes in dimensions affect the perimeter or area of triangles.

G-3.4 Apply properties of isosceles and equilateral triangles to solve problems.

G-3.5 Use interior angles, exterior angles, medians, angle bisectors, altitudes, and perpendicular bisectors to solve problems.

G-3.6 Apply the triangle sum theorem to solve problems.

G-3.7 Apply the triangle inequality theorem to solve problems.

G-3.8 Apply congruence and similarity relationships among triangles to solve problems.

G-3.9 Apply theorems to prove that triangles are either similar or congruent.

G-3.10 Use the Pythagorean theorem and its converse to solve problems.

G-3.11 Use the properties of 45-45-90 and 30-60-90 triangles to solve problems.

G-3.12 Use trigonometric ratios (including sine, cosine, and tangent) to solve problems involving right triangles.

SC.G-4 Geometry: The student will demonstrate through the mathematical processes an understanding of the properties of quadrilaterals and other polygons and the relationships between and among them.

G-4.1 Carry out a procedure to compute the perimeter of quadrilaterals, regular polygons, and composite figures.

G-4.2 Carry out a procedure to find the area of quadrilaterals, regular polygons, and composite figures.

G-4.3 Apply procedures to compute measures of interior and exterior angles of polygons.

G-4.4 Analyze how changes in dimensions affect the perimeter or area of quadrilaterals and regular polygons.

G-4.5 Apply the properties and attributes of quadrilaterals and regular polygons and their component parts to solve problems.

G-4.6 Apply congruence and similarity relationships among shapes (including quadrilaterals and polygons) to solve problems.

SC.G-5 Geometry: The student will demonstrate through the mathematical processes an understanding of the properties of circles, the lines that intersect them, and the use of their special segments.

G-5.1 Carry out a procedure to compute the circumference of circles.

G-5.2 Carry out a procedure to compute the area of circles.

G-5.3 Analyze how a change in the radius affects the circumference or area of a circle.

G-5.4 Carry out a procedure to compute the length of an arc or the area of a sector of a circle.

G-5.5 Apply the properties of the component parts of a circle (including radii, diameters, chords, sectors, arcs, and segments) to solve problems.

G-5.6 Apply the properties of lines that intersect circles (including two secants, two tangents, and a secant and a tangent) to solve problems.

G-5.7 Apply the properties of central angles, inscribed angles, and arcs of circles to solve problems.

SC.G-6 Geometry: The student will demonstrate through the mathematical processes an understanding of transformations, coordinate geometry, and vectors.

G-6.1 Use the distance formula to solve problems.

G-6.2 Use the midpoint formula to solve problems.

G-6.3 Apply transformations-translation, reflection, rotation, and dilation-to figures in the coordinate plane by using sketches and coordinates.

G-6.4 Apply transformations (including translation and dilation) to figures in the coordinate plane by using matrices.

G-6.5 Carry out a procedure to represent the sum of two vectors geometrically by using the parallelogram method.

G-6.6 Carry out a procedure to determine the magnitude and direction of the resultant of two vectors by using a scale drawing and direct measurement.

G-6.7 Carry out a procedure to compute the magnitude of the resultant of two perpendicular vectors by using the Pythagorean theorem.

G-6.8 Carry out a procedure to determine the direction of the resultant of two perpendicular vectors by using a scale drawing and direct measurement.

SC.G-7 Geometry: The student will demonstrate through the mathematical processes an understanding of the surface area and volume of three-dimensional objects.

G-7.1 Carry out a procedure to compute the surface area of three-dimensional objects (including cones, cylinders, pyramids, prisms, spheres, and hemispheres).

G-7.2 Carry out a procedure to compute the volume of three-dimensional objects (including cones, cylinders, pyramids, prisms, spheres, hemispheres, and composite objects).

G-7.3 Analyze how changes in dimensions affect the volume of objects (including cylinders, prisms, and spheres).

G-7.4 Apply congruence and similarity relationships among geometric objects to solve problems.

G-7.5 Apply a procedure to draw a top view, front view, and side view of a three-dimensional object.

G-7.6 Apply a procedure to draw an isometric view of a three-dimensional object.

SC.PC-1 Precalculus: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

PC-1.1 Communicate knowledge of algebraic and trigonometric relationships by using mathematical terminology appropriately.

PC-1.2 Connect algebra and trigonometry with other branches of mathematics.

PC-1.3 Apply algebraic methods to solve problems in real-world contexts.

PC-1.4 Judge the reasonableness of mathematical solutions.

PC-1.5 Demonstrate an understanding of algebraic and trigonometric relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

PC-1.6 Understand how algebraic and trigonometric relationships can be represented in concrete models, pictorial models, and diagrams.

PC-1.7 Understand how to represent algebraic and trigonometric relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

SC.PC-2 Precalculus: The student will demonstrate through the mathematical processes an understanding of the characteristics and behaviors of functions and the effect of operations on functions.

PC-2.1 Carry out a procedure to graph parent functions (including y = x^n, y = log base a(x), y = log base n (x), y = 1/x, y = e^x, y = a^x, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

PC-2.2 Carry out a procedure to graph transformations (including -f(x), a x f(x), f(x) + d, f(x-c), f(-x), f(bx), |f(x)|, and f(|x|)) of parent functions and combinations of transformations.

PC-2.3 Analyze a graph to describe the transformation (including -f(x), a x f(x), f(x) + d, f(x-c), f(-x), f(bx), |f(x)|, and f(|x|)) of parent functions.

PC-2.4 Carry out procedures to algebraically solve equations involving parent functions or transformations of parent functions (including y = x^n, y = log base a(x), y = log base n (x), y = 1/x, y = e^x, y = a^x, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

PC-2.5 Analyze graphs, tables, and equations to determine the domain and range of parent functions or transformations of parent functions (including y = x^n, y = log base a(x), y = log base n (x), y = 1/x, y = e^x, y = a^x, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

PC-2.6 Analyze a function or the symmetry of its graph to determine whether the function is even, odd, or neither.

PC-2.7 Recognize and use connections among significant points of a function (including roots, maximum points, and minimum points), the graph of a function, and the algebraic representation of a function.

PC-2.8 Carry out a procedure to determine whether the inverse of a function exists.

PC-2.9 Carry out a procedure to write a rule for the inverse of a function, if it exists.

SC.PC-3 Precalculus: The student will demonstrate through the mathematical processes an understanding of the behaviors of polynomial and rational functions.

PC-3.1 Carry out a procedure to graph quadratic and higher-order polynomial functions by analyzing intercepts and end behavior.

PC-3.2 Apply the rational root theorem to determine a set of possible rational roots of a polynomial equation.

PC-3.3 Carry out a procedure to calculate the zeros of polynomial functions when given a set of possible zeros.

PC-3.4 Carry out procedures to determine characteristics of rational functions (including domain, range, intercepts, asymptotes, and discontinuities).

PC-3.5 Analyze given information to write a polynomial function that models a given problem situation.

PC-3.6 Carry out a procedure to solve polynomial equations algebraically.

PC-3.7 Carry out a procedure to solve polynomial equations graphically.

PC-3.8 Carry out a procedure to solve rational equations algebraically.

PC-3.9 Carry out a procedure to solve rational equations graphically.

PC-3.10 Carry out a procedure to solve polynomial inequalities algebraically.

PC-3.11 Carry out a procedure to solve polynomial inequalities graphically.

SC.PC-4 Precalculus: The student will demonstrate through the mathematical processes an understanding of the behaviors of exponential and logarithmic functions.

PC-4.1 Carry out a procedure to graph exponential functions by analyzing intercepts and end behavior.

PC-4.2 Carry out a procedure to graph logarithmic functions by analyzing intercepts and end behavior.

PC-4.3 Carry out procedures to determine characteristics of exponential functions (including domain, range, intercepts, and asymptotes).

PC-4.4 Carry out procedures to determine characteristics of logarithmic functions (including domain, range, intercepts, and asymptotes).

PC-4.5 Apply the laws of exponents to solve problems involving rational exponents.

PC-4.6 Analyze given information to write an exponential function that models a given problem situation.

PC-4.7 Apply the laws of logarithms to solve problems.

PC-4.8 Carry out a procedure to solve exponential equations algebraically.

PC-4.9 Carry out a procedure to solve exponential equations graphically.

PC-4.10 Carry out a procedure to solve logarithmic equations algebraically.

PC-4.11 Carry out a procedure to solve logarithmic equations graphically.

SC.PC-5 Precalculus: The student will demonstrate through the mathematical processes an understanding of the behaviors of trigonometric functions.

PC-5.1 Understand how angles are measured in either degrees or radians.

PC-5.2 Carry out a procedure to convert between degree and radian measures.

PC-5.3 Carry out a procedure to plot points in the polar coordinate system.

PC-5.4 Carry out a procedure to graph trigonometric functions by analyzing intercepts, periodic behavior, and graphs of reciprocal functions.

PC-5.5 Carry out procedures to determine the characteristics of trigonometric functions (including domain, range, intercepts, and asymptotes).

PC-5.6 Apply a procedure to evaluate trigonometric expressions.

PC-5.7 Analyze given information to write a trigonometric function that models a given problem situation involving periodic phenomena.

PC-5.8 Analyze given information to write a trigonometric equation that models a given problem situation involving right triangles.

PC-5.9 Carry out a procedure to calculate the area of a triangle when given the lengths of two sides and the measure of the included angle.

PC-5.10 Carry out a procedure to solve trigonometric equations algebraically.

PC-5.11 Carry out a procedure to solve trigonometric equations graphically.

PC-5.12 Apply the laws of sines and cosines to solve problems.

PC-5.13 Apply a procedure to graph the inverse functions of sine, cosine, and tangent.

PC-5.14 Apply trigonometric relationships (including reciprocal identities; Pythagorean identities; even and odd identities; addition and subtraction formulas of sine, cosine, and tangent; and double angle formulas) to verify other trigonometric identities.

PC-5.15 Carry out a procedure to compute the slope of a line when given the angle of inclination of the line.

SC.PC-6 Precalculus: The student will demonstrate through the mathematical processes an understanding of the behavior of conic sections both geometrically and algebraically.

PC-6.1 Carry out a procedure to graph the circle whose equation is the form (x - h)^2 + (y - k)^2 = r^2.

PC-6.2 Analyze given information about the center and the radius or the center and the diameter to write an equation of a circle.

PC-6.3 Apply a procedure to calculate the coordinates of points where a line intersects a circle.

PC-6.4 Carry out a procedure to graph the ellipse whose equation is the form (x -h)^2/a^2 + (y - k)^2/b^2 = 1.

PC-6.5 Carry out a procedure to graph the hyperbola whose equation is the form (x -h)^2/a^2 + (y - k)^2/b^2 = 1.

PC-6.6 Carry out a procedure to graph the parabola whose equation is the form y - k = a(x - h)^2.

SC.DA-1 Data Analysis and Probability: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

DA-1.1 Execute procedures to conduct simple probability experiments and collect data by using manipulatives (including spinners, dice, cards, and coins).

DA-1.2 Execute procedures to find measures of probability and statistics by using tools such as handheld computing devices, spreadsheets, and statistical software.

DA-1.3 Execute procedures to conduct a simulation by using random number tables and/or technology (including handheld computing devices and computers).

DA-1.4 Design and conduct a statistical research project and produce a report that summarizes the findings.

DA-1.5 Apply the principles of probability and statistics to solve problems in real-world contexts.

DA-1.6 Communicate a knowledge of data analysis and probability by using mathematical terminology appropriately.

DA-1.7 Judge the reasonableness of mathematical solutions on the basis of the source of the data, the design of the study, the way the data are displayed, and the way the data are analyzed.

DA-1.8 Compare data sets by using graphs and summary statistics.

SC.DA-2 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of the design of a statistical study.

DA-2.1 Classify a data-collection procedure as a survey, an observational study, or a controlled experiment.

DA-2.2 Compare various random sampling techniques (including simple, stratified, cluster, and systematic).

DA-2.3 Analyze a data-collection procedure to classify the technique used as either simple cluster, systematic, or convenience sampling.

DA-2.4 Critique data-collection methods and describe how bias can be controlled.

DA-2.5 Judge which of two or more possible experimental designs will best answer a given research question.

DA-2.6 Generate a research question and design a statistical study to answer a given research question.

SC.DA-3 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of the methodology for collecting, organizing, displaying, and interpreting data.

DA-3.1 Use manipulatives, random number tables, and technology to collect data and conduct experiments and simulations.

DA-3.2 Organize and interpret data by using pictographs, bar graphs, pie charts, dot plots, histograms, time-series plots, stem-and-leaf plots, box-and-whiskers plots, and scatterplots.

DA-3.3 Select appropriate graphic display(s) from among pictographs, bar graphs, pie charts, dot plots, histograms, time-series plots, stem-and-leaf plots, box-and-whiskers plots, and scatterplots when given a data set or problem situation.

DA-3.4 Represent frequency distributions by using displays such as categorical frequency distributions/Pareto charts, histograms, frequency polygons, and cumulative frequency distributions/ogives.

DA-3.5 Classify a scatterplot by shape (including linear, quadratic, and exponential).

DA-3.6 Classify graphically and analytically the correlation between two variables as either positive, negative, or zero.

DA-3.7 Carry out a procedure to determine an equation of a trend line for a scatterplot exhibiting a linear pattern by using visual approximation.

DA-3.8 Carry out a procedure using technology to determine a line of best fit for a scatterplot exhibiting a linear pattern.

DA-3.9 Explain the meaning of the correlation coefficient r.

DA-3.10 Use interpolation or extrapolation to predict values based on the relationship between two variables.

SC.DA-4 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of basic statistical methods of analyzing data.

DA-4.1 Classify a variable as either a statistic or a parameter.

DA-4.2 Compare descriptive and inferential statistics.

DA-4.3 Classify a variable as either discrete or continuous and as either categorical or quantitative.

DA-4.4 Use procedures and/or technology to find measures of central tendency (mean, median, and mode) for given data.

DA-4.5 Predict the effect of transformations of data on measures of central tendency, variability, and the shape of the distribution.

DA-4.6 Use procedures and/or technology to find measures of spread (range, variance, standard deviation, and interquartile range) and outliers for given data.

DA-4.7 Use procedures and/or technology to find measures of position (including median, quartiles, percentiles, and standard scores) for given data.

DA-4.8 Classify a distribution as either symmetric, positively skewed, or negatively skewed.

DA-4.9 Explain the significance of the shape of a distribution.

DA-4.10 Use a knowledge of the empirical rule to solve problems involving data that are distributed normally.

DA-4.11 Use control charts to determine whether a process is in control.

SC.DA-5 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of the basic concepts of probability.

DA-5.1 Construct a sample space for an experiment and represent it as a list, chart, picture, or tree diagram.

DA-5.2 Use counting techniques to determine the number of possible outcomes for an event.

DA-5.3 Classify events as either dependent or independent.

DA-5.4 Categorize two events either as mutually exclusive or as not mutually exclusive of one another.

DA-5.5 Use the concept of complementary sets to compute probabilities.

DA-5.6 Use the binomial probability distribution to solve problems.

DA-5.7 Carry out a procedure to compute simple probabilities and compound probabilities (including conditional probabilities).

DA-5.8 Use a procedure to find geometric probability in real-world contexts.

DA-5.9 Compare theoretical and experimental probabilities.

DA-5.10 Construct and compare theoretical and experimental probability distributions.

DA-5.11 Use procedures to find the expected value of discrete random variables and construct meaning within contexts.

DA-5.12 Understand the law of large numbers.

DA-5.13 Carry out a procedure to compute conditional probability by using two-way tables.

SC.EA-1 Elementary Algebra: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

EA-1.1 Communicate a knowledge of algebraic relationships by using mathematical terminology appropriately.

EA-1.2 Connect algebra with other branches of mathematics.

EA-1.3 Apply algebraic methods to solve problems in real-world contexts.

EA-1.4 Judge the reasonableness of mathematical solutions.

EA-1.5 Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

EA-1.6 Understand how algebraic relationships can be represented in concrete models, pictorial models, and diagrams.

EA-1.7 Understand how to represent algebraic relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

SC.EA-2 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of the real number system and operations involving exponents, matrices, and algebraic expressions.

EA-2.1 Exemplify elements of the real number system (including integers, rational numbers, and irrational numbers).

EA-2.2 Apply the laws of exponents and roots to solve problems.

EA-2.3 Carry out a procedure to perform operations (including multiplication and division) with numbers written in scientific notation.

EA-2.4 Use dimensional analysis to convert units of measure within a system.

EA-2.5 Carry out a procedure using the properties of real numbers (including commutative, associative, and distributive) to simplify expressions.

EA-2.6 Carry out a procedure to evaluate an expression by substituting a value for the variable.

EA-2.7 Carry out a procedure (including addition, subtraction, multiplication, and division by a monomial) to simplify polynomial expressions.

EA-2.8 Carry out a procedure to factor binomials, trinomials, and polynomials by using various techniques (including the greatest common factor, the difference between two squares, and quadratic trinomials).

EA-2.9 Carry out a procedure to perform operations with matrices (including addition, subtraction, and scalar multiplication).

EA-2.10 Represent applied problems by using matrices.

SC.EA-3 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of relationships and functions.

EA-3.1 Classify a relationship as being either a function or not a function when given data as a table, set of ordered pairs, or graph.

EA-3.2 Use function notation to represent functional relationships.

EA-3.3 Carry out a procedure to evaluate a function for a given element in the domain.

EA-3.4 Analyze the graph of a continuous function to determine the domain and range of the function.

EA-3.5 Carry out a procedure to graph parent functions (including y = x, y = x^2, y = square root of x, y = |x|, and y = 1/x).

EA-3.6 Classify a variation as either direct or inverse.

EA-3.7 Carry out a procedure to solve literal equations for a specified variable.

EA-3.8 Apply proportional reasoning to solve problems.

SC.EA-4 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of the procedures for writing and solving linear equations and inequalities.

EA-4.1 Carry out a procedure to write an equation of a line with a given slope and a y-intercept.

EA-4.2 Carry out a procedure to write an equation of a line with a given slope passing through a given point.

EA-4.3 Carry out a procedure to write an equation of a line passing through two given points.

EA-4.4 Use a procedure to write an equation of a trend line from a given scatterplot.

EA-4.5 Analyze a scatterplot to make predictions.

EA-4.6 Represent linear equations in multiple forms (including point-slope, slope-intercept, and standard).

EA-4.7 Carry out procedures to solve linear equations for one variable algebraically.

EA-4.8 Carry out procedures to solve linear inequalities for one variable algebraically and then to graph the solution.

EA-4.9 Carry out a procedure to solve systems of two linear equations graphically.

EA-4.10 Carry out a procedure to solve systems of two linear equations algebraically.

SC.EA-5 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of the graphs and characteristics of linear equations and inequalities.

EA-5.1 Carry out a procedure to graph a line when given the equation of the line.

EA-5.2 Analyze the effects of changes in the slope, m, and the y-intercept, b, on the graph of y = mx + b.

EA-5.3 Carry out a procedure to graph the line with a given slope and a y-intercept.

EA-5.4 Carry out a procedure to graph the line with a given slope passing through a given point.

EA-5.5 Carry out a procedure to determine the x-intercept and y-intercept of lines from data given tabularly, graphically, symbolically, and verbally.

EA-5.6 Carry out a procedure to determine the slope of a line from data given tabularly, graphically, symbolically, and verbally.

EA-5.7 Apply the concept of slope as a rate of change to solve problems.

EA-5.8 Analyze the equations of two lines to determine whether the lines are perpendicular or parallel.

EA-5.9 Analyze given information to write a linear function that models a given problem situation.

EA-5.10 Analyze given information to determine the domain and range of a linear function in a problem situation.

EA-5.11 Analyze given information to write a system of linear equations that models a given problem situation.

EA-5.12 Analyze given information to write a linear inequality in one variable that models a given problem situation.

SC.EA-6 Elementary Algebra: The student will demonstrate through the mathematical processes an understanding of quadratic relationships and functions.

EA-6.1 Analyze the effects of changing the leading coefficient a on the graph of y = ax^2.

EA-6.2 Analyze the effects of changing the constant c on the graph of y = x^2 + c.

EA-6.3 Analyze the graph of a quadratic function to determine its equation.

EA-6.4 Carry out a procedure to solve quadratic equations by factoring.

EA-6.5 Carry out a graphic procedure to approximate the solutions of quadratic equations.

EA-6.6 Analyze given information to determine the domain of a quadratic function in a problem situation.

SC.IA-1 Intermediate Algebra: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

IA-1.1 Communicate a knowledge of algebraic relationships by using mathematical terminology appropriately.

IA-1.2 Connect algebra with other branches of mathematics.

IA-1.3 Apply algebraic methods to solve problems in real-world contexts.

IA-1.4 Judge the reasonableness of mathematical solutions.

IA-1.5 Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

IA-1.6 Understand how algebraic relationships can be represented in concrete models, pictorial models, and diagrams.

IA-1.7 Understand how to represent algebraic relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

SC.IA-2 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of functions, systems of equations, and systems of linear inequalities.

IA-2.1 Carry out a procedure to solve a system of linear inequalities algebraically.

IA-2.2 Carry out a procedure to solve a system of linear inequalities graphically.

IA-2.3 Analyze a problem situation to determine a system of linear inequalities that models the problem situation.

IA-2.4 Use linear programming to solve contextual problems involving a system of linear inequalities.

IA-2.5 Carry out procedures to perform operations on polynomial functions (including f(x) + g(x), f(x) - g(x), f(x) x g(x), and f(x)/g(x)).

IA-2.6 Apply a procedure to write the equation of a composition of given functions.

IA-2.7 Carry out a procedure to graph translations of parent functions (including y = x, y = x^2, y = square root of x, y = |x|, and y = 1/x).

IA-2.8 Carry out a procedure to graph transformations of parent functions (including y = x, y = x^2, y = square root of x, y = |x|.

IA-2.9 Carry out a procedure to graph discontinuous functions (including piecewise and step functions).

IA-2.10 Carry out a procedure to determine the domain and range of discontinuous functions (including piecewise and step functions).

IA-2.11 Carry out a procedure to solve a system of equations (including two linear functions and one linear function with one quadratic function).

SC.IA-3 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of quadratic equations and the complex number system.

IA-3.1 Carry out a procedure to simplify expressions involving powers of i.

IA-3.2 Carry out a procedure to perform operations with complex numbers (including addition, subtraction, multiplication, and division).

IA-3.3 Carry out a procedure to solve quadratic equations algebraically (including factoring, completing the square, and applying the quadratic formula).

IA-3.4 Use the discriminant to determine the number and type of solutions of a quadratic equation.

IA-3.5 Analyze given information (including quadratic models) to solve contextual problems.

IA-3.6 Carry out a procedure to write an equation of a quadratic function when given its roots.

SC.IA-4 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of algebraic expressions and nonlinear functions.

IA-4.1 Carry out a procedure to perform operations (including multiplication, exponentiation, and division) with polynomial expressions.

IA-4.2 Carry out a procedure to determine specified points (including zeros, maximums, and minimums) of polynomial functions.

IA-4.3 Carry out a procedure to solve polynomial equations (including factoring by grouping, factoring the difference between two squares, factoring the sum of two cubes, and factoring the difference between two cubes).

IA-4.4 Analyze given information (including polynomial models) to solve contextual problems.

IA-4.5 Carry out a procedure to simplify algebraic expressions involving rational exponents.

IA-4.6 Carry out a procedure to simplify algebraic expressions involving logarithms.

IA-4.7 Carry out a procedure to perform operations with expressions involving rational exponents (including addition, subtraction, multiplication, division, and exponentiation).

IA-4.8 Carry out a procedure to perform operations with rational expressions (including addition, subtraction, multiplication, and division).

IA-4.9 Carry out a procedure to solve radical equations algebraically.

IA-4.10 Carry out a procedure to solve logarithmic equations algebraically.

IA-4.11 Carry out a procedure to solve logarithmic equations graphically.

IA-4.12 Carry out a procedure to solve rational equations algebraically.

IA-4.13 Carry out a procedure to graph logarithmic functions.

IA-4.14 Carry out a procedure to graph exponential functions.

SC.IA-5 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of conic sections.

IA-5.1 Carry out a procedure to graph the circle whose equation is the form x^2 + y^2 = r^2.

IA-5.2 Carry out a procedure to write an equation of a circle centered at the origin when given its radius.

IA-5.3 Carry out a procedure to graph the ellipse whose equation is the form x^2/a^2 + y^2/b^2 = 1.

IA-5.4 Carry out a procedure to write an equation of an ellipse centered at the origin when given information from among length of major axis, length of minor axis, and vertices.

IA-5.5 Carry out a procedure to graph the hyperbola whose equation is the form x^2/a^2 + y^2/b^2 = 1.

IA-5.6 Carry out a procedure to write an equation of a hyperbola centered at the origin with specified vertices.

IA-5.7 Match the equation of a conic section with its graph.

SC.IA-6 Intermediate Algebra: The student will demonstrate through the mathematical processes an understanding of sequences and series.

IA-6.1 Categorize a sequence as arithmetic, geometric, or neither.

IA-6.2 Carry out a procedure to write a specified term of an arithmetic or geometric sequence when given the nth term of the sequence.

IA-6.3 Carry out a procedure to write a formula for the nth term of an arithmetic or geometric sequence when given at least four consecutive terms of the sequence.

IA-6.4 Carry out a procedure to write a formula for the nth term of an arithmetic or geometric sequence when given at least four terms of the sequence.

IA-6.5 Represent an arithmetic or geometric series by using sigma notation.

IA-6.6 Carry out a procedure to calculate the sum of an arithmetic or geometric series written in sigma notation.

IA-6.7 Carry out a procedure to determine consecutive terms of a sequence that is defined recursively.

IA-6.8 Carry out a procedure to define a sequence recursively when given four or more consecutive terms of the sequence.

IA-6.9 Translate between the explicit form and the recursive form of sequences.

SC.G-1 Geometry: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

G-1.1 Demonstrate an understanding of the axiomatic structure of geometry by using undefined terms, definitions, postulates, theorems, and corollaries.

G-1.2 Communicate knowledge of geometric relationships by using mathematical terminology appropriately.

G-1.3 Apply basic rules of logic to determine the validity of the converse, inverse, and contrapositive of a conditional statement.

G-1.4 Formulate and test conjectures by using a variety of tools such as concrete models, graphing calculators, spreadsheets, and dynamic geometry software.

G-1.5 Use inductive reasoning to formulate conjectures.

G-1.6 Use deductive reasoning to validate conjectures with formal and informal proofs, and give counterexamples to disprove a statement.

G-1.7 Understand the historical development of geometry.

G-1.8 Connect geometry with other branches of mathematics.

G-1.9 Demonstrate an understanding of how geometry applies to in real-world contexts (including architecture, construction, farming, and astronomy).

G-1.10 Demonstrate an understanding of geometric relationships (including constructions through investigations by using a variety of tools such as straightedge, compass, Patty Paper, dynamic geometry software, and handheld computing devices).

SC.G-2 Geometry: The student will demonstrate through the mathematical processes an understanding of the properties of basic geometric figures and the relationships between and among them.

G-2.1 Infer missing elements of visual or numerical geometric patterns (including triangular and rectangular numbers and the number of diagonals in polygons).

G-2.2 Apply properties of parallel lines, intersecting lines, and parallel lines cut by a transversal to solve problems.

G-2.3 Use the congruence of line segments and angles to solve problems.

G-2.4 Use direct measurement to determine the length of a segment, degree of an angle, and distance from a point to a line.

G-2.5 Carry out a procedure to create geometric constructions (including the midpoint of a line segment, the angle bisector, the perpendicular bisector of a line segment, the line through a given point that is parallel to a given line, and the line through a given point that is perpendicular to a given line).

G-2.6 Use scale factors to solve problems involving scale drawings and models.

G-2.7 Use geometric probability to solve problems.

SC.G-3 Geometry: The student will demonstrate through the mathematical processes an understanding of the properties and special segments of triangles and the relationships between and among triangles.

G-3.1 Carry out a procedure to compute the perimeter of a triangle.

G-3.2 Carry out a procedure to compute the area of a triangle.

G-3.3 Analyze how changes in dimensions affect the perimeter or area of triangles.

G-3.4 Apply properties of isosceles and equilateral triangles to solve problems.

G-3.5 Use interior angles, exterior angles, medians, angle bisectors, altitudes, and perpendicular bisectors to solve problems.

G-3.6 Apply the triangle sum theorem to solve problems.

G-3.7 Apply the triangle inequality theorem to solve problems.

G-3.8 Apply congruence and similarity relationships among triangles to solve problems.

G-3.9 Apply theorems to prove that triangles are either similar or congruent.

G-3.10 Use the Pythagorean theorem and its converse to solve problems.

G-3.11 Use the properties of 45-45-90 and 30-60-90 triangles to solve problems.

G-3.12 Use trigonometric ratios (including sine, cosine, and tangent) to solve problems involving right triangles.

SC.G-4 Geometry: The student will demonstrate through the mathematical processes an understanding of the properties of quadrilaterals and other polygons and the relationships between and among them.

G-4.1 Carry out a procedure to compute the perimeter of quadrilaterals, regular polygons, and composite figures.

G-4.2 Carry out a procedure to find the area of quadrilaterals, regular polygons, and composite figures.

G-4.3 Apply procedures to compute measures of interior and exterior angles of polygons.

G-4.4 Analyze how changes in dimensions affect the perimeter or area of quadrilaterals and regular polygons.

G-4.5 Apply the properties and attributes of quadrilaterals and regular polygons and their component parts to solve problems.

G-4.6 Apply congruence and similarity relationships among shapes (including quadrilaterals and polygons) to solve problems.

SC.G-5 Geometry: The student will demonstrate through the mathematical processes an understanding of the properties of circles, the lines that intersect them, and the use of their special segments.

G-5.1 Carry out a procedure to compute the circumference of circles.

G-5.2 Carry out a procedure to compute the area of circles.

G-5.3 Analyze how a change in the radius affects the circumference or area of a circle.

G-5.4 Carry out a procedure to compute the length of an arc or the area of a sector of a circle.

G-5.5 Apply the properties of the component parts of a circle (including radii, diameters, chords, sectors, arcs, and segments) to solve problems.

G-5.6 Apply the properties of lines that intersect circles (including two secants, two tangents, and a secant and a tangent) to solve problems.

G-5.7 Apply the properties of central angles, inscribed angles, and arcs of circles to solve problems.

SC.G-6 Geometry: The student will demonstrate through the mathematical processes an understanding of transformations, coordinate geometry, and vectors.

G-6.1 Use the distance formula to solve problems.

G-6.2 Use the midpoint formula to solve problems.

G-6.3 Apply transformations-translation, reflection, rotation, and dilation-to figures in the coordinate plane by using sketches and coordinates.

G-6.4 Apply transformations (including translation and dilation) to figures in the coordinate plane by using matrices.

G-6.5 Carry out a procedure to represent the sum of two vectors geometrically by using the parallelogram method.

G-6.6 Carry out a procedure to determine the magnitude and direction of the resultant of two vectors by using a scale drawing and direct measurement.

G-6.7 Carry out a procedure to compute the magnitude of the resultant of two perpendicular vectors by using the Pythagorean theorem.

G-6.8 Carry out a procedure to determine the direction of the resultant of two perpendicular vectors by using a scale drawing and direct measurement.

SC.G-7 Geometry: The student will demonstrate through the mathematical processes an understanding of the surface area and volume of three-dimensional objects.

G-7.1 Carry out a procedure to compute the surface area of three-dimensional objects (including cones, cylinders, pyramids, prisms, spheres, and hemispheres).

G-7.2 Carry out a procedure to compute the volume of three-dimensional objects (including cones, cylinders, pyramids, prisms, spheres, hemispheres, and composite objects).

G-7.3 Analyze how changes in dimensions affect the volume of objects (including cylinders, prisms, and spheres).

G-7.4 Apply congruence and similarity relationships among geometric objects to solve problems.

G-7.5 Apply a procedure to draw a top view, front view, and side view of a three-dimensional object.

G-7.6 Apply a procedure to draw an isometric view of a three-dimensional object.

SC.PC-1 Precalculus: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

PC-1.1 Communicate knowledge of algebraic and trigonometric relationships by using mathematical terminology appropriately.

PC-1.2 Connect algebra and trigonometry with other branches of mathematics.

PC-1.3 Apply algebraic methods to solve problems in real-world contexts.

PC-1.4 Judge the reasonableness of mathematical solutions.

PC-1.5 Demonstrate an understanding of algebraic and trigonometric relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

PC-1.6 Understand how algebraic and trigonometric relationships can be represented in concrete models, pictorial models, and diagrams.

PC-1.7 Understand how to represent algebraic and trigonometric relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

SC.PC-2 Precalculus: The student will demonstrate through the mathematical processes an understanding of the characteristics and behaviors of functions and the effect of operations on functions.

PC-2.1 Carry out a procedure to graph parent functions (including y = x^n, y = log base a(x), y = log base n (x), y = 1/x, y = e^x, y = a^x, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

PC-2.2 Carry out a procedure to graph transformations (including -f(x), a x f(x), f(x) + d, f(x-c), f(-x), f(bx), |f(x)|, and f(|x|)) of parent functions and combinations of transformations.

PC-2.3 Analyze a graph to describe the transformation (including -f(x), a x f(x), f(x) + d, f(x-c), f(-x), f(bx), |f(x)|, and f(|x|)) of parent functions.

PC-2.4 Carry out procedures to algebraically solve equations involving parent functions or transformations of parent functions (including y = x^n, y = log base a(x), y = log base n (x), y = 1/x, y = e^x, y = a^x, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

PC-2.5 Analyze graphs, tables, and equations to determine the domain and range of parent functions or transformations of parent functions (including y = x^n, y = log base a(x), y = log base n (x), y = 1/x, y = e^x, y = a^x, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

PC-2.6 Analyze a function or the symmetry of its graph to determine whether the function is even, odd, or neither.

PC-2.7 Recognize and use connections among significant points of a function (including roots, maximum points, and minimum points), the graph of a function, and the algebraic representation of a function.

PC-2.8 Carry out a procedure to determine whether the inverse of a function exists.

PC-2.9 Carry out a procedure to write a rule for the inverse of a function, if it exists.

SC.PC-3 Precalculus: The student will demonstrate through the mathematical processes an understanding of the behaviors of polynomial and rational functions.

PC-3.1 Carry out a procedure to graph quadratic and higher-order polynomial functions by analyzing intercepts and end behavior.

PC-3.2 Apply the rational root theorem to determine a set of possible rational roots of a polynomial equation.

PC-3.3 Carry out a procedure to calculate the zeros of polynomial functions when given a set of possible zeros.

PC-3.4 Carry out procedures to determine characteristics of rational functions (including domain, range, intercepts, asymptotes, and discontinuities).

PC-3.5 Analyze given information to write a polynomial function that models a given problem situation.

PC-3.6 Carry out a procedure to solve polynomial equations algebraically.

PC-3.7 Carry out a procedure to solve polynomial equations graphically.

PC-3.8 Carry out a procedure to solve rational equations algebraically.

PC-3.9 Carry out a procedure to solve rational equations graphically.

PC-3.10 Carry out a procedure to solve polynomial inequalities algebraically.

PC-3.11 Carry out a procedure to solve polynomial inequalities graphically.

SC.PC-4 Precalculus: The student will demonstrate through the mathematical processes an understanding of the behaviors of exponential and logarithmic functions.

PC-4.1 Carry out a procedure to graph exponential functions by analyzing intercepts and end behavior.

PC-4.2 Carry out a procedure to graph logarithmic functions by analyzing intercepts and end behavior.

PC-4.3 Carry out procedures to determine characteristics of exponential functions (including domain, range, intercepts, and asymptotes).

PC-4.4 Carry out procedures to determine characteristics of logarithmic functions (including domain, range, intercepts, and asymptotes).

PC-4.5 Apply the laws of exponents to solve problems involving rational exponents.

PC-4.6 Analyze given information to write an exponential function that models a given problem situation.

PC-4.7 Apply the laws of logarithms to solve problems.

PC-4.8 Carry out a procedure to solve exponential equations algebraically.

PC-4.9 Carry out a procedure to solve exponential equations graphically.

PC-4.10 Carry out a procedure to solve logarithmic equations algebraically.

PC-4.11 Carry out a procedure to solve logarithmic equations graphically.

SC.PC-5 Precalculus: The student will demonstrate through the mathematical processes an understanding of the behaviors of trigonometric functions.

PC-5.1 Understand how angles are measured in either degrees or radians.

PC-5.2 Carry out a procedure to convert between degree and radian measures.

PC-5.3 Carry out a procedure to plot points in the polar coordinate system.

PC-5.4 Carry out a procedure to graph trigonometric functions by analyzing intercepts, periodic behavior, and graphs of reciprocal functions.

PC-5.5 Carry out procedures to determine the characteristics of trigonometric functions (including domain, range, intercepts, and asymptotes).

PC-5.6 Apply a procedure to evaluate trigonometric expressions.

PC-5.7 Analyze given information to write a trigonometric function that models a given problem situation involving periodic phenomena.

PC-5.8 Analyze given information to write a trigonometric equation that models a given problem situation involving right triangles.

PC-5.9 Carry out a procedure to calculate the area of a triangle when given the lengths of two sides and the measure of the included angle.

PC-5.10 Carry out a procedure to solve trigonometric equations algebraically.

PC-5.11 Carry out a procedure to solve trigonometric equations graphically.

PC-5.12 Apply the laws of sines and cosines to solve problems.

PC-5.13 Apply a procedure to graph the inverse functions of sine, cosine, and tangent.

PC-5.14 Apply trigonometric relationships (including reciprocal identities; Pythagorean identities; even and odd identities; addition and subtraction formulas of sine, cosine, and tangent; and double angle formulas) to verify other trigonometric identities.

PC-5.15 Carry out a procedure to compute the slope of a line when given the angle of inclination of the line.

SC.PC-6 Precalculus: The student will demonstrate through the mathematical processes an understanding of the behavior of conic sections both geometrically and algebraically.

PC-6.1 Carry out a procedure to graph the circle whose equation is the form (x - h)^2 + (y - k)^2 = r^2.

PC-6.2 Analyze given information about the center and the radius or the center and the diameter to write an equation of a circle.

PC-6.3 Apply a procedure to calculate the coordinates of points where a line intersects a circle.

PC-6.4 Carry out a procedure to graph the ellipse whose equation is the form (x -h)^2/a^2 + (y - k)^2/b^2 = 1.

PC-6.5 Carry out a procedure to graph the hyperbola whose equation is the form (x -h)^2/a^2 + (y - k)^2/b^2 = 1.

PC-6.6 Carry out a procedure to graph the parabola whose equation is the form y - k = a(x - h)^2.

SC.DA-1 Data Analysis and Probability: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

DA-1.1 Execute procedures to conduct simple probability experiments and collect data by using manipulatives (including spinners, dice, cards, and coins).

DA-1.2 Execute procedures to find measures of probability and statistics by using tools such as handheld computing devices, spreadsheets, and statistical software.

DA-1.3 Execute procedures to conduct a simulation by using random number tables and/or technology (including handheld computing devices and computers).

DA-1.4 Design and conduct a statistical research project and produce a report that summarizes the findings.

DA-1.5 Apply the principles of probability and statistics to solve problems in real-world contexts.

DA-1.6 Communicate a knowledge of data analysis and probability by using mathematical terminology appropriately.

DA-1.7 Judge the reasonableness of mathematical solutions on the basis of the source of the data, the design of the study, the way the data are displayed, and the way the data are analyzed.

DA-1.8 Compare data sets by using graphs and summary statistics.

SC.DA-2 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of the design of a statistical study.

DA-2.1 Classify a data-collection procedure as a survey, an observational study, or a controlled experiment.

DA-2.2 Compare various random sampling techniques (including simple, stratified, cluster, and systematic).

DA-2.3 Analyze a data-collection procedure to classify the technique used as either simple cluster, systematic, or convenience sampling.

DA-2.4 Critique data-collection methods and describe how bias can be controlled.

DA-2.5 Judge which of two or more possible experimental designs will best answer a given research question.

DA-2.6 Generate a research question and design a statistical study to answer a given research question.

SC.DA-3 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of the methodology for collecting, organizing, displaying, and interpreting data.

DA-3.1 Use manipulatives, random number tables, and technology to collect data and conduct experiments and simulations.

DA-3.2 Organize and interpret data by using pictographs, bar graphs, pie charts, dot plots, histograms, time-series plots, stem-and-leaf plots, box-and-whiskers plots, and scatterplots.

DA-3.3 Select appropriate graphic display(s) from among pictographs, bar graphs, pie charts, dot plots, histograms, time-series plots, stem-and-leaf plots, box-and-whiskers plots, and scatterplots when given a data set or problem situation.

DA-3.4 Represent frequency distributions by using displays such as categorical frequency distributions/Pareto charts, histograms, frequency polygons, and cumulative frequency distributions/ogives.

DA-3.5 Classify a scatterplot by shape (including linear, quadratic, and exponential).

DA-3.6 Classify graphically and analytically the correlation between two variables as either positive, negative, or zero.

DA-3.7 Carry out a procedure to determine an equation of a trend line for a scatterplot exhibiting a linear pattern by using visual approximation.

DA-3.8 Carry out a procedure using technology to determine a line of best fit for a scatterplot exhibiting a linear pattern.

DA-3.9 Explain the meaning of the correlation coefficient r.

DA-3.10 Use interpolation or extrapolation to predict values based on the relationship between two variables.

SC.DA-4 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of basic statistical methods of analyzing data.

DA-4.1 Classify a variable as either a statistic or a parameter.

DA-4.2 Compare descriptive and inferential statistics.

DA-4.3 Classify a variable as either discrete or continuous and as either categorical or quantitative.

DA-4.4 Use procedures and/or technology to find measures of central tendency (mean, median, and mode) for given data.

DA-4.5 Predict the effect of transformations of data on measures of central tendency, variability, and the shape of the distribution.

DA-4.6 Use procedures and/or technology to find measures of spread (range, variance, standard deviation, and interquartile range) and outliers for given data.

DA-4.7 Use procedures and/or technology to find measures of position (including median, quartiles, percentiles, and standard scores) for given data.

DA-4.8 Classify a distribution as either symmetric, positively skewed, or negatively skewed.

DA-4.9 Explain the significance of the shape of a distribution.

DA-4.10 Use a knowledge of the empirical rule to solve problems involving data that are distributed normally.

DA-4.11 Use control charts to determine whether a process is in control.

SC.DA-5 Data Analysis and Probability: The student will demonstrate through the mathematical processes an understanding of the basic concepts of probability.

DA-5.1 Construct a sample space for an experiment and represent it as a list, chart, picture, or tree diagram.

DA-5.2 Use counting techniques to determine the number of possible outcomes for an event.

DA-5.3 Classify events as either dependent or independent.

DA-5.4 Categorize two events either as mutually exclusive or as not mutually exclusive of one another.

DA-5.5 Use the concept of complementary sets to compute probabilities.

DA-5.6 Use the binomial probability distribution to solve problems.

DA-5.7 Carry out a procedure to compute simple probabilities and compound probabilities (including conditional probabilities).

DA-5.8 Use a procedure to find geometric probability in real-world contexts.

DA-5.9 Compare theoretical and experimental probabilities.

DA-5.10 Construct and compare theoretical and experimental probability distributions.

DA-5.11 Use procedures to find the expected value of discrete random variables and construct meaning within contexts.

DA-5.12 Understand the law of large numbers.

DA-5.13 Carry out a procedure to compute conditional probability by using two-way tables.