Texas State Standards for Mathematics:

TX.111.12 (K.1) Number, operation, and quantitative reasoning. The student uses numbers to name quantities.

K.1) (A) The student is expected to use one-to-one correspondence and language such as more than, same number as, or two less than to describe relative sizes of sets of concrete objects.

K.1) (B) The student is expected to use sets of concrete objects to represent quantities given in verbal or written form (through 20).

K.1) (C) The student is expected to use numbers to describe how many objects are in a set (through 20) using verbal and symbolic descriptions.

TX.111.12 (K.2) Number, operation, and quantitative reasoning. The student describes order of events or objects.

K.2) (A) The student is expected to use language such as before or after to describe relative position in a sequence of events or objects.

K.2) (B) The student is expected to name the ordinal positions in a sequence such as first, second, third, etc.

TX.111.12 (K.3) Number, operation, and quantitative reasoning. The student recognizes that there are quantities less than a whole.

K.3) (A) The student is expected to share a whole by separating it into two equal parts.

K.3) (B) The student is expected to explain why a given part is half of the whole.

TX.111.12 (K.4) Number, operation, and quantitative reasoning. The student models addition (joining) and subtraction (separating).

K.4) (A) The student is expected to model and create addition and subtraction problems in real situations with concrete objects.

TX.111.12 (K.5) Patterns, relationships, and algebraic thinking. The student identifies, extends, and creates patterns.

K.5) (A) The student is expected to identify, extend, and create patterns of sounds, physical movement, and concrete objects.

TX.111.12 (K.6) Patterns, relationships, and algebraic thinking. The student uses patterns to make predictions.

K.6) (A) The student is expected to use patterns to predict what comes next, including cause-and-effect relationships.

K.6) (B) The student is expected to count by ones to 100.

TX.111.12 (K.7) Geometry and spatial reasoning. The student describes the relative positions of objects.

K.7) (A) The student is expected to describe one object in relation to another using informal language such as over, under, above, and below.

K.7) (B) The student is expected to place an object in a specified position.

TX.111.12 (K.8) Geometry and spatial reasoning. The student uses attributes to determine how objects are alike and different.

K.8) (A) The student is expected to describe and identify an object by its attributes using informal language.

K.8) (B) The student is expected to compare two objects based on their attributes.

K.8) (C) The student is expected to sort a variety of objects including two- and three-dimensional geometric figures according to their attributes and describe how the objects are sorted.

TX.111.12 (K.9) Geometry and spatial reasoning. The student recognizes attributes of two- and three-dimensional geometric figures.

K.9) (A) The student is expected to describe and compare the attributes of real-life objects such as balls, boxes, cans, and cones or models of three-dimensional geometric figures.

K.9) (B) The student is expected to recognize shapes in real-life three-dimensional geometric figures or models of three-dimensional geometric figures.

K.9) (C) The student is expected to describe, identify, and compare circles, triangles, rectangles, and squares (a special type of rectangle).

TX.111.12 (K.10) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and/or relative temperature. The student uses comparative language to solve problems and answer questions.

K.10) (A) The student is expected to compare and order two or three concrete objects according to length (longer/shorter than, or the same).

K.10) (B) The student is expected to compare the areas of two flat surfaces of two-dimensional figures (covers more, covers less, or covers the same).

K.10) (C) The student is expected to compare two containers according to capacity (holds more, holds less, or holds the same).

K.10) (D) The student is expected to compare two objects according to weight/mass (heavier than, lighter than or equal to).

K.10) (E) The student is expected to compare situations or objects according to relative temperature (hotter/colder than, or the same as).

TX.111.12 (K.11) Measurement. The student uses time to describe, compare, and order events and situations.

K.11) (A) The student is expected to compare events according to duration such as more time than or less time than.

K.11) (B) The student is expected to sequence events (up to three).

K.11) (C) The student is expected to read a calendar using days, weeks, and months.

TX.111.12 (K.12) Probability and statistics. The student constructs and uses graphs of real objects or pictures to answer questions.

K.12) (A) The student is expected to construct graphs using real objects or pictures in order to answer questions.

K.12) (B) The student is expected to use information from a graph of real objects or pictures in order to answer questions.

TX.111.12 (K.13) Underlying processes and mathematical tools. The student applies Kindergarten mathematics to solve problems connected to everyday experiences and activities in and outside of school.

K.13) (A) The student is expected to identify mathematics in everyday situations.

K.13) (B) The student is expected to solve problems with guidance that incorporates the processes of understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.

K.13) (C) The student is expected to select or develop an appropriate problem-solving strategy including drawing a picture, looking for a pattern, systematic guessing and checking, or acting it out in order to solve a problem.

K.13) (D) The student is expected to use tools such as real objects, manipulatives, and technology to solve problems.

TX.111.12 (K.14) Underlying processes and mathematical tools. The student communicates about Kindergarten mathematics using informal language.

K.14) (A) The student is expected to communicate mathematical ideas using objects, words, pictures, numbers, and technology.

K.14) (B) The student is expected to relate everyday language to mathematical language and symbols.

TX.111.12 (K.15) Underlying processes and mathematical tools. The student uses logical reasoning.

K.15) (A) The student is expected to justify his or her thinking using objects, words, pictures, numbers, and technology.

TX.111.13 (1.1) Number, operation, and quantitative reasoning. The student uses whole numbers to describe and compare quantities.

(1.1) (A) The student is expected to compare and order whole numbers up to 99 (less than, greater than, or equal to) using sets of concrete objects and pictorial models.

(1.1) (B) The student is expected to create sets of tens and ones using concrete objects to describe, compare, and order whole numbers.

(1.1) (C) The student is expected to identify individual coins by name and value and describe relationships among them.

(1.1) (D) The student is expected to read and write numbers to 99 to describe sets of concrete objects.

TX.111.13 (1.2) Number, operation, and quantitative reasoning. The student uses pairs of whole numbers to describe fractional parts of whole objects or sets of objects.

(1.2) (A) The student is expected to separate a whole into two, three, or four equal parts and use appropriate language to describe the parts such as three out of four equal parts.

(1.2) (B) The student is expected to use appropriate language to describe part of a set such as three out of the eight crayons are red.

TX.111.13 (1.3) Number, operation, and quantitative reasoning. The student recognizes and solves problems in addition and subtraction situations.

(1.3) (A) The student is expected to model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences.

(1.3) (B) The student is expected to use concrete and pictorial models to apply basic addition and subtraction facts (up to 9 + 9 = 18 and 18 - 9 = 9).

TX.111.13 (1.4) Patterns, relationships, and algebraic thinking. The student uses repeating patterns and additive patterns to make predictions.

(1.4) (A) The student is expected to identify, describe, and extend concrete and pictorial patterns in order to make predictions and solve problems.

TX.111.13 (1.5) Patterns, relationships, and algebraic thinking. The student recognizes patterns in numbers and operations.

(1.5) (A) The student is expected to use patterns to skip count by twos, fives, and tens.

(1.5) (B) The student is expected to find patterns in numbers, including odd and even.

(1.5) (C) The student is expected to compare and order whole numbers using place value.

(1.5) (D) The student is expected to use patterns to develop strategies to solve basic addition and basic subtraction problems.

(1.5) (E) The student is expected to identify patterns in related addition and subtraction sentences (fact families for sums to 18) such as 2 + 3 = 5, 3 + 2 = 5, 5 - 2 = 3, and 5 - 3 = 2.

TX.111.13 (1.6) Geometry and spatial reasoning. The student uses attributes to identify two- and three-dimensional geometric figures. The student compares and contrasts two- and three-dimensional geometric figures or both.

(1.6) (A) The student is expected to describe and identify two-dimensional geometric figures, including circles, triangles, rectangles, and squares (a special type of rectangle).

(1.6) (B) The student is expected to describe and identify three-dimensional geometric figures, including spheres, rectangular prisms (including cubes), cylinders, and cones.

(1.6) (C) The student is expected to describe and identify two- and three-dimensional geometric figures in order to sort them according to a given attribute using informal and formal language.

(1.6) (D) The student is expected to use concrete models to combine two-dimensional geometric figures to make new geometric figures.

TX.111.13 (1.7) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and temperature. The student uses comparative language to solve problems and answer questions. The student selects and uses nonstandard units to describe length.

(1.7) (A) The student is expected to estimate and measure length using nonstandard units such as paper clips or sides of color tiles.

(1.7) (B) The student is expected to compare and order two or more concrete objects according to length (from longest to shortest).

(1.7) (C) The student is expected to describe the relationship between the size of the unit and the number of units needed to measure the length of an object.

(1.7) (D) The student is expected to compare and order the area of two or more two-dimensional surfaces (from covers the most to covers the least).

(1.7) (E) The student is expected to compare and order two or more containers according to capacity (from holds the most to holds the least).

(1.7) (F) The student is expected to compare and order two or more objects according to weight/mass (from heaviest to lightest).

(1.7) (G) The student is expected to compare and order two or more objects according to relative temperature (from hottest to coldest).

TX.111.13 (1.8) Measurement. The student understands that time can be measured. The student uses time to describe and compare situations.

(1.8) (A) The student is expected to order three or more events according to duration.

(1.8) (B) The student is expected to read time to the hour and half-hour using analog and digital clocks.

TX.111.13 (1.9) Probability and statistics. The student displays data in an organized form.

(1.9) (A) The student is expected to collect and sort data.

(1.9) (B) The student is expected to use organized data to construct real object graphs, picture graphs, and bar type graphs.

TX.111.13 (1.10) Probability and statistics. The student uses information from organized data.

(1.10) (A) The student is expected to draw conclusions and answer questions using information organized in real-object graphs, picture graphs, and bar-type graphs.

(1.10) (B) The student is expected to identify events as certain or impossible such as drawing a red crayon from a bag of green crayons.

TX.111.13 (1.11) Underlying processes and mathematical tools. The student applies Grade 1 mathematics to solve problems connected to everyday experiences and activities in and outside of school.

(1.11) (A) The student is expected to identify mathematics in everyday situations.

(1.11) (B) The student is expected to solve problems with guidance that incorporates the processes of understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.

(1.11) (C) The student is expected to select or develop an appropriate problem-solving plan or strategy including drawing a picture, looking for a pattern, systematic guessing and checking, or acting it out in order to solve a problem.

(1.11) (D) The student is expected to use tools such as real objects, manipulatives, and technology to solve problems.

TX.111.13 (1.12) Underlying processes and mathematical tools. The student communicates about Grade 1 mathematics using informal language.

(1.12) (A) The student is expected to explain and record observations using objects, words, pictures, numbers, and technology.

(1.12) (B) The student is expected to relate informal language to mathematical language and symbols.

TX.111.13 (1.13) Underlying processes and mathematical tools. The student uses logical reasoning.

(1.13) (A) The student is expected to justify his or her thinking using objects, words, pictures, numbers, and technology.

TX.111.14 (2.1) Number, operation, and quantitative reasoning. The student understands how place value is used to represent whole numbers.

(2.1) (A) The student is expected to use concrete models of hundreds, tens, and ones to represent a given whole number (up to 999) in various ways.

(2.1) (B) The student is expected to use place value to read, write, and describe the value of whole numbers to 999.

(2.1) (C) The student is expected to use place value to compare and order whole numbers to 999 and record the comparisons using numbers and symbols (<, =, >).

TX.111.14 (2.2) Number, operation, and quantitative reasoning. The student describes how fractions are used to name parts of whole objects or sets of objects.

(2.2) (A) The student is expected to use concrete models to represent and name fractional parts of a whole object (with denominators of 12 or less).

(2.2) (B) The student is expected to use concrete models to represent and name fractional parts of a set of objects (with denominators of 12 or less).

(2.2) (C) The student is expected to use concrete models to determine if a fractional part of a whole is closer to 0, 1/2 or 1.

TX.111.14 (2.3) Number, operation, and quantitative reasoning. The student adds and subtracts whole numbers to solve problems.

(2.3) (A) The student is expected to recall and apply basic addition and subtraction facts to 18.

(2.3) (B) The student is expected to model addition and subtraction of two digit numbers with objects, pictures, words, and numbers.

(2.3) (C) The student is expected to select addition or subtraction to solve problems using two-digit numbers, whether or not regrouping is necessary.

(2.3) (D) The student is expected to determine the value of a collection of coins up to one dollar.

(2.3) (E) The student is expected to describe how the cent symbol, dollar symbol, and the decimal point are used to name the value of a collection of coins.

TX.111.14 (2.4) Number, operation, and quantitative reasoning. The student models multiplication and division.

(2.4) (A) The student is expected to model, create, and describe multiplication situations in which equivalent sets of concrete objects are joined.

(2.4) (B) The student is expected to model, create, and describe division situations in which a set of concrete objects is separated into equivalent sets.

TX.111.14 (2.5) Patterns, relationships, and algebraic thinking. The student uses patterns in numbers and operations.

(2.5) (A) The student is expected to find patterns in numbers such as in a 100s chart.

(2.5) (B) The student is expected to use patterns in place value to compare and order whole numbers through 999.

(2.5) (C) The student is expected to use patterns and relationships to develop strategies to remember basic addition and subtraction facts. Determine patterns in related addition and subtraction number sentences (including fact families) such as 8 + 9 = 17, 9 + 8 = 17, 17 - 8 = 9, and 17 - 9 = 8.

TX.111.14 (2.6) Patterns, relationships, and algebraic thinking. The student uses patterns to describe relationships and make predictions.

(2.6) (A) The student is expected to generate a list of paired numbers based on a real-life situation such as number of tricycles related to number of wheels.

(2.6) (B) The student is expected to identify patterns in a list of related number pairs based on a real-life situation and extend the list.

(2.6) (C) The student is expected to identify, describe, and extend repeating and additive patterns to make predictions and solve problems.

TX.111.14 (2.7) Geometry and spatial reasoning. The student uses attributes to identify two- and three-dimensional geometric figures. The student compares and contrasts two- and three-dimensional geometric figures or both.

(2.7) (A) The student is expected to describe attributes (the number of vertices, faces, edges, sides) of two- and three-dimensional geometric figures such as circles, polygons, spheres, cones, cylinders, prisms, and pyramids, etc.

(2.7) (B) The student is expected to use attributes to describe how 2 two-dimensional figures or 2 three-dimensional geometric figures are alike or different.

(2.7) (C) The student is expected to cut two-dimensional geometric figures apart and identify the new geometric figures formed.

TX.111.14 (2.8) Geometry and spatial reasoning. The student recognizes that a line can be used to represent a set of numbers and its properties.

(2.8) (A) The student is expected to use whole numbers to locate and name points on a number line.

TX.111.14 (2.9) Measurement. The student directly compares the attributes of length, area, weight/mass, and capacity, and uses comparative language to solve problems and answer questions. The student selects and uses nonstandard units to describe length, area, capacity, and weight/mass. The student recognizes and uses models that approximate standard units (from both SI, also known as metric, and customary systems) of length, weight/mass, capacity, and time.

(2.9) (A) The student is expected to identify concrete models that approximate standard units of length and use them to measure length.

(2.9) (B) The student is expected to select a non-standard unit of measure such as square tiles to determine the area of a two-dimensional surface.

(2.9) (C) The student is expected to select a non-standard unit of measure such as a bathroom cup or a jar to determine the capacity of a given container.

(2.9) (D) The student is expected to select a non-standard unit of measure such as beans or marbles to determine the weight/mass of a given object.

TX.111.14 (2.10) Measurement. The student uses standard tools to estimate and measure time and temperature (in degrees Fahrenheit).

(2.10) (A) The student is expected to read a thermometer to gather data.

(2.10) (B) The student is expected to read and write times shown on analog and digital clocks using five-minute increments.

(2.10) (C) The student is expected to describe activities that take approximately one second, one minute, and one hour.

TX.111.14 (2.11) Probability and statistics. The student organizes data to make it useful for interpreting information.

(2.11) (A) The student is expected to construct picture graphs and bar-type graphs.

(2.11) (B) The student is expected to draw conclusions and answer questions based on picture graphs and bar-type graphs.

(2.11) (C) The student is expected to use data to describe events as more likely or less likely such as drawing a certain color crayon from a bag of seven red crayons and three green crayons.

TX.111.14 (2.12) Underlying processes and mathematical tools. The student applies Grade 2 mathematics to solve problems connected to everyday experiences and activities in and outside of school.

(2.12) (A) The student is expected to identify the mathematics in everyday situations.

(2.12) (B) The student is expected to solve problems with guidance that incorporates the processes of understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.

(2.12) (C) The student is expected to select or develop an appropriate problem-solving plan or strategy including drawing a picture, looking for a pattern, systematic guessing and checking, or acting it out in order to solve a problem.

(2.12) (D) The student is expected to use tools such as real objects, manipulatives, and technology to solve problems.

TX.111.14 (2.13) Underlying processes and mathematical tools. The student communicates about Grade 2 mathematics using informal language.

(2.13) (A) The student is expected to explain and record observations using objects, words, pictures, numbers, and technology.

(2.13) (B) The student is expected to relate informal language to mathematical language and symbols.

TX.111.14 (2.14) Underlying processes and mathematical tools. The student uses logical reasoning.

(2.14) (A) The student is expected to justify his or her thinking using objects, words, pictures, numbers, and technology.

TX.111.15 (3.1) Number, operation, and quantitative reasoning. The student uses place value to communicate about increasingly large whole numbers in verbal and written form, including money.

(3.1) (A) The student is expected to use place value to read, write (in symbols and words), and describe the value of whole numbers through 999,999.

(3.1) (B) The student is expected to use place value to compare and order whole numbers through 9,999.

(3.1) (C) The student is expected to determine the value of a collection of coins and bills.

TX.111.15 (3.2) Number, operation, and quantitative reasoning. The student uses fraction names and symbols (with denominators of 12 or less) to describe fractional parts of whole objects or sets of objects.

(3.2) (A) The student is expected to construct concrete models of fractions.

(3.2) (B) The student is expected to compare fractional parts of whole objects or sets of objects in a problem situation using concrete models.

(3.2) (C) The student is expected to use fraction names and symbols to describe fractional parts of whole objects or sets of objects.

(3.2) (D) The student is expected to construct concrete models of equivalent fractions for fractional parts of whole objects.

TX.111.15 (3.3) Number, operation, and quantitative reasoning. The student adds and subtracts to solve meaningful problems involving whole numbers.

(3.3) (A) The student is expected to model addition and subtraction using pictures, words, and numbers.

(3.3) (B) The student is expected to select addition or subtraction and use the operation to solve problems involving whole numbers through 999.

TX.111.15 (3.4) Number, operation, and quantitative reasoning. The student recognizes and solves problems in multiplication and division situations.

(3.4) (A) The student is expected to learn and apply multiplication facts through 12 by 12 using concrete models and objects.

(3.4) (B) The student is expected to solve and record multiplication problems (up to two digits times one digit).

(3.4) (C) The student is expected to use models to solve division problems and use number sentences to record the solutions.

TX.111.15 (3.5) Number, operation, and quantitative reasoning. The student estimates to determine reasonable results.

(3.5) (A) The student is expected to round whole numbers to the nearest ten or hundred to approximate reasonable results in problem situations.

(3.5) (B) The student is expected to use strategies including rounding and compatible numbers to estimate solutions to addition and subtraction problems.

TX.111.15 (3.6) Patterns, relationships, and algebraic thinking. The student uses patterns to solve problems.

(3.6) (A) The student is expected to identify and extend whole-number and geometric patterns to make predictions and solve problems.

(3.6) (B) The student is expected to identify patterns in multiplication facts using concrete objects, pictorial models, or technology.

(3.6) (C) The student is expected to identify patterns in related multiplication and division sentences (fact families) such as 2 x 3 = 6, 3 x 2 = 6, 6 / 2 = 3, 6 / 3 = 2.

TX.111.15 (3.7) Patterns, relationships, and algebraic thinking. The student uses lists, tables, and charts to express patterns and relationships.

(3.7) (A) The student is expected to generate a table of paired numbers based on a real-life situation such as insects and legs.

(3.7) (B) The student is expected to identify and describe patterns in a table of related number pairs based on a meaningful problem and extend the table.

TX.111.15 (3.8) Geometry and spatial reasoning. The student uses formal geometric vocabulary.

(3.8) (A) The student is expected to identify, classify, and describe two- and three-dimensional geometric figures by their attributes. The student compares two-dimensional figures, three-dimensional figures, or both by their attributes using formal geometry vocabulary.

TX.111.15 (3.9) Geometry and spatial reasoning. The student recognizes congruence and symmetry.

(3.9) (A) The student is expected to identify congruent two-dimensional figures.

(3.9) (B) The student is expected to create two-dimensional figures with lines of symmetry using concrete models and technology.

(3.9) (C) The student is expected to identify lines of symmetry in two-dimensional geometric figures.

TX.111.15 (3.10) Geometry and spatial reasoning. The student recognizes that a line can be used to represent numbers and fractions and their properties and relationships.

(3.10) (A) The student is expected to locate and name points on a number line using whole numbers and fractions , including halves and fourths.

TX.111.15 (3.11) Measurement. The student directly compares the attributes of length, area, weight/mass, and capacity, and uses comparative language to solve problems and answer questions. The student selects and uses standard units to describe length, area, capacity/volume, and weight/mass.

(3.11) (A) The student is expected to use linear measurement tools to estimate and measure lengths using standard units.

(3.11) (B) The student is expected to use standard units to find the perimeter of a shape.

(3.11) (C) The student is expected to use concrete and pictorial models of square units to determine the area of two-dimensional surfaces.

(3.11) (D) The student is expected to identify concrete models that approximate standard units of weight/mass and use them to measure weight/mass.

(3.11) (E) The student is expected to identify concrete models that approximate standard units for capacity and use them to measure capacity.

(3.11) (F) The student is expected to use concrete models that approximate cubic units to determine the volume of a given container or other three-dimensional geometric figure.

TX.111.15 (3.12) Measurement. The student reads and writes time and measures temperature in degrees Fahrenheit to solve problems.

(3.12) (A) The student is expected to use a thermometer to measure temperature.

(3.12) (B) The student is expected to tell and write time shown on analog and digital clocks.

TX.111.15 (3.13) Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data.

(3.13) (A) The student is expected to collect, organize, record, and display data in pictographs and bar graphs where each picture or cell might represent more than one piece of data.

(3.13) (B) The student is expected to interpret information from pictographs and bar graphs.

(3.13) (C) The student is expected to use data to describe events as more likely than, less likely than, or equally likely as.

TX.111.15 (3.14) Underlying processes and mathematical tools. The student applies Grade 3 mathematics to solve problems connected to everyday experiences and activities in and outside of school.

(3.14) (A) The student is expected to identify the mathematics in everyday situations.

(3.14) (B) The student is expected to solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.

(3.14) (C) The student is expected to select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.

(3.14) (D) The student is expected to use tools such as real objects, manipulatives, and technology to solve problems.

TX.111.15 (3.15) Underlying processes and mathematical tools. The student communicates about Grade 3 mathematics using informal language.

(3.15) (A) The student is expected to explain and record observations using objects, words, pictures, numbers, and technology.

(3.15) (B) The student is expected to relate informal language to mathematical language and symbols.

TX.111.15 (3.16) Underlying processes and mathematical tools. The student uses logical reasoning.

(3.16) (A) The student is expected to make generalizations from patterns or sets of examples and non-examples.

(3.16) (B) The student is expected to justify why an answer is reasonable and explain the solution process.

TX.111.16 (4.1) Number, operation, and quantitative reasoning. The student uses place value to represent whole numbers and decimals.

(4.1) (A) The student is expected to use place value to read, write, compare, and order whole numbers through 999,999,999.

(4.1) (B) The student is expected to use place value to read, write, compare, and order decimals involving tenths and hundredths, including money, using concrete objects and pictorial models.

TX.111.16 (4.2) Number, operation, and quantitative reasoning. The student describes and compares fractional parts of whole objects or sets of objects.

(4.2) (A) The student is expected to use concrete objects and pictorial models to generate equivalent fractions.

(4.2) (B) The student is expected to model fraction quantities greater than one using concrete objects and pictorial models.

(4.2) (C) The student is expected to compare and order fractions using concrete objects and pictorial models.

(4.2) (D) The student is expected to relate decimals to fractions that name tenths and hundredths using concrete objects and pictorial models.

TX.111.16 (4.3) Number, operation, and quantitative reasoning. The student adds and subtracts to solve meaningful problems involving whole numbers and decimals.

(4.3) (A) The student is expected to use addition and subtraction to solve problems involving whole numbers.

(4.3) (B) The student is expected to add and subtract decimals to the hundredths place using concrete objects and pictorial models.

TX.111.16 (4.4) Number, operation, and quantitative reasoning. The student multiplies and divides to solve meaningful problems involving whole numbers.

(4.4) (A) The student is expected to model factors and products using arrays and area models.

(4.4) (B) The student is expected to represent multiplication and division situations in picture, word, and number form.

(4.4) (C) The student is expected to recall and apply multiplication facts through 12 x 12.

(4.4) (D) The student is expected to use multiplication to solve problems (no more than two digits times two digits without technology).

(4.4) (E) The student is expected to use division to solve problems (no more than one-digit divisors and three digit dividends without technology).

TX.111.16 (4.5) Number, operation, and quantitative reasoning. The student estimates to determine reasonable results.

(4.5) (A) The student is expected to round whole numbers to the nearest ten, hundred, or thousand to approximate reasonable results in problem situations.

(4.5) (B) The student is expected to use strategies including rounding and compatible numbers to estimate solutions to multiplication and division problems.

TX.111.16 (4.6) Patterns, relationships, and algebraic thinking. The student uses patterns in multiplication and division.

(4.6) (A) The student is expected to use patterns and relationships to develop strategies to remember basic multiplication and division facts (such as the patterns in related multiplication and division number sentences (fact families) such as 9 x 9 = 81 and 81 / 9 = 9).

(4.6) (B) The student is expected to use patterns to multiply by 10 and 100.

TX.111.16 (4.7) Patterns, relationships, and algebraic thinking. The student uses organizational structures to analyze and describe patterns and relationships.

(4.7) (A) The student is expected to describe the relationship between two sets of related data such as ordered pairs in a table.

TX.111.16 (4.8) Geometry and spatial reasoning. The student identifies and describes attributes of geometric figures using formal geometric language.

(4.8) (A) The student is expected to identify and describe right, acute, and obtuse angles.

(4.8) (B) The student is expected to identify and describe parallel and intersecting (including perpendicular) lines using concrete objects and pictorial models.

(4.8) (C) The student is expected to use essential attributes to define two- and three-dimensional geometric figures.

TX.111.16 (4.9) Geometry and spatial reasoning. The student connects transformations to congruence and symmetry.

(4.9) (A) The student is expected to demonstrate translations, reflections, and rotations using concrete models.

(4.9) (B) The student is expected to use translations, reflections, and rotations to verify that two shapes are congruent.

(4.9) (C) The student is expected to use reflections to verify that a shape has symmetry.

TX.111.16 (4.10) Geometry and spatial reasoning. The student recognizes the connection between numbers and their properties and points on a line.

(4.10) (A) The student is expected to locate and name points on a number line using whole numbers, fractions such as halves and fourths, and decimals such as tenths.

TX.111.16 (4.11) Measurement. The student applies measurement concepts. The student is expected to estimate and measure to solve problems involving length (including perimeter) and area. The student uses measurement tools to measure capacity/volume and weight/mass.

(4.11) (A) The student is expected to estimate and use measurement tools to determine length (including perimeter), area, capacity and weight/mass using standard units SI (metric) and customary.

(4.11) (B) The student is expected to perform simple conversions between different units of length, between different units of capacity, and between different units of weight within the customary measurement system.

(4.11) (C) The student is expected to use concrete models of standard cubic units to measure volume.

(4.11) (D) The student is expected to estimate volume in cubic units.

(4.11) (E) The student is expected to explain the difference between weight and mass.

TX.111.16 (4.12) Measurement. The student applies measurement concepts. The student measures time and temperature (in degrees Fahrenheit and Celsius).

(4.12) (A) The student is expected to use a thermometer to measure temperature and changes in temperature.

(4.12) (B) The student is expected to use tools such as a clock with gears or a stopwatch to solve problems involving elapsed time.

TX.111.16 (4.13) Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data.

(4.13) (A) The student is expected to use concrete objects or pictures to make generalizations about determining all possible combinations of a given set of data or of objects in a problem situation.

(4.13) (B) The student is expected to interpret bar graphs.

TX.111.16 (4.14) Underlying processes and mathematical tools. The student applies Grade 4 mathematics to solve problems connected to everyday experiences and activities in and outside of school.

(4.14) (A) The student is expected to identify the mathematics in everyday situations.

(4.14) (B) The student is expected to solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.

(4.14) (C) The student is expected to select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.

(4.14) (D) The student is expected to use tools such as real objects, manipulatives, and technology to solve problems.

TX.111.16 (4.15) Underlying processes and mathematical tools. The student communicates about Grade 4 mathematics using informal language.

(4.15) (A) The student is expected to explain and record observations using objects, words, pictures, numbers, and technology.

(4.15) (B) The student is expected to relate informal language to mathematical language and symbols.

TX.111.16 (4.16) Underlying processes and mathematical tools. The student uses logical reasoning.

(4.16) (A) The student is expected to make generalizations from patterns or sets of examples and non-examples.

(4.16) (B) The student is expected to justify why an answer is reasonable and explain the solution process.

TX.111.17 (5.1) Number, operation, and quantitative reasoning. The student uses place value to represent whole numbers and decimals.

(5.1) (A) The student is expected to use place value to read, write, compare, and order whole numbers through the 999,999,999,999.

(5.1) (B) The student is expected to use place value to read, write, compare, and order decimals through the thousandths place.

TX.111.17 (5.2) Number, operation, and quantitative reasoning. The student uses fractions in problem-solving situations.

(5.2) (A) The student is expected to generate a fraction equivalent to a given fraction such as 1/2 and 3/6 or 4/12 and 1/3.

(5.2) (B) The student is expected to generate a mixed number equivalent to a given improper fraction or generate an improper fraction equivalent to a given mixed number.

(5.2) (C) The student is expected to compare two fractional quantities in problem-solving situations using a variety of methods, including common denominators.

(5.2) (D) The student is expected to use models to relate decimals to fractions that name tenths, hundredths, and thousandths.

TX.111.17 (5.3) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve meaningful problems.

(5.3) (A) The student is expected to use addition and subtraction to solve problems involving whole numbers and decimals.

(5.3) (B) The student is expected to use multiplication to solve problems involving whole numbers (no more than three digits times two digits without technology).

(5.3) (C) The student is expected to use division to solve problems involving whole numbers (no more than two-digit divisors and three-digit dividends without technology) , including interpreting the remainder within a given context.

(5.3) (D) The student is expected to identify common factors of a set of whole numbers.

(5.3) (E) The student is expected to model situations using addition and/or subtraction involving fractions with like denominators using concrete objects, pictures, words, and numbers.

TX.111.17 (5.4) Number, operation, and quantitative reasoning. The student estimates to determine reasonable results.

(5.4) (A) The student is expected to use strategies, including rounding and compatible numbers to estimate solutions to addition, subtraction, multiplication, and division problems.

TX.111.17 (5.5) Patterns, relationships, and algebraic thinking. The student makes generalizations based on observed patterns and relationships.

(5.5) (A) The student is expected to describe the relationship between sets of data in graphic organizers such as lists, tables, charts, and diagrams.

(5.5) (B) The student is expected to identify prime and composite numbers using concrete objects, pictorial models , and patterns in factor pairs.

TX.111.17 (5.6) Patterns, relationships, and algebraic thinking. The student describes relationships mathematically.

(5.6) (A) The student is expected to select from and use diagrams and equations such as y = 5 + 3 to represent meaningful problem situations.

TX.111.17 (5.7) Geometry and spatial reasoning. The student generates geometric definitions using critical attributes.

(5.7) (A) The student is expected to identify essential attributes including parallel, perpendicular, and congruent parts of two- and three-dimensional geometric figures.

TX.111.17 (5.8) Geometry and spatial reasoning. The student models transformations.

(5.8) (A) The student is expected to sketch the results of translations, rotations, and reflections on a Quadrant I coordinate grid.

(5.8) (B) The student is expected to identify the transformation that generates one figure from the other when given two congruent figures on a Quadrant I coordinate grid.

TX.111.17 (5.9) Geometry and spatial reasoning. The student recognizes the connection between ordered pairs of numbers and locations of points on a plane.

(5.9) (A) The student is expected to locate and name points on a coordinate grid using ordered pairs of whole numbers.

TX.111.17 (5.10) Measurement. The student applies measurement concepts involving length (including perimeter), area, capacity/volume, and weight/mass to solve problems.

(5.10) (A) The student is expected to perform simple conversions within the same measurement system (SI (metric) or customary).

(5.10) (B) The student is expected to connect models for perimeter, area, and volume with their respective formulas.

(5.10) (C) The student is expected to select and use appropriate units and formulas to measure length, perimeter, area, and volume.

TX.111.17 (5.11) Measurement. The student applies measurement concepts. The student measures time and temperature (in degrees Fahrenheit and Celsius).

(5.11) (A) The student is expected to solve problems involving changes in temperature.

(5.11) (B) The student is expected to solve problems involving elapsed time.

TX.111.17 (5.12) Probability and statistics. The student describes and predicts the results of a probability experiment.

(5.12) (A) The student is expected to use fractions to describe the results of an experiment.

(5.12) (B) The student is expected to use experimental results to make predictions.

(5.12) (C) The student is expected to list all possible outcomes of a probability experiment such as tossing a coin.

TX.111.17 (5.13) Probability and statistics. The student solves problems by collecting, organizing, displaying, and interpreting sets of data.

(5.13) (A) The student is expected to use tables of related number pairs to make line graphs;

(5.13) (B) The student is expected to describe characteristics of data presented in tables and graphs including median, mode, and range.

(5.13) (C) The student is expected to graph a given set of data using an appropriate graphical representation such as a picture or line graph.

TX.111.17 (5.14) Underlying processes and mathematical tools. The student applies Grade 5 mathematics to solve problems connected to everyday experiences and activities in and outside of school.

(5.14) (A) The student is expected to identify the mathematics in everyday situations.

(5.14) (B) The student is expected to solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.

(5.14) (C) The student is expected to select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.

(5.14) (D) The student is expected to use tools such as real objects, manipulatives, and technology to solve problems.

TX.111.17 (5.15) Underlying processes and mathematical tools. The student communicates about Grade 5 mathematics using informal language.

(5.15) (A) The student is expected to explain and record observations using objects, words, pictures, numbers, and technology.

(5.15) (B) The student is expected to relate informal language to mathematical language and symbols.

TX.111.17 (5.16) Underlying processes and mathematical tools. The student uses logical reasoning.

(5.16) (A) The student is expected to make generalizations from patterns or sets of examples and non-examples.

(5.16) (B) The student is expected to justify why an answer is reasonable and explain the solution process.

TX.111.22 (6.1) Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of equivalent forms.

(6.1) (A) The student is expected to compare and order non-negative rational numbers.

(6.1) (B) The student is expected to generate equivalent forms of rational numbers including whole numbers, fractions, and decimals.

(6.1) (C) The student is expected to use integers to represent real-life situations.

(6.1) (D) The student is expected to write prime factorizations using exponents.

(6.1) (E) The student is expected to identify factors of a positive integer, common factors, and the greatest common factor of a set of positive integers.

(6.1) (F) The student is expected to identify multiples of a positive integer and common multiples and the least common multiple of a set of positive integers.

TX.111.22 (6.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve problems and justify solutions.

(6.2) (A) The student is expected to model addition and subtraction situations involving fractions with objects, pictures, words, and numbers.

(6.2) (B) The student is expected to use addition and subtraction to solve problems involving fractions and decimals.

(6.2) (C) The student is expected to use multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates.

(6.2) (D) The student is expected to estimate and round to approximate reasonable results and to solve problems where exact answers are not required.

(6.2) (E) The student is expected to use order of operations to simplify whole number expressions (without exponents) in problem solving situations.

TX.111.22 (6.3) Patterns, relationships, and algebraic thinking. The student solves problems involving direct proportional relationships.

(6.3) (A) The student is expected to use ratios to describe proportional situations.

(6.3) (B) The student is expected to represent ratios and percents with concrete models, fractions, and decimals.

(6.3) (C) The student is expected to use ratios to make predictions in proportional situations.

TX.111.22 (6.4) Patterns, relationships, and algebraic thinking. The student uses letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes.

(6.4) (A) The student is expected to use tables and symbols to represent and describe proportional and other relationships such as those involving conversions, arithmetic sequences (with a constant rate of change), perimeter and area.

(6.4) (B) The student is expected to use tables of data to generate formulas representing relationships involving perimeter, area, volume of a rectangular prism, etc.

TX.111.22 (6.5) Patterns, relationships, and algebraic thinking. The student uses letters to represent an unknown in an equation.

(6.5) (A) The student is expected to formulate equations from problem situations described by linear relationships.

TX.111.22 (6.6) Geometry and spatial reasoning. The student uses geometric vocabulary to describe angles, polygons, and circles.

(6.6) (A) The student is expected to use angle measurements to classify angles as acute, obtuse, or right.

(6.6) (B) The student is expected to identify relationships involving angles in triangles and quadrilaterals.

(6.6) (C) The student is expected to describe the relationship between radius, diameter, and circumference of a circle.

TX.111.22 (6.7) Geometry and spatial reasoning. The student uses coordinate geometry to identify location in two dimensions.

(6.7) (A) The student is expected to locate and name points on a coordinate plane using ordered pairs of non-negative rational numbers.

TX.111.22 (6.8) Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and angles.

(6.8) (A) The student is expected to estimate measurements (including circumference) and evaluate reasonableness of results.

(6.8) (B) The student is expected to select and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter), area, time, temperature, volume, and weight.

(6.8) (C) The student is expected to measure angles.

(6.8) (D) The student is expected to convert measures within the same measurement system (customary and metric) based on relationships between units.

TX.111.22 (6.9) Probability and statistics. The student uses experimental and theoretical probability to make predictions.

(6.9) (A) The student is expected to construct sample spaces using lists and tree diagrams.

(6.9) (B) The student is expected to find the probabilities of a simple event and its complement and describe the relationship between the two.

TX.111.22 (6.10) Probability and statistics. The student uses statistical representations to analyze data.

(6.10) (A) The student is expected to select and use an appropriate representation for presenting and displaying different graphical representations of the same data including line plot, line graph, bar graph, and stem and leaf plot.

(6.10) (B) The student is expected to identify mean (using concrete objects and pictorial models), median, mode, and range of a set of data.

(6.10) (C) The student is expected to sketch circle graphs to display data.

(6.10) (D) The student is expected to solve problems by collecting, organizing, displaying, and interpreting data.

TX.111.22 (6.11) Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school.

(6.11) (A) The student is expected to identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics.

(6.11) (B) The student is expected to use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.

(6.11) (C) The student is expected to select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.

(6.11) (D) The student is expected to select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.

TX.111.22 (6.12) Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models.

(6.12) (A) The student is expected to communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models.

(6.12) (B) The student is expected to evaluate the effectiveness of different representations to communicate ideas.

TX.111.22 (6.13) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions.

(6.13) (A) The student is expected to make conjectures from patterns or sets of examples and non-examples.

(6.13) (B) The student is expected to validate his/her conclusions using mathematical properties and relationships.

TX.111.23 (7.1) Number, operation, and quantitative reasoning. The student represents and uses numbers in a variety of equivalent forms.

(7.1) (A) The student is expected to compare and order integers and positive rational numbers.

(7.1) (B) The student is expected to convert between fractions, decimals, whole numbers, and percents mentally, on paper, or with a calculator.

(7.1) (C) The student is expected to represent squares and square roots using geometric models.

TX.111.23 (7.2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, or divides to solve problems and justify solutions.

(7.2) (A) The student is expected to represent multiplication and division situations involving fractions and decimals with models, including concrete objects, pictures, words, and numbers.

(7.2) (B) The student is expected to use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals.

(7.2) (C) The student is expected to use models, such as concrete objects, pictorial models, and number lines, to add, subtract, multiply, and divide integers and connect the actions to algorithms.

(7.2) (D) The student is expected to use division to find unit rates and ratios in proportional relationships such as speed, density, price, recipes, and student-teacher ratio.

(7.2) (E) The student is expected to simplify numerical expressions involving order of operations and exponents.

(7.2) (F) The student is expected to select and use appropriate operations to solve problems and justify the selections.

(7.2) (G) The student is expected to determine the reasonableness of a solution to a problem.

TX.111.23 (7.3) Patterns, relationships, and algebraic thinking. The student solves problems involving direct proportional relationships.

(7.3) (A) The student is expected to estimate and find solutions to application problems involving percent.

(7.3) (B) The student is expected to estimate and find solutions to application problems involving proportional relationships such as similarity, scaling, unit costs, and related measurement units.

TX.111.23 (7.4) Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal, and symbolic form.

(7.4) (A) The student is expected to generate formulas involving unit conversions, perimeter, area, circumference, volume, and scaling.

(7.4) (B) The student is expected to graph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling.

(7.4) (C) The student is expected to use words and symbols to describe the relationship between the terms in an arithmetic sequence (with a constant rate of change) and their positions in the sequence.

TX.111.23 (7.5) Patterns, relationships, and algebraic thinking. The student uses equations to solve problems.

(7.5) (A) The student is expected to use concrete and pictorial models to solve equations and use symbols to record the actions.

(7.5) (B) The student is expected to formulate problem situations when given a simple equation and formulate an equation when given a problem situation.

TX.111.23 (7.6) Geometry and spatial reasoning. The student compares and classifies two- and three-dimensional figures using geometric vocabulary and properties.

(7.6) (A) The student is expected to use angle measurements to classify pairs of angles as complementary or supplementary.

(7.6) (B) The student is expected to use properties to classify triangles and quadrilaterals.

(7.6) (C) The student is expected to use properties to classify three-dimensional figures, including pyramids, cones, prisms, and cylinders.

(7.6) (D) The student is expected to use critical attributes to define similarity.

TX.111.23 (7.7) Geometry and spatial reasoning. The student uses coordinate geometry to describe location on a plane.

(7.7) (A) The student is expected to locate and name points on a coordinate plane using ordered pairs of integers.

(7.7) (B) The student is expected to graph reflections across the horizontal or vertical axis and graph translations on a coordinate plane.

TX.111.23 (7.8) Geometry and spatial reasoning. The student uses geometry to model and describe the physical world.

(7.8) (A) The student is expected to sketch three-dimensional figures when given the top, side, and front views.

(7.8) (B) The student is expected to make a net (two-dimensional model) of the surface area of a three-dimensional figure.

(7.8) (C) The student is expected to use geometric concepts and properties to solve problems in fields such as art and architecture.

TX.111.23 (7.9) Measurement. The student solves application problems involving estimation and measurement.

(7.9) (A) The student is expected to estimate measurements and solve application problems involving length (including perimeter and circumference) and area of polygons and other shapes.

(7.9) (B) The student is expected to connect models for volume of prisms (triangular and rectangular) and cylinders to formulas of prisms (triangular and rectangular) and cylinders.

(7.9) (C) The student is expected to estimate measurements and solve application problems involving volume of prisms (rectangular and triangular) and cylinders.

TX.111.23 (7.10) Probability and statistics. The student recognizes that a physical or mathematical model can be used to describe the experimental and theoretical probability of real-life events.

(7.10) (A) The student is expected to construct sample spaces for simple or composite experiments.

(7.10) (B) The student is expected to find the probability of independent events.

TX.111.23 (7.11) Probability and statistics. The student understands that the way a set of data is displayed influences its interpretation.

(7.11) (A) The student is expected to select and use an appropriate representation for presenting and displaying relationships among collected data, including line plot, line graph, bar graph, stem and leaf plot, circle graph, and Venn diagrams, and justify the selection.

(7.11) (B) The student is expected to make inferences and convincing arguments based on an analysis of given or collected data.

TX.111.23 (7.12) Probability and statistics. The student uses measures of central tendency and range to describe a set of data.

(7.12) (A) The student is expected to describe a set of data using mean, median, mode, and range.

(7.12) (B) The student is expected to choose among mean, median, mode, or range to describe a set of data and justify the choice for a particular situation.

TX.111.23 (7.13) Underlying processes and mathematical tools. The student applies Grade 7 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school.

(7.13) (A) The student is expected to identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics.

(7.13) (B) The student is expected to use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.

(7.13) (C) The student is expected to select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.

(7.13) (D) The student is expected to select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.

TX.111.23 (7.14) Underlying processes and mathematical tools. The student communicates about Grade 7 mathematics through informal and mathematical language, representations, and models.

(7.14) (A) The student is expected to communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models.

(7.14) (B) The student is expected to evaluate the effectiveness of different representations to communicate ideas.

TX.111.23 (7.15) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions.

(7.15) (A) The student is expected to make conjectures from patterns or sets of examples and non-examples.

(7.15) (B) The student is expected to validate his/her conclusions using mathematical properties and relationships.

TX.111.24 (8.1) Number, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate for different situations.

(8.1) (A) The student is expected to compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals.

(8.1) (B) The student is expected to select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships.

(8.1) (C) The student is expected to approximate (mentally and with calculators) the value of irrational numbers as they arise from problem situations (such as pi, square root of 2).

(8.1) (D) The student is expected to express numbers in scientific notation, including negative exponents, in appropriate problem situations.

TX.111.24 (8.2) Number, operation, and quantitative reasoning. The student selects and uses appropriate operations to solve problems and justify solutions.

(8.2) (A) The student is expected to select appropriate operations to solve problems involving rational numbers and justify the selections.

(8.2) (B) The student is expected to use appropriate operations to solve problems involving rational numbers in problem situations.

(8.2) (C) The student is expected to evaluate a solution for reasonableness.

(8.2) (D) The student is expected to use multiplication by a constant factor (unit rate) to represent proportional relationships.

TX.111.24 (8.3) Patterns, relationships, and algebraic thinking. The student identifies proportional or non-proportional linear relationships in problem situations and solves problems.

(8.3) (A) The student is expected to compare and contrast proportional and non-proportional linear relationships.

(8.3) (B) The student is expected to estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates.

TX.111.24 (8.4) Patterns, relationships, and algebraic thinking. The student makes connections among various representations of a numerical relationship.

(8.4) (A) The student is expected to generate a different representation of data given another representation of data (such as a table, graph, equation, or verbal description).

TX.111.24 (8.5) Patterns, relationships, and algebraic thinking. The student uses graphs, tables, and algebraic representations to make predictions and solve problems.

(8.5) (A) The student is expected to predict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations.

(8.5) (B) The student is expected to find and evaluate an algebraic expression to determine any term in an arithmetic sequence (with a constant rate of change).

TX.111.24 (8.6) Geometry and spatial reasoning. The student uses transformational geometry to develop spatial sense.

(8.6) (A) The student is expected to generate similar figures using dilations including enlargements and reductions.

(8.6) (B) The student is expected to graph dilations, reflections, and translations on a coordinate plane.

TX.111.24 (8.7) Geometry and spatial reasoning. The student uses geometry to model and describe the physical world.

(8.7) (A) The student is expected to draw three-dimensional figures from different perspectives.

(8.7) (B) The student is expected to use geometric concepts and properties to solve problems in fields such as art and architecture.

(8.7) (C) The student is expected to use pictures or models to demonstrate the Pythagorean Theorem.

(8.7) (D) The student is expected to locate and name points on a coordinate plane using ordered pairs of rational numbers.

TX.111.24 (8.8) Measurement. The student uses procedures to determine measures of three-dimensional figures.

(8.8) (A) The student is expected to find lateral and total surface area of prisms, pyramids, and cylinders using concrete models and nets (two-dimensional models).

(8.8) (B) The student is expected to connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects.

(8.8) (C) The student is expected to estimate measurements and use formulas to solve application problems involving lateral and total surface area and volume.

TX.111.24 (8.9) Measurement. The student uses indirect measurement to solve problems.

(8.9) (A) The student is expected to use the Pythagorean Theorem to solve real-life problems.

(8.9) (B) The student is expected to use proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements.

TX.111.24 (8.10) Measurement. The student describes how changes in dimensions affect linear, area, and volume measures.

(8.10) (A) The student is expected to describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally.

(8.10) (B) The student is expected to describe the resulting effect on volume when dimensions of a solid are changed proportionally.

TX.111.24 (8.11) Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions.

(8.11) (A) The student is expected to find the probabilities of dependent and independent events.

(8.11) (B) The student is expected to use theoretical probabilities and experimental results to make predictions and decisions.

(8.11) (C) The student is expected to select and use different models to simulate an event.

TX.111.24 (8.12) Probability and statistics. The student uses statistical procedures to describe data.

(8.12) (A) The student is expected to select the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situation.

(8.12) (B) The student is expected to draw conclusions and make predictions by analyzing trends in scatterplots.

(8.12) (C) The student is expected to select and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, stem and leaf plots, circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams, with and without the use of technology.

TX.111.24 (8.13) Probability and statistics. The student evaluates predictions and conclusions based on statistical data.

(8.13) (A) The student is expected to evaluate methods of sampling to determine validity of an inference made from a set of data.

(8.13) (B) The student is expected to recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis.

TX.111.24 (8.14) Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school.

(8.14) (A) The student is expected to identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics.

(8.14) (B) The student is expected to use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.

(8.14) (C) The student is expected to select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.

(8.14) (D) The student is expected to select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.

TX.111.24 (8.15) Underlying processes and mathematical tools. The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models.

(8.15) (A) The student is expected to communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models.

(8.15) (B) The student is expected to evaluate the effectiveness of different representations to communicate ideas.

TX.111.24 (8.16) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions.

(8.16) (A) The student is expected to make conjectures from patterns or sets of examples and non-examples.

(8.16) (B) The student is expected to validate his/her conclusions using mathematical properties and relationships.

TX.111.32 (A.1) Algebra I: Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways.

(A.1) (A) The student is expected to describe independent and dependent quantities in functional relationships;

(A.1) (B) The student is expected to gather and record data and use data sets to determine functional relationships between quantities;

(A.1) (C) The student is expected to describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations;

(A.1) (D) The student is expected to represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities;

(A.1) (E) The student is expected to interpret and make decisions, predictions, and critical judgments from functional relationships.

TX.111.32 (A.2) Algebra I: Foundations for functions. The student uses the properties and attributes of functions.

(A.2) (A) The student is expected to identify and sketch the general forms of linear (y = x) and quadratic (y = x^2) parent functions;

(A.2) (B) The student is expected to identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete;

(A.2) (C) The student is expected to interpret situations in terms of given graphs or creates situations that fit given graphs;

(A.2) (D) The student is expected to collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations.

TX.111.32 (A.3) Algebra I: Foundations for functions. The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations.

(A.3) (A) The student is expected to use symbols to represent unknowns and variables;

(A.3) (B) The student is expected to look for patterns and represent generalizations algebraically.

TX.111.32 (A.4) Algebra I: Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations.

(A.4) (A) The student is expected to find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations;

(A.4) (B) The student is expected to use the commutative, associative, and distributive properties to simplify algebraic expressions;

(A.4) (C) The student is expected to connect equation notation with function notation, such as y = x + 1 and f(x) = x + 1.

TX.111.32 (A.5) Algebra I: Linear functions. The student understands that linear functions can be represented in different ways and translates among their various representations.

(A.5) (A) The student is expected to determine whether or not given situations can be represented by linear functions;

(A.5) (B) The student is expected to determine the domain and range for linear functions in given situations;

(A.5) (C) The student is expected to use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions.

TX.111.32 (A.6) Algebra I: Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations.

(A.6) (A) The student is expected to develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations;

(A.6) (B) The student is expected to interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs;

(A.6) (C) The student is expected to investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b;

(A.6) (D) The student is expected to graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept;

(A.6) (E) The student is expected to determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations;

(A.6) (F) The student is expected to interpret and predict the effects of changing slope and y-intercept in applied situations;

(A.6) (G) The student is expected to relate direct variation to linear functions and solve problems involving proportional change.

TX.111.32 (A.7) Algebra I: Linear functions. The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(A.7) (A) The student is expected to analyze situations involving linear functions and formulate linear equations or inequalities to solve problems;

(A.7) (B) The student is expected to investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities;

(A.7) (C) The student is expected to interpret and determine the reasonableness of solutions to linear equations and inequalities.

TX.111.32 (A.8) Algebra I: Linear functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(A.8) (A) The student is expected to analyze situations and formulate systems of linear equations in two unknowns to solve problems;

(A.8) (B) The student is expected to solve systems of linear equations using concrete models, graphs, tables, and algebraic methods;

(A.8) (C) The student is expected to interpret and determine the reasonableness of solutions to systems of linear equations.

TX.111.32 (A.9) Algebra I: Quadratic and other nonlinear functions. The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions.

(A.9) (A) The student is expected to determine the domain and range for quadratic functions in given situations;

(A.9) (B) The student is expected to investigate, describe, and predict the effects of changes in a on the graph of y = ax^2 + c;

(A.9) (C) The student is expected to investigate, describe, and predict the effects of changes in c on the graph of y = ax^2 + c;

(A.9) (D) The student is expected to analyze graphs of quadratic functions and draw conclusions.

TX.111.32 (A.10) Algebra I: Quadratic and other nonlinear functions. The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods.

(A.10) (A) The student is expected to solve quadratic equations using concrete models, tables, graphs, and algebraic methods;

(A.10) (B) The student is expected to make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function.

TX.111.32 (A.11) Algebra I: Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations.

(A.11) (A) The student is expected to use patterns to generate the laws of exponents and apply them in problem-solving situations;

(A.11) (B) The student is expected to analyze data and represent situations involving inverse variation using concrete models, tables, graphs, or algebraic methods;

(A.11) (C) The student is expected to analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods.

TX.111.33 (2A.1) Algebra II: Foundations for functions. The student uses properties and attributes of functions and applies functions to problem situations.

(2A.1) (A) The student is expected to identify the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous and discrete situations;

(2A.1) (B) The student is expected to collect and organize data, make and interpret scatterplots, fit the graph of a function to the data, interpret the results, and proceed to model, predict, and make decisions and critical judgments.

TX.111.33 (2A.2) Algebra II: Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations.

(2A.2) (A) The student is expected to use tools including factoring and properties of exponents to simplify expressions and to transform and solve equations;

(2A.2) (B) The student is expected to use complex numbers to describe the solutions of quadratic equations.

TX.111.33 (2A.3) Algebra II: Foundations for functions. The student formulates systems of equations and inequalities from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situations.

(2A.3) (A) The student is expected to analyze situations and formulate systems of equations in two or more unknowns or inequalities in two unknowns to solve problems;

(2A.3) (B) The student is expected to use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities;

(2A.3) (C) The student is expected to interpret and determine the reasonableness of solutions to systems of equations or inequalities for given contexts.

TX.111.33 (2A.4) Algebra II: Algebra and geometry. The student connects algebraic and geometric representations of functions.

(2A.4) (A) The student is expected to identify and sketch graphs of parent functions, including linear (f(x) = x), quadratic (f(x) = x^2), exponential (f(x) = a^x), and logarithmic (f(x) = log base a of x) functions, absolute value of x (f(x) = |x|), square root of x (f(x) = square root of x), and reciprocal of x (f(x) = 1/x);

(2A.4) (B) The student is expected to extend parent functions with parameters such as a in f(x) = a/x and describe the effects of the parameter changes on the graph of parent functions;

(2A.4) (C) The student is expected to describe and analyze the relationship between a function and its inverse.

TX.111.33 (2A.5) Algebra II: Algebra and geometry. The student knows the relationship between the geometric and algebraic descriptions of conic sections.

(2A.5) (A) The student is expected to describe a conic section as the intersection of a plane and a cone;

(2A.5) (B) The student is expected to sketch graphs of conic sections to relate simple parameter changes in the equation to corresponding changes in the graph;

(2A.5) (C) The student is expected to identify symmetries from graphs of conic sections;

(2A.5) (D) The student is expected to identify the conic section from a given equation;

(2A.5) (E) The student is expected to use the method of completing the square.

TX.111.33 (2A.6) Algebra II: Quadratic and square root functions. The student understands that quadratic functions can be represented in different ways and translates among their various representations.

(2A.6) (A) The student is expected to determine the reasonable domain and range values of quadratic functions, as well as interpret and determine the reasonableness of solutions to quadratic equations and inequalities;

(2A.6) (B) The student is expected to relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions;

(2A.6) (C) The student is expected to determine a quadratic function from its roots or a graph.

TX.111.33 (2A.7) Algebra II: Quadratic and square root functions. The student interprets and describes the effects of changes in the parameters of quadratic functions in applied and mathematical situations.

(2A.7) (A) The student is expected to use characteristics of the quadratic parent function to sketch the related graphs and connect between the y = ax^2 + bx + c and the y = a(x - h)^2 + k symbolic representations of quadratic functions;

(2A.7) (B) The student is expected to use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(x - h)^2 + k form of a function in applied and purely mathematical situations.

TX.111.33 (2A.8) Algebra II: Quadratic and square root functions. The student formulates equations and inequalities based on quadratic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(2A.8) (A) The student is expected to analyze situations involving quadratic functions and formulate quadratic equations or inequalities to solve problems;

(2A.8) (B) The student is expected to analyze and interpret the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula;

(2A.8) (C) The student is expected to compare and translate between algebraic and graphical solutions of quadratic equations;

(2A.8) (D) The student is expected to solve quadratic equations and inequalities using graphs, tables, and algebraic methods.

TX.111.33 (2A.9) Algebra II: Quadratic and square root functions. The student formulates equations and inequalities based on square root functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(2A.9) (A) The student is expected to use the parent function to investigate, describe, and predict the effects of parameter changes on the graphs of square root functions and describe limitations on the domains and ranges;

(2A.9) (B) The student is expected to relate representations of square root functions, such as algebraic, tabular, graphical, and verbal descriptions;

(2A.9) (C) The student is expected to determine the reasonable domain and range values of square root functions, as well as interpret and determine the reasonableness of solutions to square root equations and inequalities;

(2A.9) (D) The student is expected to determine solutions of square root equations using graphs, tables, and algebraic methods;

(2A.9) (E) The student is expected to determine solutions of square root inequalities using graphs and tables;

(2A.9) (F) The student is expected to analyze situations modeled by square root functions, formulate equations or inequalities, select a method, and solve problems;

(2A.9) (G) The student is expected to connect inverses of square root functions with quadratic functions.

TX.111.33 (2A.10) Algebra II: Rational functions. The student formulates equations and inequalities based on rational functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(2A.10) (A) The student is expected to use quotients of polynomials to describe the graphs of rational functions, predict the effects of parameter changes, describe limitations on the domains and ranges, and examine asymptotic behavior;

(2A.10) (B) The student is expected to analyze various representations of rational functions with respect to problem situations;

(2A.10) (C) The student is expected to determine the reasonable domain and range values of rational functions, as well as interpret and determine the reasonableness of solutions to rational equations and inequalities;

(2A.10) (D) The student is expected to determine the solutions of rational equations using graphs, tables, and algebraic methods;

(2A.10) (E) The student is expected to determine solutions of rational inequalities using graphs and tables;

(2A.10) (F) The student is expected to analyze a situation modeled by a rational function, formulate an equation or inequality composed of a linear or quadratic function, and solve the problem;

(2A.10) (G) The student is expected to use functions to model and make predictions in problem situations involving direct and inverse variation.

TX.111.33 (2A.11) Algebra II: Exponential and logarithmic functions. The student formulates equations and inequalities based on exponential and logarithmic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(2A.11) (A) The student is expected to develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses;

(2A.11) (B) The student is expected to use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describe limitations on the domains and ranges, and examine asymptotic behavior;

(2A.11) (C) The student is expected to determine the reasonable domain and range values of exponential and logarithmic functions, as well as interpret and determine the reasonableness of solutions to exponential and logarithmic equations and inequalities;

(2A.11) (D) The student is expected to determine solutions of exponential and logarithmic equations using graphs, tables, and algebraic methods;

(2A.11) (E) The student is expected to determine solutions of exponential and logarithmic inequalities using graphs and tables;

(2A.11) (F) The student is expected to analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem.

TX.111.34 (G.1) Geometry: Geometric structure. The student understands the structure of, and relationships within, an axiomatic system.

(G.1) (A) The student is expected to develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems;

(G.1) (B) The student is expected to recognize the historical development of geometric systems and know mathematics is developed for a variety of purposes;

(G.1) (C) The student is expected to compare and contrast the structures and implications of Euclidean and non-Euclidean geometries.

TX.111.34 (G.2) Geometry: Geometric structure. The student analyzes geometric relationships in order to make and verify conjectures.

(G.2) (A) The student is expected to use constructions to explore attributes of geometric figures and to make conjectures about geometric relationships;

(G.2) (B) The student is expected to make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.

TX.111.34 (G.3) Geometry: Geometric structure. The student applies logical reasoning to justify and prove mathematical statements.

(G.3) (A) The student is expected to determine the validity of a conditional statement, its converse, inverse, and contrapositive;

(G.3) (B) The student is expected to construct and justify statements about geometric figures and their properties;

(G.3) (C) The student is expected to use logical reasoning to prove statements are true and find counter examples to disprove statements that are false;

(G.3) (D) The student is expected to use inductive reasoning to formulate a conjecture;

(G.3) (E) The student is expected to use deductive reasoning to prove a statement.

TX.111.34 (G.4) Geometry: Geometric structure. The student uses a variety of representations to describe geometric relationships and solve problems.

(G.4) (A) The student is expected to select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems.

TX.111.34 (G.5) Geometry: Geometric patterns. The student uses a variety of representations to describe geometric relationships and solve problems.

(G.5) (A) The student is expected to use numeric and geometric patterns to develop algebraic expressions representing geometric properties;

(G.5) (B) The student is expected to use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles;

(G.5) (C) The student is expected to use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations;

(G.5) (D) The student is expected to identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.

TX.111.34 (G.6) Geometry: Dimensionality and the geometry of location. The student analyzes the relationship between three-dimensional geometric figures and related two-dimensional representations and uses these representations to solve problems.

(G.6) (A) The student is expected to describe and draw the intersection of a given plane with various three-dimensional geometric figures;

(G.6) (B) The student is expected to use nets to represent and construct three-dimensional geometric figures;

(G.6) (C) The student is expected to use orthographic and isometric views of three-dimensional geometric figures to represent and construct three-dimensional geometric figures and solve problems.

TX.111.34 (G.7) Geometry: Dimensionality and the geometry of location. The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly.

(G.7) (A) The student is expected to use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures;

(G.7) (B) The student is expected to use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons;

(G.7) (C) The student is expected to derive and use formulas involving length, slope, and midpoint.

TX.111.34 (G.8) Geometry: Congruence and the geometry of size. The student uses tools to determine measurements of geometric figures and extends measurement concepts to find perimeter, area, and volume in problem situations.

(G.8) (A) The student is expected to find areas of regular polygons, circles, and composite figures;

(G.8) (B) The student is expected to find areas of sectors and arc lengths of circles using proportional reasoning;

(G.8) (C) The student is expected to derive, extend, and use the Pythagorean Theorem;

(G.8) (D) The student is expected to find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations.

TX.111.34 (G.9) Geometry: Congruence and the geometry of size. The student analyzes properties and describes relationships in geometric figures.

(G.9) (A) The student is expected to formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models;

(G.9) (B) The student is expected to formulate and test conjectures about the properties and attributes of polygons and their component parts based on explorations and concrete models;

(G.9) (C) The student is expected to formulate and test conjectures about the properties and attributes of circles and the lines that intersect them based on explorations and concrete models;

(G.9) (D) The student is expected to analyze the characteristics of polyhedra and other three-dimensional figures and their component parts based on explorations and concrete models.

TX.111.34 (G.10) Geometry: Congruence and the geometry of size. The student applies the concept of congruence to justify properties of figures and solve problems.

(G.10) (A) The student is expected to use congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane;

(G.10) (B) The student is expected to justify and apply triangle congruence relationships.

TX.111.34 (G.11) Geometry: Similarity and the geometry of shape. The student applies the concepts of similarity to justify properties of figures and solve problems.

(G.11) (A) The student is expected to use and extend similarity properties and transformations to explore and justify conjectures about geometric figures;

(G.11) (B) The student is expected to use ratios to solve problems involving similar figures;

(G.11) (C) The student is expected to develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples using a variety of methods;

(G.11) (D) The student is expected to describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems.

TX.111.35 (P.1) Precalculus: The student defines functions, describes characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, power (including radical), exponential, logarithmic, trigonometric, and piecewise-defined functions.

(P.1) (A) The student is expected to describe parent functions symbolically and graphically, including f(x) = x^n, f(x) = ln(x), f(x) = log base a of x, f(x) = 1/x, f(x) = e^x, f(x) = |x|, f(x) = a^x, f(x) = sin x, f(x) = arcsin x, etc.;

(P.1) (B) The student is expected to determine the domain and range of functions using graphs, tables, and symbols;

(P.1) (C) The student is expected to describe symmetry of graphs of even and odd functions;

(P.1) (D) The student is expected to recognize and use connections among significant values of a function (zeros, maximum values, minimum values, etc.), points on the graph of a function, and the symbolic representation of a function;

(P.1) (E) The student is expected to investigate the concepts of continuity, end behavior, asymptotes, and limits and connect these characteristics to functions represented graphically and numerically.

TX.111.35 (P.2) Precalculus: The student interprets the meaning of the symbolic representations of functions and operations on functions to solve meaningful problems.

(P.2) (A) The student is expected to apply basic transformations, including a*f(x), f(x) + d, f(x - c), f(b*x), and compositions with absolute value functions, including |f(x)|, and f(|x|), to the parent functions;

(P.2) (B) The student is expected to perform operations including composition on functions, find inverses, and describe these procedures and results verbally, numerically, symbolically, and graphically;

(P.2) (C) The student is expected to investigate identities graphically and verify them symbolically, including logarithmic properties, trigonometric identities, and exponential properties.

TX.111.35 (P.3) Precalculus: The student uses functions and their properties, tools and technology, to model and solve meaningful problems.

(P.3) (A) The student is expected to investigate properties of trigonometric and polynomial functions;

(P.3) (B) The student is expected to use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data;

(P.3) (C) The student is expected to use regression to determine the appropriateness of a linear function to model real-life data (including using technology to determine the correlation coefficient);

(P.3) (D) The student is expected to use properties of functions to analyze and solve problems and make predictions;

(P.3) (E) The student is expected to solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of Cosines, and area formulas and incorporate radian measure where needed.

TX.111.35 (P.4) Precalculus: The student uses sequences and series as well as tools and technology to represent, analyze, and solve real-life problems.

(P.4) (A) The student is expected to represent patterns using arithmetic and geometric sequences and series;

(P.4) (B) The student is expected to use arithmetic, geometric, and other sequences and series to solve real-life problems;

(P.4) (C) The student is expected to describe limits of sequences and apply their properties to investigate convergent and divergent series;

(P.4) (D) The student is expected to apply sequences and series to solve problems including sums and binomial expansion.

TX.111.35 (P.5) Precalculus: The student uses conic sections, their properties, and parametric representations, as well as tools and technology, to model physical situations.

(P.5) (A) The student is expected to use conic sections to model motion, such as the graph of velocity vs. position of a pendulum and motions of planets;

(P.5) (B) The student is expected to use properties of conic sections to describe physical phenomena such as the reflective properties of light and sound;

(P.5) (C) The student is expected to convert between parametric and rectangular forms of functions and equations to graph them;

(P.5) (D) The student is expected to use parametric functions to simulate problems involving motion.

TX.111.35 (P.6) Precalculus: The student uses vectors to model physical situations.

(P.6) (A) The student is expected to use the concept of vectors to model situations defined by magnitude and direction;

(P.6) (B) The student is expected to analyze and solve vector problems generated by real-life situations.

TX.111.36 (M.1) Mathematical Models with Applications: The student uses a variety of strategies and approaches to solve both routine and non-routine problems.

(M.1) (A) The student is expected to compare and analyze various methods for solving a real-life problem;

(M.1) (B) The student is expected to use multiple approaches (algebraic, graphical, and geometric methods) to solve problems from a variety of disciplines;

(M.1) (C) The student is expected to select a method to solve a problem, defend the method, and justify the reasonableness of the results.

TX.111.36 (M.2) Mathematical Models with Applications: The student uses graphical and numerical techniques to study patterns and analyze data.

(M.2) (A) The student is expected to interpret information from various graphs, including line graphs, bar graphs, circle graphs, histograms, scatterplots, line plots, stem and leaf plots, and box and whisker plots to draw conclusions from the data;

(M.2) (B) The student is expected to analyze numerical data using measures of central tendency, variability, and correlation in order to make inferences;

(M.2) (C) The student is expected to analyze graphs from journals, newspapers, and other sources to determine the validity of stated arguments;

(M.2) (D) The student is expected to use regression methods available through technology to describe various models for data such as linear, quadratic, exponential, etc., select the most appropriate model, and use the model to interpret information.

TX.111.36 (M.3) Mathematical Models with Applications: The student develops and implements a plan for collecting and analyzing data in order to make decisions.

(M.3) (A) The student is expected to formulate a meaningful question, determine the data needed to answer the question, gather the appropriate data, analyze the data, and draw reasonable conclusions;

(M.3) (B) The student is expected to communicate methods used, analyses conducted, and conclusions drawn for a data-analysis project by written report, visual display, oral report, or multi-media presentation;

(M.3) (C) The student is expected to determine the appropriateness of a model for making predictions from a given set of data.

TX.111.36 (M.4) Mathematical Models with Applications: The student uses probability models to describe everyday situations involving chance.

(M.4) (A) The student is expected to compare theoretical and empirical probability;

(M.4) (B) The student is expected to use experiments to determine the reasonableness of a theoretical model such as binomial, geometric, etc.

TX.111.36 (M.5) Mathematical Models with Applications: The student uses functional relationships to solve problems related to personal income.

(M.5) (A) The student is expected to use rates, linear functions, and direct variation to solve problems involving personal finance and budgeting, including compensations and deductions;

(M.5) (B) The student is expected to solve problems involving personal taxes;

(M.5) (C) The student is expected to analyze data to make decisions about banking.

TX.111.36 (M.6) Mathematical Models with Applications: The student uses algebraic formulas, graphs, and amortization models to solve problems involving credit.

(M.6) (A) The student is expected to analyze methods of payment available in retail purchasing and compare relative advantages and disadvantages of each option;

(M.6) (B) The student is expected to use amortization models to investigate home financing and compare buying and renting a home;

(M.6) (C) The student is expected to use amortization models to investigate automobile financing and compare buying and leasing a vehicle.

TX.111.36 (M.7) Mathematical Models with Applications: The student uses algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning.

(M.7) (A) The student is expected to analyze types of savings options involving simple and compound interest and compare relative advantages of these options;

(M.7) (B) The student is expected to analyze and compare coverage options and rates in insurance;

(M.7) (C) The student is expected to investigate and compare investment options including stocks, bonds, annuities, and retirement plans.

TX.111.36 (M.8) Mathematical Models with Applications: The student uses algebraic and geometric models to describe situations and solve problems.

(M.8) (A) The student is expected to use geometric models available through technology to model growth and decay in areas such as population, biology, and ecology;

(M.8) (B) The student is expected to use trigonometric ratios and functions available through technology to calculate distances and model periodic motion;

(M.8) (C) The student is expected to use direct and inverse variation to describe physical laws such as Hook's, Newton's, and Boyle's laws.

TX.111.36 (M.9) Mathematical Models with Applications: The student uses algebraic and geometric models to represent patterns and structures.

(M.9) (A) The student is expected to use geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and architecture;

(M.9) (B) The student is expected to use geometric transformations, proportions, and periodic motion to describe mathematical patterns and structure in music.

TX.111.32 (A.1) Algebra I: Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways.

(A.1) (A) The student is expected to describe independent and dependent quantities in functional relationships;

(A.1) (B) The student is expected to gather and record data and use data sets to determine functional relationships between quantities;

(A.1) (C) The student is expected to describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations;

(A.1) (D) The student is expected to represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities;

(A.1) (E) The student is expected to interpret and make decisions, predictions, and critical judgments from functional relationships.

TX.111.32 (A.2) Algebra I: Foundations for functions. The student uses the properties and attributes of functions.

(A.2) (A) The student is expected to identify and sketch the general forms of linear (y = x) and quadratic (y = x^2) parent functions;

(A.2) (B) The student is expected to identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete;

(A.2) (C) The student is expected to interpret situations in terms of given graphs or creates situations that fit given graphs;

(A.2) (D) The student is expected to collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations.

TX.111.32 (A.3) Algebra I: Foundations for functions. The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations.

(A.3) (A) The student is expected to use symbols to represent unknowns and variables;

(A.3) (B) The student is expected to look for patterns and represent generalizations algebraically.

TX.111.32 (A.4) Algebra I: Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations.

(A.4) (A) The student is expected to find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations;

(A.4) (B) The student is expected to use the commutative, associative, and distributive properties to simplify algebraic expressions;

(A.4) (C) The student is expected to connect equation notation with function notation, such as y = x + 1 and f(x) = x + 1.

TX.111.32 (A.5) Algebra I: Linear functions. The student understands that linear functions can be represented in different ways and translates among their various representations.

(A.5) (A) The student is expected to determine whether or not given situations can be represented by linear functions;

(A.5) (B) The student is expected to determine the domain and range for linear functions in given situations;

(A.5) (C) The student is expected to use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions.

TX.111.32 (A.6) Algebra I: Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations.

(A.6) (A) The student is expected to develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations;

(A.6) (B) The student is expected to interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs;

(A.6) (C) The student is expected to investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b;

(A.6) (D) The student is expected to graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept;

(A.6) (E) The student is expected to determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations;

(A.6) (F) The student is expected to interpret and predict the effects of changing slope and y-intercept in applied situations;

(A.6) (G) The student is expected to relate direct variation to linear functions and solve problems involving proportional change.

TX.111.32 (A.7) Algebra I: Linear functions. The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(A.7) (A) The student is expected to analyze situations involving linear functions and formulate linear equations or inequalities to solve problems;

(A.7) (B) The student is expected to investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities;

(A.7) (C) The student is expected to interpret and determine the reasonableness of solutions to linear equations and inequalities.

TX.111.32 (A.8) Algebra I: Linear functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(A.8) (A) The student is expected to analyze situations and formulate systems of linear equations in two unknowns to solve problems;

(A.8) (B) The student is expected to solve systems of linear equations using concrete models, graphs, tables, and algebraic methods;

(A.8) (C) The student is expected to interpret and determine the reasonableness of solutions to systems of linear equations.

TX.111.32 (A.9) Algebra I: Quadratic and other nonlinear functions. The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions.

(A.9) (A) The student is expected to determine the domain and range for quadratic functions in given situations;

(A.9) (B) The student is expected to investigate, describe, and predict the effects of changes in a on the graph of y = ax^2 + c;

(A.9) (C) The student is expected to investigate, describe, and predict the effects of changes in c on the graph of y = ax^2 + c;

(A.9) (D) The student is expected to analyze graphs of quadratic functions and draw conclusions.

TX.111.32 (A.10) Algebra I: Quadratic and other nonlinear functions. The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods.

(A.10) (A) The student is expected to solve quadratic equations using concrete models, tables, graphs, and algebraic methods;

(A.10) (B) The student is expected to make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function.

TX.111.32 (A.11) Algebra I: Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations.

(A.11) (A) The student is expected to use patterns to generate the laws of exponents and apply them in problem-solving situations;

(A.11) (B) The student is expected to analyze data and represent situations involving inverse variation using concrete models, tables, graphs, or algebraic methods;

(A.11) (C) The student is expected to analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods.

TX.111.33 (2A.1) Algebra II: Foundations for functions. The student uses properties and attributes of functions and applies functions to problem situations.

(2A.1) (A) The student is expected to identify the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous and discrete situations;

(2A.1) (B) The student is expected to collect and organize data, make and interpret scatterplots, fit the graph of a function to the data, interpret the results, and proceed to model, predict, and make decisions and critical judgments.

TX.111.33 (2A.2) Algebra II: Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations.

(2A.2) (A) The student is expected to use tools including factoring and properties of exponents to simplify expressions and to transform and solve equations;

(2A.2) (B) The student is expected to use complex numbers to describe the solutions of quadratic equations.

TX.111.33 (2A.3) Algebra II: Foundations for functions. The student formulates systems of equations and inequalities from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situations.

(2A.3) (A) The student is expected to analyze situations and formulate systems of equations in two or more unknowns or inequalities in two unknowns to solve problems;

(2A.3) (B) The student is expected to use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities;

(2A.3) (C) The student is expected to interpret and determine the reasonableness of solutions to systems of equations or inequalities for given contexts.

TX.111.33 (2A.4) Algebra II: Algebra and geometry. The student connects algebraic and geometric representations of functions.

(2A.4) (A) The student is expected to identify and sketch graphs of parent functions, including linear (f(x) = x), quadratic (f(x) = x^2), exponential (f(x) = a^x), and logarithmic (f(x) = log base a of x) functions, absolute value of x (f(x) = |x|), square root of x (f(x) = square root of x), and reciprocal of x (f(x) = 1/x);

(2A.4) (B) The student is expected to extend parent functions with parameters such as a in f(x) = a/x and describe the effects of the parameter changes on the graph of parent functions;

(2A.4) (C) The student is expected to describe and analyze the relationship between a function and its inverse.

TX.111.33 (2A.5) Algebra II: Algebra and geometry. The student knows the relationship between the geometric and algebraic descriptions of conic sections.

(2A.5) (A) The student is expected to describe a conic section as the intersection of a plane and a cone;

(2A.5) (B) The student is expected to sketch graphs of conic sections to relate simple parameter changes in the equation to corresponding changes in the graph;

(2A.5) (C) The student is expected to identify symmetries from graphs of conic sections;

(2A.5) (D) The student is expected to identify the conic section from a given equation;

(2A.5) (E) The student is expected to use the method of completing the square.

TX.111.33 (2A.6) Algebra II: Quadratic and square root functions. The student understands that quadratic functions can be represented in different ways and translates among their various representations.

(2A.6) (A) The student is expected to determine the reasonable domain and range values of quadratic functions, as well as interpret and determine the reasonableness of solutions to quadratic equations and inequalities;

(2A.6) (B) The student is expected to relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions;

(2A.6) (C) The student is expected to determine a quadratic function from its roots or a graph.

TX.111.33 (2A.7) Algebra II: Quadratic and square root functions. The student interprets and describes the effects of changes in the parameters of quadratic functions in applied and mathematical situations.

(2A.7) (A) The student is expected to use characteristics of the quadratic parent function to sketch the related graphs and connect between the y = ax^2 + bx + c and the y = a(x - h)^2 + k symbolic representations of quadratic functions;

(2A.7) (B) The student is expected to use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(x - h)^2 + k form of a function in applied and purely mathematical situations.

TX.111.33 (2A.8) Algebra II: Quadratic and square root functions. The student formulates equations and inequalities based on quadratic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(2A.8) (A) The student is expected to analyze situations involving quadratic functions and formulate quadratic equations or inequalities to solve problems;

(2A.8) (B) The student is expected to analyze and interpret the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula;

(2A.8) (C) The student is expected to compare and translate between algebraic and graphical solutions of quadratic equations;

(2A.8) (D) The student is expected to solve quadratic equations and inequalities using graphs, tables, and algebraic methods.

TX.111.33 (2A.9) Algebra II: Quadratic and square root functions. The student formulates equations and inequalities based on square root functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(2A.9) (A) The student is expected to use the parent function to investigate, describe, and predict the effects of parameter changes on the graphs of square root functions and describe limitations on the domains and ranges;

(2A.9) (B) The student is expected to relate representations of square root functions, such as algebraic, tabular, graphical, and verbal descriptions;

(2A.9) (C) The student is expected to determine the reasonable domain and range values of square root functions, as well as interpret and determine the reasonableness of solutions to square root equations and inequalities;

(2A.9) (D) The student is expected to determine solutions of square root equations using graphs, tables, and algebraic methods;

(2A.9) (E) The student is expected to determine solutions of square root inequalities using graphs and tables;

(2A.9) (F) The student is expected to analyze situations modeled by square root functions, formulate equations or inequalities, select a method, and solve problems;

(2A.9) (G) The student is expected to connect inverses of square root functions with quadratic functions.

TX.111.33 (2A.10) Algebra II: Rational functions. The student formulates equations and inequalities based on rational functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(2A.10) (A) The student is expected to use quotients of polynomials to describe the graphs of rational functions, predict the effects of parameter changes, describe limitations on the domains and ranges, and examine asymptotic behavior;

(2A.10) (B) The student is expected to analyze various representations of rational functions with respect to problem situations;

(2A.10) (C) The student is expected to determine the reasonable domain and range values of rational functions, as well as interpret and determine the reasonableness of solutions to rational equations and inequalities;

(2A.10) (D) The student is expected to determine the solutions of rational equations using graphs, tables, and algebraic methods;

(2A.10) (E) The student is expected to determine solutions of rational inequalities using graphs and tables;

(2A.10) (F) The student is expected to analyze a situation modeled by a rational function, formulate an equation or inequality composed of a linear or quadratic function, and solve the problem;

(2A.10) (G) The student is expected to use functions to model and make predictions in problem situations involving direct and inverse variation.

TX.111.33 (2A.11) Algebra II: Exponential and logarithmic functions. The student formulates equations and inequalities based on exponential and logarithmic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(2A.11) (A) The student is expected to develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses;

(2A.11) (B) The student is expected to use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describe limitations on the domains and ranges, and examine asymptotic behavior;

(2A.11) (C) The student is expected to determine the reasonable domain and range values of exponential and logarithmic functions, as well as interpret and determine the reasonableness of solutions to exponential and logarithmic equations and inequalities;

(2A.11) (D) The student is expected to determine solutions of exponential and logarithmic equations using graphs, tables, and algebraic methods;

(2A.11) (E) The student is expected to determine solutions of exponential and logarithmic inequalities using graphs and tables;

(2A.11) (F) The student is expected to analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem.

TX.111.34 (G.1) Geometry: Geometric structure. The student understands the structure of, and relationships within, an axiomatic system.

(G.1) (A) The student is expected to develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems;

(G.1) (B) The student is expected to recognize the historical development of geometric systems and know mathematics is developed for a variety of purposes;

(G.1) (C) The student is expected to compare and contrast the structures and implications of Euclidean and non-Euclidean geometries.

TX.111.34 (G.2) Geometry: Geometric structure. The student analyzes geometric relationships in order to make and verify conjectures.

(G.2) (A) The student is expected to use constructions to explore attributes of geometric figures and to make conjectures about geometric relationships;

(G.2) (B) The student is expected to make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.

TX.111.34 (G.3) Geometry: Geometric structure. The student applies logical reasoning to justify and prove mathematical statements.

(G.3) (A) The student is expected to determine the validity of a conditional statement, its converse, inverse, and contrapositive;

(G.3) (B) The student is expected to construct and justify statements about geometric figures and their properties;

(G.3) (C) The student is expected to use logical reasoning to prove statements are true and find counter examples to disprove statements that are false;

(G.3) (D) The student is expected to use inductive reasoning to formulate a conjecture;

(G.3) (E) The student is expected to use deductive reasoning to prove a statement.

TX.111.34 (G.4) Geometry: Geometric structure. The student uses a variety of representations to describe geometric relationships and solve problems.

(G.4) (A) The student is expected to select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems.

TX.111.34 (G.5) Geometry: Geometric patterns. The student uses a variety of representations to describe geometric relationships and solve problems.

(G.5) (A) The student is expected to use numeric and geometric patterns to develop algebraic expressions representing geometric properties;

(G.5) (B) The student is expected to use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles;

(G.5) (C) The student is expected to use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations;

(G.5) (D) The student is expected to identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.

TX.111.34 (G.6) Geometry: Dimensionality and the geometry of location. The student analyzes the relationship between three-dimensional geometric figures and related two-dimensional representations and uses these representations to solve problems.

(G.6) (A) The student is expected to describe and draw the intersection of a given plane with various three-dimensional geometric figures;

(G.6) (B) The student is expected to use nets to represent and construct three-dimensional geometric figures;

(G.6) (C) The student is expected to use orthographic and isometric views of three-dimensional geometric figures to represent and construct three-dimensional geometric figures and solve problems.

TX.111.34 (G.7) Geometry: Dimensionality and the geometry of location. The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly.

(G.7) (A) The student is expected to use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures;

(G.7) (B) The student is expected to use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons;

(G.7) (C) The student is expected to derive and use formulas involving length, slope, and midpoint.

TX.111.34 (G.8) Geometry: Congruence and the geometry of size. The student uses tools to determine measurements of geometric figures and extends measurement concepts to find perimeter, area, and volume in problem situations.

(G.8) (A) The student is expected to find areas of regular polygons, circles, and composite figures;

(G.8) (B) The student is expected to find areas of sectors and arc lengths of circles using proportional reasoning;

(G.8) (C) The student is expected to derive, extend, and use the Pythagorean Theorem;

(G.8) (D) The student is expected to find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations.

TX.111.34 (G.9) Geometry: Congruence and the geometry of size. The student analyzes properties and describes relationships in geometric figures.

(G.9) (A) The student is expected to formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models;

(G.9) (B) The student is expected to formulate and test conjectures about the properties and attributes of polygons and their component parts based on explorations and concrete models;

(G.9) (C) The student is expected to formulate and test conjectures about the properties and attributes of circles and the lines that intersect them based on explorations and concrete models;

(G.9) (D) The student is expected to analyze the characteristics of polyhedra and other three-dimensional figures and their component parts based on explorations and concrete models.

TX.111.34 (G.10) Geometry: Congruence and the geometry of size. The student applies the concept of congruence to justify properties of figures and solve problems.

(G.10) (A) The student is expected to use congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane;

(G.10) (B) The student is expected to justify and apply triangle congruence relationships.

TX.111.34 (G.11) Geometry: Similarity and the geometry of shape. The student applies the concepts of similarity to justify properties of figures and solve problems.

(G.11) (A) The student is expected to use and extend similarity properties and transformations to explore and justify conjectures about geometric figures;

(G.11) (B) The student is expected to use ratios to solve problems involving similar figures;

(G.11) (C) The student is expected to develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples using a variety of methods;

(G.11) (D) The student is expected to describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems.

TX.111.35 (P.1) Precalculus: The student defines functions, describes characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, power (including radical), exponential, logarithmic, trigonometric, and piecewise-defined functions.

(P.1) (A) The student is expected to describe parent functions symbolically and graphically, including f(x) = x^n, f(x) = ln(x), f(x) = log base a of x, f(x) = 1/x, f(x) = e^x, f(x) = |x|, f(x) = a^x, f(x) = sin x, f(x) = arcsin x, etc.;

(P.1) (B) The student is expected to determine the domain and range of functions using graphs, tables, and symbols;

(P.1) (C) The student is expected to describe symmetry of graphs of even and odd functions;

(P.1) (D) The student is expected to recognize and use connections among significant values of a function (zeros, maximum values, minimum values, etc.), points on the graph of a function, and the symbolic representation of a function;

(P.1) (E) The student is expected to investigate the concepts of continuity, end behavior, asymptotes, and limits and connect these characteristics to functions represented graphically and numerically.

TX.111.35 (P.2) Precalculus: The student interprets the meaning of the symbolic representations of functions and operations on functions to solve meaningful problems.

(P.2) (A) The student is expected to apply basic transformations, including a*f(x), f(x) + d, f(x - c), f(b*x), and compositions with absolute value functions, including |f(x)|, and f(|x|), to the parent functions;

(P.2) (B) The student is expected to perform operations including composition on functions, find inverses, and describe these procedures and results verbally, numerically, symbolically, and graphically;

(P.2) (C) The student is expected to investigate identities graphically and verify them symbolically, including logarithmic properties, trigonometric identities, and exponential properties.

TX.111.35 (P.3) Precalculus: The student uses functions and their properties, tools and technology, to model and solve meaningful problems.

(P.3) (A) The student is expected to investigate properties of trigonometric and polynomial functions;

(P.3) (B) The student is expected to use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data;

(P.3) (C) The student is expected to use regression to determine the appropriateness of a linear function to model real-life data (including using technology to determine the correlation coefficient);

(P.3) (D) The student is expected to use properties of functions to analyze and solve problems and make predictions;

(P.3) (E) The student is expected to solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of Cosines, and area formulas and incorporate radian measure where needed.

TX.111.35 (P.4) Precalculus: The student uses sequences and series as well as tools and technology to represent, analyze, and solve real-life problems.

(P.4) (A) The student is expected to represent patterns using arithmetic and geometric sequences and series;

(P.4) (B) The student is expected to use arithmetic, geometric, and other sequences and series to solve real-life problems;

(P.4) (C) The student is expected to describe limits of sequences and apply their properties to investigate convergent and divergent series;

(P.4) (D) The student is expected to apply sequences and series to solve problems including sums and binomial expansion.

TX.111.35 (P.5) Precalculus: The student uses conic sections, their properties, and parametric representations, as well as tools and technology, to model physical situations.

(P.5) (A) The student is expected to use conic sections to model motion, such as the graph of velocity vs. position of a pendulum and motions of planets;

(P.5) (B) The student is expected to use properties of conic sections to describe physical phenomena such as the reflective properties of light and sound;

(P.5) (C) The student is expected to convert between parametric and rectangular forms of functions and equations to graph them;

(P.5) (D) The student is expected to use parametric functions to simulate problems involving motion.

TX.111.35 (P.6) Precalculus: The student uses vectors to model physical situations.

(P.6) (A) The student is expected to use the concept of vectors to model situations defined by magnitude and direction;

(P.6) (B) The student is expected to analyze and solve vector problems generated by real-life situations.

TX.111.36 (M.1) Mathematical Models with Applications: The student uses a variety of strategies and approaches to solve both routine and non-routine problems.

(M.1) (A) The student is expected to compare and analyze various methods for solving a real-life problem;

(M.1) (B) The student is expected to use multiple approaches (algebraic, graphical, and geometric methods) to solve problems from a variety of disciplines;

(M.1) (C) The student is expected to select a method to solve a problem, defend the method, and justify the reasonableness of the results.

TX.111.36 (M.2) Mathematical Models with Applications: The student uses graphical and numerical techniques to study patterns and analyze data.

(M.2) (A) The student is expected to interpret information from various graphs, including line graphs, bar graphs, circle graphs, histograms, scatterplots, line plots, stem and leaf plots, and box and whisker plots to draw conclusions from the data;

(M.2) (B) The student is expected to analyze numerical data using measures of central tendency, variability, and correlation in order to make inferences;

(M.2) (C) The student is expected to analyze graphs from journals, newspapers, and other sources to determine the validity of stated arguments;

(M.2) (D) The student is expected to use regression methods available through technology to describe various models for data such as linear, quadratic, exponential, etc., select the most appropriate model, and use the model to interpret information.

TX.111.36 (M.3) Mathematical Models with Applications: The student develops and implements a plan for collecting and analyzing data in order to make decisions.

(M.3) (A) The student is expected to formulate a meaningful question, determine the data needed to answer the question, gather the appropriate data, analyze the data, and draw reasonable conclusions;

(M.3) (B) The student is expected to communicate methods used, analyses conducted, and conclusions drawn for a data-analysis project by written report, visual display, oral report, or multi-media presentation;

(M.3) (C) The student is expected to determine the appropriateness of a model for making predictions from a given set of data.

TX.111.36 (M.4) Mathematical Models with Applications: The student uses probability models to describe everyday situations involving chance.

(M.4) (A) The student is expected to compare theoretical and empirical probability;

(M.4) (B) The student is expected to use experiments to determine the reasonableness of a theoretical model such as binomial, geometric, etc.

TX.111.36 (M.5) Mathematical Models with Applications: The student uses functional relationships to solve problems related to personal income.

(M.5) (A) The student is expected to use rates, linear functions, and direct variation to solve problems involving personal finance and budgeting, including compensations and deductions;

(M.5) (B) The student is expected to solve problems involving personal taxes;

(M.5) (C) The student is expected to analyze data to make decisions about banking.

TX.111.36 (M.6) Mathematical Models with Applications: The student uses algebraic formulas, graphs, and amortization models to solve problems involving credit.

(M.6) (A) The student is expected to analyze methods of payment available in retail purchasing and compare relative advantages and disadvantages of each option;

(M.6) (B) The student is expected to use amortization models to investigate home financing and compare buying and renting a home;

(M.6) (C) The student is expected to use amortization models to investigate automobile financing and compare buying and leasing a vehicle.

TX.111.36 (M.7) Mathematical Models with Applications: The student uses algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning.

(M.7) (A) The student is expected to analyze types of savings options involving simple and compound interest and compare relative advantages of these options;

(M.7) (B) The student is expected to analyze and compare coverage options and rates in insurance;

(M.7) (C) The student is expected to investigate and compare investment options including stocks, bonds, annuities, and retirement plans.

TX.111.36 (M.8) Mathematical Models with Applications: The student uses algebraic and geometric models to describe situations and solve problems.

(M.8) (A) The student is expected to use geometric models available through technology to model growth and decay in areas such as population, biology, and ecology;

(M.8) (B) The student is expected to use trigonometric ratios and functions available through technology to calculate distances and model periodic motion;

(M.8) (C) The student is expected to use direct and inverse variation to describe physical laws such as Hook's, Newton's, and Boyle's laws.

TX.111.36 (M.9) Mathematical Models with Applications: The student uses algebraic and geometric models to represent patterns and structures.

(M.9) (A) The student is expected to use geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and architecture;

(M.9) (B) The student is expected to use geometric transformations, proportions, and periodic motion to describe mathematical patterns and structure in music.

TX.111.32 (A.1) Algebra I: Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways.

(A.1) (A) The student is expected to describe independent and dependent quantities in functional relationships;

(A.1) (B) The student is expected to gather and record data and use data sets to determine functional relationships between quantities;

(A.1) (C) The student is expected to describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations;

(A.1) (D) The student is expected to represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities;

(A.1) (E) The student is expected to interpret and make decisions, predictions, and critical judgments from functional relationships.

TX.111.32 (A.2) Algebra I: Foundations for functions. The student uses the properties and attributes of functions.

(A.2) (A) The student is expected to identify and sketch the general forms of linear (y = x) and quadratic (y = x^2) parent functions;

(A.2) (B) The student is expected to identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete;

(A.2) (C) The student is expected to interpret situations in terms of given graphs or creates situations that fit given graphs;

(A.2) (D) The student is expected to collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations.

TX.111.32 (A.3) Algebra I: Foundations for functions. The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations.

(A.3) (A) The student is expected to use symbols to represent unknowns and variables;

(A.3) (B) The student is expected to look for patterns and represent generalizations algebraically.

TX.111.32 (A.4) Algebra I: Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations.

(A.4) (A) The student is expected to find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations;

(A.4) (B) The student is expected to use the commutative, associative, and distributive properties to simplify algebraic expressions;

(A.4) (C) The student is expected to connect equation notation with function notation, such as y = x + 1 and f(x) = x + 1.

TX.111.32 (A.5) Algebra I: Linear functions. The student understands that linear functions can be represented in different ways and translates among their various representations.

(A.5) (A) The student is expected to determine whether or not given situations can be represented by linear functions;

(A.5) (B) The student is expected to determine the domain and range for linear functions in given situations;

(A.5) (C) The student is expected to use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions.

TX.111.32 (A.6) Algebra I: Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations.

(A.6) (A) The student is expected to develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations;

(A.6) (B) The student is expected to interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs;

(A.6) (C) The student is expected to investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b;

(A.6) (D) The student is expected to graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept;

(A.6) (E) The student is expected to determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations;

(A.6) (F) The student is expected to interpret and predict the effects of changing slope and y-intercept in applied situations;

(A.6) (G) The student is expected to relate direct variation to linear functions and solve problems involving proportional change.

TX.111.32 (A.7) Algebra I: Linear functions. The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(A.7) (A) The student is expected to analyze situations involving linear functions and formulate linear equations or inequalities to solve problems;

(A.7) (B) The student is expected to investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities;

(A.7) (C) The student is expected to interpret and determine the reasonableness of solutions to linear equations and inequalities.

TX.111.32 (A.8) Algebra I: Linear functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(A.8) (A) The student is expected to analyze situations and formulate systems of linear equations in two unknowns to solve problems;

(A.8) (B) The student is expected to solve systems of linear equations using concrete models, graphs, tables, and algebraic methods;

(A.8) (C) The student is expected to interpret and determine the reasonableness of solutions to systems of linear equations.

TX.111.32 (A.9) Algebra I: Quadratic and other nonlinear functions. The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions.

(A.9) (A) The student is expected to determine the domain and range for quadratic functions in given situations;

(A.9) (B) The student is expected to investigate, describe, and predict the effects of changes in a on the graph of y = ax^2 + c;

(A.9) (C) The student is expected to investigate, describe, and predict the effects of changes in c on the graph of y = ax^2 + c;

(A.9) (D) The student is expected to analyze graphs of quadratic functions and draw conclusions.

TX.111.32 (A.10) Algebra I: Quadratic and other nonlinear functions. The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods.

(A.10) (A) The student is expected to solve quadratic equations using concrete models, tables, graphs, and algebraic methods;

(A.10) (B) The student is expected to make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function.

TX.111.32 (A.11) Algebra I: Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations.

(A.11) (A) The student is expected to use patterns to generate the laws of exponents and apply them in problem-solving situations;

(A.11) (B) The student is expected to analyze data and represent situations involving inverse variation using concrete models, tables, graphs, or algebraic methods;

(A.11) (C) The student is expected to analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods.

TX.111.33 (2A.1) Algebra II: Foundations for functions. The student uses properties and attributes of functions and applies functions to problem situations.

(2A.1) (A) The student is expected to identify the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous and discrete situations;

(2A.1) (B) The student is expected to collect and organize data, make and interpret scatterplots, fit the graph of a function to the data, interpret the results, and proceed to model, predict, and make decisions and critical judgments.

TX.111.33 (2A.2) Algebra II: Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations.

(2A.2) (A) The student is expected to use tools including factoring and properties of exponents to simplify expressions and to transform and solve equations;

(2A.2) (B) The student is expected to use complex numbers to describe the solutions of quadratic equations.

TX.111.33 (2A.3) Algebra II: Foundations for functions. The student formulates systems of equations and inequalities from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situations.

(2A.3) (A) The student is expected to analyze situations and formulate systems of equations in two or more unknowns or inequalities in two unknowns to solve problems;

(2A.3) (B) The student is expected to use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities;

(2A.3) (C) The student is expected to interpret and determine the reasonableness of solutions to systems of equations or inequalities for given contexts.

TX.111.33 (2A.4) Algebra II: Algebra and geometry. The student connects algebraic and geometric representations of functions.

(2A.4) (A) The student is expected to identify and sketch graphs of parent functions, including linear (f(x) = x), quadratic (f(x) = x^2), exponential (f(x) = a^x), and logarithmic (f(x) = log base a of x) functions, absolute value of x (f(x) = |x|), square root of x (f(x) = square root of x), and reciprocal of x (f(x) = 1/x);

(2A.4) (B) The student is expected to extend parent functions with parameters such as a in f(x) = a/x and describe the effects of the parameter changes on the graph of parent functions;

(2A.4) (C) The student is expected to describe and analyze the relationship between a function and its inverse.

TX.111.33 (2A.5) Algebra II: Algebra and geometry. The student knows the relationship between the geometric and algebraic descriptions of conic sections.

(2A.5) (A) The student is expected to describe a conic section as the intersection of a plane and a cone;

(2A.5) (B) The student is expected to sketch graphs of conic sections to relate simple parameter changes in the equation to corresponding changes in the graph;

(2A.5) (C) The student is expected to identify symmetries from graphs of conic sections;

(2A.5) (D) The student is expected to identify the conic section from a given equation;

(2A.5) (E) The student is expected to use the method of completing the square.

TX.111.33 (2A.6) Algebra II: Quadratic and square root functions. The student understands that quadratic functions can be represented in different ways and translates among their various representations.

(2A.6) (A) The student is expected to determine the reasonable domain and range values of quadratic functions, as well as interpret and determine the reasonableness of solutions to quadratic equations and inequalities;

(2A.6) (B) The student is expected to relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions;

(2A.6) (C) The student is expected to determine a quadratic function from its roots or a graph.

TX.111.33 (2A.7) Algebra II: Quadratic and square root functions. The student interprets and describes the effects of changes in the parameters of quadratic functions in applied and mathematical situations.

(2A.7) (A) The student is expected to use characteristics of the quadratic parent function to sketch the related graphs and connect between the y = ax^2 + bx + c and the y = a(x - h)^2 + k symbolic representations of quadratic functions;

(2A.7) (B) The student is expected to use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(x - h)^2 + k form of a function in applied and purely mathematical situations.

TX.111.33 (2A.8) Algebra II: Quadratic and square root functions. The student formulates equations and inequalities based on quadratic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(2A.8) (A) The student is expected to analyze situations involving quadratic functions and formulate quadratic equations or inequalities to solve problems;

(2A.8) (B) The student is expected to analyze and interpret the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula;

(2A.8) (C) The student is expected to compare and translate between algebraic and graphical solutions of quadratic equations;

(2A.8) (D) The student is expected to solve quadratic equations and inequalities using graphs, tables, and algebraic methods.

TX.111.33 (2A.9) Algebra II: Quadratic and square root functions. The student formulates equations and inequalities based on square root functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(2A.9) (A) The student is expected to use the parent function to investigate, describe, and predict the effects of parameter changes on the graphs of square root functions and describe limitations on the domains and ranges;

(2A.9) (B) The student is expected to relate representations of square root functions, such as algebraic, tabular, graphical, and verbal descriptions;

(2A.9) (C) The student is expected to determine the reasonable domain and range values of square root functions, as well as interpret and determine the reasonableness of solutions to square root equations and inequalities;

(2A.9) (D) The student is expected to determine solutions of square root equations using graphs, tables, and algebraic methods;

(2A.9) (E) The student is expected to determine solutions of square root inequalities using graphs and tables;

(2A.9) (F) The student is expected to analyze situations modeled by square root functions, formulate equations or inequalities, select a method, and solve problems;

(2A.9) (G) The student is expected to connect inverses of square root functions with quadratic functions.

TX.111.33 (2A.10) Algebra II: Rational functions. The student formulates equations and inequalities based on rational functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(2A.10) (A) The student is expected to use quotients of polynomials to describe the graphs of rational functions, predict the effects of parameter changes, describe limitations on the domains and ranges, and examine asymptotic behavior;

(2A.10) (B) The student is expected to analyze various representations of rational functions with respect to problem situations;

(2A.10) (C) The student is expected to determine the reasonable domain and range values of rational functions, as well as interpret and determine the reasonableness of solutions to rational equations and inequalities;

(2A.10) (D) The student is expected to determine the solutions of rational equations using graphs, tables, and algebraic methods;

(2A.10) (E) The student is expected to determine solutions of rational inequalities using graphs and tables;

(2A.10) (F) The student is expected to analyze a situation modeled by a rational function, formulate an equation or inequality composed of a linear or quadratic function, and solve the problem;

(2A.10) (G) The student is expected to use functions to model and make predictions in problem situations involving direct and inverse variation.

TX.111.33 (2A.11) Algebra II: Exponential and logarithmic functions. The student formulates equations and inequalities based on exponential and logarithmic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(2A.11) (A) The student is expected to develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses;

(2A.11) (B) The student is expected to use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describe limitations on the domains and ranges, and examine asymptotic behavior;

(2A.11) (C) The student is expected to determine the reasonable domain and range values of exponential and logarithmic functions, as well as interpret and determine the reasonableness of solutions to exponential and logarithmic equations and inequalities;

(2A.11) (D) The student is expected to determine solutions of exponential and logarithmic equations using graphs, tables, and algebraic methods;

(2A.11) (E) The student is expected to determine solutions of exponential and logarithmic inequalities using graphs and tables;

(2A.11) (F) The student is expected to analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem.

TX.111.34 (G.1) Geometry: Geometric structure. The student understands the structure of, and relationships within, an axiomatic system.

(G.1) (A) The student is expected to develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems;

(G.1) (B) The student is expected to recognize the historical development of geometric systems and know mathematics is developed for a variety of purposes;

(G.1) (C) The student is expected to compare and contrast the structures and implications of Euclidean and non-Euclidean geometries.

TX.111.34 (G.2) Geometry: Geometric structure. The student analyzes geometric relationships in order to make and verify conjectures.

(G.2) (A) The student is expected to use constructions to explore attributes of geometric figures and to make conjectures about geometric relationships;

(G.2) (B) The student is expected to make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.

TX.111.34 (G.3) Geometry: Geometric structure. The student applies logical reasoning to justify and prove mathematical statements.

(G.3) (A) The student is expected to determine the validity of a conditional statement, its converse, inverse, and contrapositive;

(G.3) (B) The student is expected to construct and justify statements about geometric figures and their properties;

(G.3) (C) The student is expected to use logical reasoning to prove statements are true and find counter examples to disprove statements that are false;

(G.3) (D) The student is expected to use inductive reasoning to formulate a conjecture;

(G.3) (E) The student is expected to use deductive reasoning to prove a statement.

TX.111.34 (G.4) Geometry: Geometric structure. The student uses a variety of representations to describe geometric relationships and solve problems.

(G.4) (A) The student is expected to select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems.

TX.111.34 (G.5) Geometry: Geometric patterns. The student uses a variety of representations to describe geometric relationships and solve problems.

(G.5) (A) The student is expected to use numeric and geometric patterns to develop algebraic expressions representing geometric properties;

(G.5) (B) The student is expected to use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles;

(G.5) (C) The student is expected to use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations;

(G.5) (D) The student is expected to identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.

TX.111.34 (G.6) Geometry: Dimensionality and the geometry of location. The student analyzes the relationship between three-dimensional geometric figures and related two-dimensional representations and uses these representations to solve problems.

(G.6) (A) The student is expected to describe and draw the intersection of a given plane with various three-dimensional geometric figures;

(G.6) (B) The student is expected to use nets to represent and construct three-dimensional geometric figures;

(G.6) (C) The student is expected to use orthographic and isometric views of three-dimensional geometric figures to represent and construct three-dimensional geometric figures and solve problems.

TX.111.34 (G.7) Geometry: Dimensionality and the geometry of location. The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly.

(G.7) (A) The student is expected to use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures;

(G.7) (B) The student is expected to use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons;

(G.7) (C) The student is expected to derive and use formulas involving length, slope, and midpoint.

TX.111.34 (G.8) Geometry: Congruence and the geometry of size. The student uses tools to determine measurements of geometric figures and extends measurement concepts to find perimeter, area, and volume in problem situations.

(G.8) (A) The student is expected to find areas of regular polygons, circles, and composite figures;

(G.8) (B) The student is expected to find areas of sectors and arc lengths of circles using proportional reasoning;

(G.8) (C) The student is expected to derive, extend, and use the Pythagorean Theorem;

(G.8) (D) The student is expected to find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations.

TX.111.34 (G.9) Geometry: Congruence and the geometry of size. The student analyzes properties and describes relationships in geometric figures.

(G.9) (A) The student is expected to formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models;

(G.9) (B) The student is expected to formulate and test conjectures about the properties and attributes of polygons and their component parts based on explorations and concrete models;

(G.9) (C) The student is expected to formulate and test conjectures about the properties and attributes of circles and the lines that intersect them based on explorations and concrete models;

(G.9) (D) The student is expected to analyze the characteristics of polyhedra and other three-dimensional figures and their component parts based on explorations and concrete models.

TX.111.34 (G.10) Geometry: Congruence and the geometry of size. The student applies the concept of congruence to justify properties of figures and solve problems.

(G.10) (A) The student is expected to use congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane;

(G.10) (B) The student is expected to justify and apply triangle congruence relationships.

TX.111.34 (G.11) Geometry: Similarity and the geometry of shape. The student applies the concepts of similarity to justify properties of figures and solve problems.

(G.11) (A) The student is expected to use and extend similarity properties and transformations to explore and justify conjectures about geometric figures;

(G.11) (B) The student is expected to use ratios to solve problems involving similar figures;

(G.11) (C) The student is expected to develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples using a variety of methods;

(G.11) (D) The student is expected to describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems.

TX.111.35 (P.1) Precalculus: The student defines functions, describes characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, power (including radical), exponential, logarithmic, trigonometric, and piecewise-defined functions.

(P.1) (A) The student is expected to describe parent functions symbolically and graphically, including f(x) = x^n, f(x) = ln(x), f(x) = log base a of x, f(x) = 1/x, f(x) = e^x, f(x) = |x|, f(x) = a^x, f(x) = sin x, f(x) = arcsin x, etc.;

(P.1) (B) The student is expected to determine the domain and range of functions using graphs, tables, and symbols;

(P.1) (C) The student is expected to describe symmetry of graphs of even and odd functions;

(P.1) (D) The student is expected to recognize and use connections among significant values of a function (zeros, maximum values, minimum values, etc.), points on the graph of a function, and the symbolic representation of a function;

(P.1) (E) The student is expected to investigate the concepts of continuity, end behavior, asymptotes, and limits and connect these characteristics to functions represented graphically and numerically.

TX.111.35 (P.2) Precalculus: The student interprets the meaning of the symbolic representations of functions and operations on functions to solve meaningful problems.

(P.2) (A) The student is expected to apply basic transformations, including a*f(x), f(x) + d, f(x - c), f(b*x), and compositions with absolute value functions, including |f(x)|, and f(|x|), to the parent functions;

(P.2) (B) The student is expected to perform operations including composition on functions, find inverses, and describe these procedures and results verbally, numerically, symbolically, and graphically;

(P.2) (C) The student is expected to investigate identities graphically and verify them symbolically, including logarithmic properties, trigonometric identities, and exponential properties.

TX.111.35 (P.3) Precalculus: The student uses functions and their properties, tools and technology, to model and solve meaningful problems.

(P.3) (A) The student is expected to investigate properties of trigonometric and polynomial functions;

(P.3) (B) The student is expected to use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data;

(P.3) (C) The student is expected to use regression to determine the appropriateness of a linear function to model real-life data (including using technology to determine the correlation coefficient);

(P.3) (D) The student is expected to use properties of functions to analyze and solve problems and make predictions;

(P.3) (E) The student is expected to solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of Cosines, and area formulas and incorporate radian measure where needed.

TX.111.35 (P.4) Precalculus: The student uses sequences and series as well as tools and technology to represent, analyze, and solve real-life problems.

(P.4) (A) The student is expected to represent patterns using arithmetic and geometric sequences and series;

(P.4) (B) The student is expected to use arithmetic, geometric, and other sequences and series to solve real-life problems;

(P.4) (C) The student is expected to describe limits of sequences and apply their properties to investigate convergent and divergent series;

(P.4) (D) The student is expected to apply sequences and series to solve problems including sums and binomial expansion.

TX.111.35 (P.5) Precalculus: The student uses conic sections, their properties, and parametric representations, as well as tools and technology, to model physical situations.

(P.5) (A) The student is expected to use conic sections to model motion, such as the graph of velocity vs. position of a pendulum and motions of planets;

(P.5) (B) The student is expected to use properties of conic sections to describe physical phenomena such as the reflective properties of light and sound;

(P.5) (C) The student is expected to convert between parametric and rectangular forms of functions and equations to graph them;

(P.5) (D) The student is expected to use parametric functions to simulate problems involving motion.

TX.111.35 (P.6) Precalculus: The student uses vectors to model physical situations.

(P.6) (A) The student is expected to use the concept of vectors to model situations defined by magnitude and direction;

(P.6) (B) The student is expected to analyze and solve vector problems generated by real-life situations.

TX.111.36 (M.1) Mathematical Models with Applications: The student uses a variety of strategies and approaches to solve both routine and non-routine problems.

(M.1) (A) The student is expected to compare and analyze various methods for solving a real-life problem;

(M.1) (B) The student is expected to use multiple approaches (algebraic, graphical, and geometric methods) to solve problems from a variety of disciplines;

(M.1) (C) The student is expected to select a method to solve a problem, defend the method, and justify the reasonableness of the results.

TX.111.36 (M.2) Mathematical Models with Applications: The student uses graphical and numerical techniques to study patterns and analyze data.

(M.2) (A) The student is expected to interpret information from various graphs, including line graphs, bar graphs, circle graphs, histograms, scatterplots, line plots, stem and leaf plots, and box and whisker plots to draw conclusions from the data;

(M.2) (B) The student is expected to analyze numerical data using measures of central tendency, variability, and correlation in order to make inferences;

(M.2) (C) The student is expected to analyze graphs from journals, newspapers, and other sources to determine the validity of stated arguments;

(M.2) (D) The student is expected to use regression methods available through technology to describe various models for data such as linear, quadratic, exponential, etc., select the most appropriate model, and use the model to interpret information.

TX.111.36 (M.3) Mathematical Models with Applications: The student develops and implements a plan for collecting and analyzing data in order to make decisions.

(M.3) (A) The student is expected to formulate a meaningful question, determine the data needed to answer the question, gather the appropriate data, analyze the data, and draw reasonable conclusions;

(M.3) (B) The student is expected to communicate methods used, analyses conducted, and conclusions drawn for a data-analysis project by written report, visual display, oral report, or multi-media presentation;

(M.3) (C) The student is expected to determine the appropriateness of a model for making predictions from a given set of data.

TX.111.36 (M.4) Mathematical Models with Applications: The student uses probability models to describe everyday situations involving chance.

(M.4) (A) The student is expected to compare theoretical and empirical probability;

(M.4) (B) The student is expected to use experiments to determine the reasonableness of a theoretical model such as binomial, geometric, etc.

TX.111.36 (M.5) Mathematical Models with Applications: The student uses functional relationships to solve problems related to personal income.

(M.5) (A) The student is expected to use rates, linear functions, and direct variation to solve problems involving personal finance and budgeting, including compensations and deductions;

(M.5) (B) The student is expected to solve problems involving personal taxes;

(M.5) (C) The student is expected to analyze data to make decisions about banking.

TX.111.36 (M.6) Mathematical Models with Applications: The student uses algebraic formulas, graphs, and amortization models to solve problems involving credit.

(M.6) (A) The student is expected to analyze methods of payment available in retail purchasing and compare relative advantages and disadvantages of each option;

(M.6) (B) The student is expected to use amortization models to investigate home financing and compare buying and renting a home;

(M.6) (C) The student is expected to use amortization models to investigate automobile financing and compare buying and leasing a vehicle.

TX.111.36 (M.7) Mathematical Models with Applications: The student uses algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning.

(M.7) (A) The student is expected to analyze types of savings options involving simple and compound interest and compare relative advantages of these options;

(M.7) (B) The student is expected to analyze and compare coverage options and rates in insurance;

(M.7) (C) The student is expected to investigate and compare investment options including stocks, bonds, annuities, and retirement plans.

TX.111.36 (M.8) Mathematical Models with Applications: The student uses algebraic and geometric models to describe situations and solve problems.

(M.8) (A) The student is expected to use geometric models available through technology to model growth and decay in areas such as population, biology, and ecology;

(M.8) (B) The student is expected to use trigonometric ratios and functions available through technology to calculate distances and model periodic motion;

(M.8) (C) The student is expected to use direct and inverse variation to describe physical laws such as Hook's, Newton's, and Boyle's laws.

TX.111.36 (M.9) Mathematical Models with Applications: The student uses algebraic and geometric models to represent patterns and structures.

(M.9) (A) The student is expected to use geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and architecture;

(M.9) (B) The student is expected to use geometric transformations, proportions, and periodic motion to describe mathematical patterns and structure in music.

TX.111.32 (A.1) Algebra I: Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways.

(A.1) (A) The student is expected to describe independent and dependent quantities in functional relationships;

(A.1) (B) The student is expected to gather and record data and use data sets to determine functional relationships between quantities;

(A.1) (C) The student is expected to describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations;

(A.1) (D) The student is expected to represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities;

(A.1) (E) The student is expected to interpret and make decisions, predictions, and critical judgments from functional relationships.

TX.111.32 (A.2) Algebra I: Foundations for functions. The student uses the properties and attributes of functions.

(A.2) (A) The student is expected to identify and sketch the general forms of linear (y = x) and quadratic (y = x^2) parent functions;

(A.2) (B) The student is expected to identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete;

(A.2) (C) The student is expected to interpret situations in terms of given graphs or creates situations that fit given graphs;

(A.2) (D) The student is expected to collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations.

TX.111.32 (A.3) Algebra I: Foundations for functions. The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations.

(A.3) (A) The student is expected to use symbols to represent unknowns and variables;

(A.3) (B) The student is expected to look for patterns and represent generalizations algebraically.

TX.111.32 (A.4) Algebra I: Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations.

(A.4) (A) The student is expected to find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations;

(A.4) (B) The student is expected to use the commutative, associative, and distributive properties to simplify algebraic expressions;

(A.4) (C) The student is expected to connect equation notation with function notation, such as y = x + 1 and f(x) = x + 1.

TX.111.32 (A.5) Algebra I: Linear functions. The student understands that linear functions can be represented in different ways and translates among their various representations.

(A.5) (A) The student is expected to determine whether or not given situations can be represented by linear functions;

(A.5) (B) The student is expected to determine the domain and range for linear functions in given situations;

(A.5) (C) The student is expected to use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions.

TX.111.32 (A.6) Algebra I: Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations.

(A.6) (A) The student is expected to develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations;

(A.6) (B) The student is expected to interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs;

(A.6) (C) The student is expected to investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b;

(A.6) (D) The student is expected to graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept;

(A.6) (E) The student is expected to determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations;

(A.6) (F) The student is expected to interpret and predict the effects of changing slope and y-intercept in applied situations;

(A.6) (G) The student is expected to relate direct variation to linear functions and solve problems involving proportional change.

TX.111.32 (A.7) Algebra I: Linear functions. The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(A.7) (A) The student is expected to analyze situations involving linear functions and formulate linear equations or inequalities to solve problems;

(A.7) (B) The student is expected to investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities;

(A.7) (C) The student is expected to interpret and determine the reasonableness of solutions to linear equations and inequalities.

TX.111.32 (A.8) Algebra I: Linear functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(A.8) (A) The student is expected to analyze situations and formulate systems of linear equations in two unknowns to solve problems;

(A.8) (B) The student is expected to solve systems of linear equations using concrete models, graphs, tables, and algebraic methods;

(A.8) (C) The student is expected to interpret and determine the reasonableness of solutions to systems of linear equations.

TX.111.32 (A.9) Algebra I: Quadratic and other nonlinear functions. The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions.

(A.9) (A) The student is expected to determine the domain and range for quadratic functions in given situations;

(A.9) (B) The student is expected to investigate, describe, and predict the effects of changes in a on the graph of y = ax^2 + c;

(A.9) (C) The student is expected to investigate, describe, and predict the effects of changes in c on the graph of y = ax^2 + c; and

(A.9) (D) The student is expected to analyze graphs of quadratic functions and draw conclusions.

TX.111.32 (A.10) Algebra I: Quadratic and other nonlinear functions. The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods.

(A.10) (A) The student is expected to solve quadratic equations using concrete models, tables, graphs, and algebraic methods;

(A.10) (B) The student is expected to make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function.

TX.111.32 (A.11) Algebra I: Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations.

(A.11) (A) The student is expected to use patterns to generate the laws of exponents and apply them in problem-solving situations;

(A.11) (B) The student is expected to analyze data and represent situations involving inverse variation using concrete models, tables, graphs, or algebraic methods;

(A.11) (C) The student is expected to analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods.

TX.111.33 (2A.1) Algebra II: Foundations for functions. The student uses properties and attributes of functions and applies functions to problem situations.

(2A.1) (A) The student is expected to identify the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous and discrete situations;

(2A.1) (B) The student is expected to collect and organize data, make and interpret scatterplots, fit the graph of a function to the data, interpret the results, and proceed to model, predict, and make decisions and critical judgments.

TX.111.33 (2A.2) Algebra II: Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations.

(2A.2) (A) The student is expected to use tools including factoring and properties of exponents to simplify expressions and to transform and solve equations;

(2A.2) (B) The student is expected to use complex numbers to describe the solutions of quadratic equations.

TX.111.33 (2A.3) Algebra II: Foundations for functions. The student formulates systems of equations and inequalities from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situations.

(2A.3) (A) The student is expected to analyze situations and formulate systems of equations in two or more unknowns or inequalities in two unknowns to solve problems;

(2A.3) (B) The student is expected to use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities;

(2A.3) (C) The student is expected to interpret and determine the reasonableness of solutions to systems of equations or inequalities for given contexts.

TX.111.33 (2A.4) Algebra II: Algebra and geometry. The student connects algebraic and geometric representations of functions.

(2A.4) (A) The student is expected to identify and sketch graphs of parent functions, including linear (f(x) = x), quadratic (f(x) = x^2), exponential (f(x) = a^x), and logarithmic (f(x) = log base a of x) functions, absolute value of x (f(x) = |x|), square root of x (f(x) = square root of x), and reciprocal of x (f(x) = 1/x);

(2A.4) (B) The student is expected to extend parent functions with parameters such as a in f(x) = a/x and describe the effects of the parameter changes on the graph of parent functions;

(2A.4) (C) The student is expected to describe and analyze the relationship between a function and its inverse.

TX.111.33 (2A.5) Algebra II: Algebra and geometry. The student knows the relationship between the geometric and algebraic descriptions of conic sections.

(2A.5) (A) The student is expected to describe a conic section as the intersection of a plane and a cone;

(2A.5) (B) The student is expected to sketch graphs of conic sections to relate simple parameter changes in the equation to corresponding changes in the graph;

(2A.5) (C) The student is expected to identify symmetries from graphs of conic sections;

(2A.5) (D) The student is expected to identify the conic section from a given equation;

(2A.5) (E) The student is expected to use the method of completing the square.

TX.111.33 (2A.6) Algebra II: Quadratic and square root functions. The student understands that quadratic functions can be represented in different ways and translates among their various representations.

(2A.6) (A) The student is expected to determine the reasonable domain and range values of quadratic functions, as well as interpret and determine the reasonableness of solutions to quadratic equations and inequalities;

(2A.6) (B) The student is expected to relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions;

(2A.6) (C) The student is expected to determine a quadratic function from its roots or a graph.

TX.111.33 (2A.7) Algebra II: Quadratic and square root functions. The student interprets and describes the effects of changes in the parameters of quadratic functions in applied and mathematical situations.

(2A.7) (A) The student is expected to use characteristics of the quadratic parent function to sketch the related graphs and connect between the y = ax^2 + bx + c and the y = a(x - h)^2 + k symbolic representations of quadratic functions;

(2A.7) (B) The student is expected to use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(x - h)^2 + k form of a function in applied and purely mathematical situations.

TX.111.33 (2A.8) Algebra II: Quadratic and square root functions. The student formulates equations and inequalities based on quadratic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(2A.8) (A) The student is expected to analyze situations involving quadratic functions and formulate quadratic equations or inequalities to solve problems;

(2A.8) (B) The student is expected to analyze and interpret the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula;

(2A.8) (C) The student is expected to compare and translate between algebraic and graphical solutions of quadratic equations;

(2A.8) (D) The student is expected to solve quadratic equations and inequalities using graphs, tables, and algebraic methods.

TX.111.33 (2A.9) Algebra II: Quadratic and square root functions. The student formulates equations and inequalities based on square root functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(2A.9) (A) The student is expected to use the parent function to investigate, describe, and predict the effects of parameter changes on the graphs of square root functions and describe limitations on the domains and ranges;

(2A.9) (B) The student is expected to relate representations of square root functions, such as algebraic, tabular, graphical, and verbal descriptions;

(2A.9) (C) The student is expected to determine the reasonable domain and range values of square root functions, as well as interpret and determine the reasonableness of solutions to square root equations and inequalities;

(2A.9) (D) The student is expected to determine solutions of square root equations using graphs, tables, and algebraic methods;

(2A.9) (E) The student is expected to determine solutions of square root inequalities using graphs and tables;

(2A.9) (F) The student is expected to analyze situations modeled by square root functions, formulate equations or inequalities, select a method, and solve problems;

(2A.9) (G) The student is expected to connect inverses of square root functions with quadratic functions.

TX.111.33 (2A.10) Algebra II: Rational functions. The student formulates equations and inequalities based on rational functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(2A.10) (A) The student is expected to use quotients of polynomials to describe the graphs of rational functions, predict the effects of parameter changes, describe limitations on the domains and ranges, and examine asymptotic behavior;

(2A.10) (B) The student is expected to analyze various representations of rational functions with respect to problem situations;

(2A.10) (C) The student is expected to determine the reasonable domain and range values of rational functions, as well as interpret and determine the reasonableness of solutions to rational equations and inequalities;

(2A.10) (D) The student is expected to determine the solutions of rational equations using graphs, tables, and algebraic methods;

(2A.10) (E) The student is expected to determine solutions of rational inequalities using graphs and tables;

(2A.10) (F) The student is expected to analyze a situation modeled by a rational function, formulate an equation or inequality composed of a linear or quadratic function, and solve the problem;

(2A.10) (G) The student is expected to use functions to model and make predictions in problem situations involving direct and inverse variation.

TX.111.33 (2A.11) Algebra II: Exponential and logarithmic functions. The student formulates equations and inequalities based on exponential and logarithmic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(2A.11) (A) The student is expected to develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses;

(2A.11) (B) The student is expected to use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describe limitations on the domains and ranges, and examine asymptotic behavior;

(2A.11) (C) The student is expected to determine the reasonable domain and range values of exponential and logarithmic functions, as well as interpret and determine the reasonableness of solutions to exponential and logarithmic equations and inequalities;

(2A.11) (D) The student is expected to determine solutions of exponential and logarithmic equations using graphs, tables, and algebraic methods;

(2A.11) (E) The student is expected to determine solutions of exponential and logarithmic inequalities using graphs and tables;

(2A.11) (F) The student is expected to analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem.

TX.111.34 (G.1) Geometry: Geometric structure. The student understands the structure of, and relationships within, an axiomatic system.

(G.1) (A) The student is expected to develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems;

(G.1) (B) The student is expected to recognize the historical development of geometric systems and know mathematics is developed for a variety of purposes;

(G.1) (C) The student is expected to compare and contrast the structures and implications of Euclidean and non-Euclidean geometries.

TX.111.34 (G.2) Geometry: Geometric structure. The student analyzes geometric relationships in order to make and verify conjectures.

(G.2) (A) The student is expected to use constructions to explore attributes of geometric figures and to make conjectures about geometric relationships;

(G.2) (B) The student is expected to make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.

TX.111.34 (G.3) Geometry: Geometric structure. The student applies logical reasoning to justify and prove mathematical statements.

(G.3) (A) The student is expected to determine the validity of a conditional statement, its converse, inverse, and contrapositive;

(G.3) (B) The student is expected to construct and justify statements about geometric figures and their properties;

(G.3) (C) The student is expected to use logical reasoning to prove statements are true and find counter examples to disprove statements that are false;

(G.3) (D) The student is expected to use inductive reasoning to formulate a conjecture;

(G.3) (E) The student is expected to use deductive reasoning to prove a statement.

TX.111.34 (G.4) Geometry: Geometric structure. The student uses a variety of representations to describe geometric relationships and solve problems.

(G.4) (A) The student is expected to select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems.

TX.111.34 (G.5) Geometry: Geometric patterns. The student uses a variety of representations to describe geometric relationships and solve problems.

(G.5) (A) The student is expected to use numeric and geometric patterns to develop algebraic expressions representing geometric properties;

(G.5) (B) The student is expected to use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles;

(G.5) (C) The student is expected to use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations;

(G.5) (D) The student is expected to identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.

TX.111.34 (G.6) Geometry: Dimensionality and the geometry of location. The student analyzes the relationship between three-dimensional geometric figures and related two-dimensional representations and uses these representations to solve problems.

(G.6) (A) The student is expected to describe and draw the intersection of a given plane with various three-dimensional geometric figures;

(G.6) (B) The student is expected to use nets to represent and construct three-dimensional geometric figures;

(G.6) (C) The student is expected to use orthographic and isometric views of three-dimensional geometric figures to represent and construct three-dimensional geometric figures and solve problems.

TX.111.34 (G.7) Geometry: Dimensionality and the geometry of location. The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly.

(G.7) (A) The student is expected to use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures;

(G.7) (B) The student is expected to use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons;

(G.7) (C) The student is expected to derive and use formulas involving length, slope, and midpoint.

TX.111.34 (G.8) Geometry: Congruence and the geometry of size. The student uses tools to determine measurements of geometric figures and extends measurement concepts to find perimeter, area, and volume in problem situations.

(G.8) (A) The student is expected to find areas of regular polygons, circles, and composite figures;

(G.8) (B) The student is expected to find areas of sectors and arc lengths of circles using proportional reasoning;

(G.8) (C) The student is expected to derive, extend, and use the Pythagorean Theorem;

(G.8) (D) The student is expected to find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations.

TX.111.34 (G.9) Geometry: Congruence and the geometry of size. The student analyzes properties and describes relationships in geometric figures.

(G.9) (A) The student is expected to formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models;

(G.9) (B) The student is expected to formulate and test conjectures about the properties and attributes of polygons and their component parts based on explorations and concrete models;

(G.9) (C) The student is expected to formulate and test conjectures about the properties and attributes of circles and the lines that intersect them based on explorations and concrete models;

(G.9) (D) The student is expected to analyze the characteristics of polyhedra and other three-dimensional figures and their component parts based on explorations and concrete models.

TX.111.34 (G.10) Geometry: Congruence and the geometry of size. The student applies the concept of congruence to justify properties of figures and solve problems.

(G.10) (A) The student is expected to use congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane;

(G.10) (B) The student is expected to justify and apply triangle congruence relationships.

TX.111.34 (G.11) Geometry: Similarity and the geometry of shape. The student applies the concepts of similarity to justify properties of figures and solve problems.

(G.11) (A) The student is expected to use and extend similarity properties and transformations to explore and justify conjectures about geometric figures;

(G.11) (B) The student is expected to use ratios to solve problems involving similar figures;

(G.11) (C) The student is expected to develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples using a variety of methods;

(G.11) (D) The student is expected to describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems.

TX.111.35 (P.1) Precalculus: The student defines functions, describes characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, power (including radical), exponential, logarithmic, trigonometric, and piecewise-defined functions.

(P.1) (A) The student is expected to describe parent functions symbolically and graphically, including f(x) = x^n, f(x) = ln(x), f(x) = log base a of x, f(x) = 1/x, f(x) = e^x, f(x) = |x|, f(x) = a^x, f(x) = sin x, f(x) = arcsin x, etc.;

(P.1) (B) The student is expected to determine the domain and range of functions using graphs, tables, and symbols;

(P.1) (C) The student is expected to describe symmetry of graphs of even and odd functions;

(P.1) (D) The student is expected to recognize and use connections among significant values of a function (zeros, maximum values, minimum values, etc.), points on the graph of a function, and the symbolic representation of a function;

(P.1) (E) The student is expected to investigate the concepts of continuity, end behavior, asymptotes, and limits and connect these characteristics to functions represented graphically and numerically.

TX.111.35 (P.2) Precalculus: The student interprets the meaning of the symbolic representations of functions and operations on functions to solve meaningful problems.

(P.2) (A) The student is expected to apply basic transformations, including a*f(x), f(x) + d, f(x - c), f(b*x), and compositions with absolute value functions, including |f(x)|, and f(|x|), to the parent functions;

(P.2) (B) The student is expected to perform operations including composition on functions, find inverses, and describe these procedures and results verbally, numerically, symbolically, and graphically;

(P.2) (C) The student is expected to investigate identities graphically and verify them symbolically, including logarithmic properties, trigonometric identities, and exponential properties.

TX.111.35 (P.3) Precalculus: The student uses functions and their properties, tools and technology, to model and solve meaningful problems.

(P.3) (A) The student is expected to investigate properties of trigonometric and polynomial functions;

(P.3) (B) The student is expected to use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data;

(P.3) (C) The student is expected to use regression to determine the appropriateness of a linear function to model real-life data (including using technology to determine the correlation coefficient);

(P.3) (D) The student is expected to use properties of functions to analyze and solve problems and make predictions;

(P.3) (E) The student is expected to solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of Cosines, and area formulas and incorporate radian measure where needed.

TX.111.35 (P.4) Precalculus: The student uses sequences and series as well as tools and technology to represent, analyze, and solve real-life problems.

(P.4) (A) The student is expected to represent patterns using arithmetic and geometric sequences and series;

(P.4) (B) The student is expected to use arithmetic, geometric, and other sequences and series to solve real-life problems;

(P.4) (C) The student is expected to describe limits of sequences and apply their properties to investigate convergent and divergent series;

(P.4) (D) The student is expected to apply sequences and series to solve problems including sums and binomial expansion.

TX.111.35 (P.5) Precalculus: The student uses conic sections, their properties, and parametric representations, as well as tools and technology, to model physical situations.

(P.5) (A) The student is expected to use conic sections to model motion, such as the graph of velocity vs. position of a pendulum and motions of planets;

(P.5) (B) The student is expected to use properties of conic sections to describe physical phenomena such as the reflective properties of light and sound;

(P.5) (C) The student is expected to convert between parametric and rectangular forms of functions and equations to graph them;

(P.5) (D) The student is expected to use parametric functions to simulate problems involving motion.

TX.111.35 (P.6) Precalculus: The student uses vectors to model physical situations.

(P.6) (A) The student is expected to use the concept of vectors to model situations defined by magnitude and direction;

(P.6) (B) The student is expected to analyze and solve vector problems generated by real-life situations.

TX.111.36 (M.1) Mathematical Models with Applications: The student uses a variety of strategies and approaches to solve both routine and non-routine problems.

(M.1) (A) The student is expected to compare and analyze various methods for solving a real-life problem;

(M.1) (B) The student is expected to use multiple approaches (algebraic, graphical, and geometric methods) to solve problems from a variety of disciplines;

(M.1) (C) The student is expected to select a method to solve a problem, defend the method, and justify the reasonableness of the results.

TX.111.36 (M.2) Mathematical Models with Applications: The student uses graphical and numerical techniques to study patterns and analyze data.

(M.2) (A) The student is expected to interpret information from various graphs, including line graphs, bar graphs, circle graphs, histograms, scatterplots, line plots, stem and leaf plots, and box and whisker plots to draw conclusions from the data;

(M.2) (B) The student is expected to analyze numerical data using measures of central tendency, variability, and correlation in order to make inferences;

(M.2) (C) The student is expected to analyze graphs from journals, newspapers, and other sources to determine the validity of stated arguments;

(M.2) (D) The student is expected to use regression methods available through technology to describe various models for data such as linear, quadratic, exponential, etc., select the most appropriate model, and use the model to interpret information.

TX.111.36 (M.3) Mathematical Models with Applications: The student develops and implements a plan for collecting and analyzing data in order to make decisions.

(M.3) (A) The student is expected to formulate a meaningful question, determine the data needed to answer the question, gather the appropriate data, analyze the data, and draw reasonable conclusions;

(M.3) (B) The student is expected to communicate methods used, analyses conducted, and conclusions drawn for a data-analysis project by written report, visual display, oral report, or multi-media presentation;

(M.3) (C) The student is expected to determine the appropriateness of a model for making predictions from a given set of data.

TX.111.36 (M.4) Mathematical Models with Applications: The student uses probability models to describe everyday situations involving chance.

(M.4) (A) The student is expected to compare theoretical and empirical probability;

(M.4) (B) The student is expected to use experiments to determine the reasonableness of a theoretical model such as binomial, geometric, etc.

TX.111.36 (M.5) Mathematical Models with Applications: The student uses functional relationships to solve problems related to personal income.

(M.5) (A) The student is expected to use rates, linear functions, and direct variation to solve problems involving personal finance and budgeting, including compensations and deductions;

(M.5) (B) The student is expected to solve problems involving personal taxes;

(M.5) (C) The student is expected to analyze data to make decisions about banking.

TX.111.36 (M.6) Mathematical Models with Applications: The student uses algebraic formulas, graphs, and amortization models to solve problems involving credit.

(M.6) (A) The student is expected to analyze methods of payment available in retail purchasing and compare relative advantages and disadvantages of each option;

(M.6) (B) The student is expected to use amortization models to investigate home financing and compare buying and renting a home;

(M.6) (C) The student is expected to use amortization models to investigate automobile financing and compare buying and leasing a vehicle.

TX.111.36 (M.7) Mathematical Models with Applications: The student uses algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning.

(M.7) (A) The student is expected to analyze types of savings options involving simple and compound interest and compare relative advantages of these options;

(M.7) (B) The student is expected to analyze and compare coverage options and rates in insurance;

(M.7) (C) The student is expected to investigate and compare investment options including stocks, bonds, annuities, and retirement plans.

TX.111.36 (M.8) Mathematical Models with Applications: The student uses algebraic and geometric models to describe situations and solve problems.

(M.8) (A) The student is expected to use geometric models available through technology to model growth and decay in areas such as population, biology, and ecology;

(M.8) (B) The student is expected to use trigonometric ratios and functions available through technology to calculate distances and model periodic motion;

(M.8) (C) The student is expected to use direct and inverse variation to describe physical laws such as Hook's, Newton's, and Boyle's laws.

TX.111.36 (M.9) Mathematical Models with Applications: The student uses algebraic and geometric models to represent patterns and structures.

(M.9) (A) The student is expected to use geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and architecture;

(M.9) (B) The student is expected to use geometric transformations, proportions, and periodic motion to describe mathematical patterns and structure in music.