## State-aligned Pathways to Support Standards

Think Through Math (now Imagine Math), helps students in Texas grades 3 and above develop higher order thinking and problem-solving skills, preparing them for success on the STAAR exam, as well as a smooth transition to college or a career.

## Download Texas Pathways

Imagine Math assesses your students’ performance on each standard instantly, so you’ll have all the information you need to prepare them for standardized testing.

Download printable versions of the Texas pathways and standards or see interactive version below.

## Grade 3

## Texas Learning Pathway

## Number and Operations in Base Ten

**Visualizing Whole Numbers**

Introductory Lesson

**Visualizing Place Value**

Introductory Lesson

## Operations and Algebraic Thinking

**Visualizing Addition**

Introductory Lesson

**Visualizing Subtraction**

Introductory Lesson

## Number and Operations in Base Ten

**Place Value with Whole Numbers I**

3.2.A compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate

3.2.B describe the mathematical relationships found in the base-10 place value system through the hundred thousands place

**Place Value with Whole Numbers II**

3.2.A compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate

**Reasoning About Place Value and Rounding**

3.2.C represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers

3.2.D compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =

**Rounding to the Nearest Ten and Hundred**

3.2.C represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers

## Operations and Algebraic Thinking

**Equal Groups II**

3.4.D determine the total number of objects when equally-sized groups of objects are combined or arranged in arrays up to 10 by 10

## Number and Operations in Base Ten

**Reasoning About Addition and Subtraction Within 1,000**

3.4.A solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction

3.5.A represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations

## Operations and Algebraic Thinking

**Concept of Multiplication – Grouping**

3.4.E represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting

3.4.K solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

**Concept of Multiplication – Word Problems**

3.4.E represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting

3.4.F recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts

3.4.G use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties

3.4.K solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

**Concept of Multiplication – Arrays**

3.4.E represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting

3.4.K solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

3.5.B represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations

**Properties of Addition and Multiplication**

3.4.G use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties

**Applying Properties of Addition and Multiplication to Area Models**

3.4.K solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

**Multiplication as a Comparison – Word Problems**

3.5.C describe a multiplication expression as a comparison such as 3 x 24 represents 3 times as much as 24

**Multiplication as a Comparison – Equations**

3.5.C describe a multiplication expression as a comparison such as 3 x 24 represents 3 times as much as 24

**Concept of Division**

3.4.F recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts

3.4.H determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally

**Interpreting Division Problems **

3.4.K solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts

**Constructing Division Problems**

3.5.B represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations

**Relationship Between Multiplication and Division**

3.4.J determine a quotient using the relationship between multiplication and division

**Multiplication and Division Fact Families**

3.4.J determine a quotient using the relationship between multiplication and division

3.5.D determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is either a missing factor or product

**Odd or Even**

3.4.I determine if a number is even or odd using divisibility rules

**Solving Multiplication and Division Equations**

3.5.B represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations

**Division as an Unknown-Factor Problem**

3.4.J determine a quotient using the relationship between multiplication and division

3.5.D determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is either a missing factor or product

## Number and Operations in Base Ten

**Multiplying by Multiples of Ten**

3.4.F recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts

3.4.G use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties

## Number and Operations - Fractions

**Understanding Fractions – Equal Areas**

3.3.A represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines

3.3.D compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b

3.3.E solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8

**Understanding Fractions – Notation**

3.3.A represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines

3.3.E solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8

**Unit Fractions on the Number Line**

3.3.A represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines

3.3.B determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line

3.3.C explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number

3.7.A represent fractions of halves, fourths, and eighths as distances from zero on a number line

**Fractions on the Number Line**

3.3.A represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines

3.3.B determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line

3.3.C explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number

**Modeling Equivalent Fractions with Number Lines**

3.3.F represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines

3.3.G explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model

**Visual Models of Equivalent Fractions**

3.3.F represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines

3.3.G explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model

**Whole Numbers as Fractions**

3.3.F represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines

**Whole Numbers as Fractions on the Number Line**

3.3.F represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines

**Comparing Fractions with the Same Numerator or Denominator**

3.3.H compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models

**Recognizing Valid Fraction Comparisons I**

3.3.H compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models

## Measurement and Data

**Money Sense**

3.4.C determine the value of a collection of coins and bills Adding and Subtracting Time

3.7.C determine the solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15-minute event plus a 30-minute event equals 45 minutes

**Unit Squares**

3.6.C determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row

**Concept of Area**

3.6.C determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row

**Area of Rectangles**

3.6.C determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row

**Recognizing Area as Additive**

3.6.D decompose composite figures formed by rectangles into non-overlapping rectangles to determine the area of the original figure using the additive property of area

**Area of Basic Composite Figures**

3.6.D decompose composite figures formed by rectangles into non-overlapping rectangles to determine the area of the original figure using the additive property of area

3.6.E decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identical wholes need not have the same shape

**Perimeter**

3.7.B determine the perimeter of a polygon or a missing length when given perimeter and remaining side lengths in problems

**Capacity or Weight**

3.7.D determine when it is appropriate to use measurements of liquid volume (capacity) or weight

3.7.E determine liquid volume (capacity) or weight using appropriate units and tools

## Geometry

**Classifying Quadrilaterals I**

3.6.B use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories

**Classifying 3-Dimensional Figures**

3.6.A classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language

## Measurement and Data

**Introduction to Data Displays**

3.8.A summarize a data set with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals

3.8.B solve one- and two-step problems using categorical data represented with a frequency table, dot plot, pictograph, or bar graph with scaled intervals

## Operations and Algebraic Thinking

**Input-Output Tables**

3.5.E represent real-world relationships using number pairs in a table and verbal descriptions

## Financial Literacy

**Supply and Cost**

3.9.B describe the relationship between the availability or scarcity of resources and how that impacts cost

**Credit Sense**

3.9.D explain that credit is used when wants or needs exceed the ability to pay and that it is the borrower’s responsibility to pay it back to the lender, usually with interest

**Saving Money**

3.9.E list reasons to save and explain the benefit of a savings plan, including for college

**Money Decisions**

3.9.F identify decisions involving income, spending, saving, credit, and charitable giving

## Grade 4

## Texas Learning Pathway

## Number and Operations in Base Ten

**Visualizing Place Value Relationships**

Introductory Lesson

**Visualizing Rounding**

Introductory Lesson

## Operations and Algebraic Thinking

**Visualizing Addition and Subtraction**

Introductory Lesson

**Visualizing Multiplication and Division**

Introductory Lesson

## Number and Operations in Base Ten

**Understanding Place Value Relationships**

4.2.A interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left

4.2.B represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals

**Using Place Value Concepts to Compare Whole Numbers**

4.2.C compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >, <, or =

**Rounding Whole Numbers**

4.2.D round whole numbers to a given place value through the hundred thousands place

**Using Rounding in Problem Solving**

4.2.D round whole numbers to a given place value through the hundred thousands place

**Place Value Relationships Within Whole Numbers and Decimals**

4.2.B represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals

## Operations and Algebraic Thinking

**Estimating Sums and Differences – Application**

4.4.G round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers

## Number and Operations in Base Ten

**Adding Whole Numbers**

4.4.A add and subtract whole numbers and decimals to the hundredths place using the standard algorithm

**Adding and Subtracting with the Standard Algorithm**

4.4.A add and subtract whole numbers and decimals to the hundredths place using the standard algorithm

## Operations and Algebraic Thinking

**Solving Multiplication and Division Equations**

4.4.C represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15

4.4.E represent the quotient of up to a four-digit whole number divided by a one-digit whole number using arrays, area models, or equations

**Multiplication and Division Word Problems – Visual Models**

4.4.C represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15

4.4.E represent the quotient of up to a four-digit whole number divided by a one-digit whole number using arrays, area models, or equations

**Multiplication and Division Word Problems – Equations**

4.4.C represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15

4.4.E represent the quotient of up to a four-digit whole number divided by a one-digit whole number using arrays, area models, or equations

**Multiplication and Division Word Problems – Solutions**

4.4.H solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders

**Interpreting Remainders**

4.4.H solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders

4.4.C represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15

## Number and Operations in Base Ten

**Multiplying Whole Numbers**

4.4.C represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15

**Multiplying Whole Numbers – Standard Algorithm**

4.4.D use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a onedigit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties

**Dividing Whole Numbers – One-Digit Divisors**

4.4.E represent the quotient of up to a four-digit whole number divided by a one-digit whole number using arrays, area models, or equations

4.4.F use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor

## Operations and Algebraic Thinking

**Solving Two-Step Word Problems**

4.5.A represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity

**Modeling and Solving Two-Step Word Problems**

4.5.A represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity

## Number and Operations - Fractions

**Modeling Equivalent Fractions**

4.3.C determine if two given fractions are equivalent using a variety of methods

**Generating Equivalent Fractions**

4.3.A represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b > 0, including when a > b

4.3.C determine if two given fractions are equivalent using a variety of methods

**Reducing Fractions**

4.3.C determine if two given fractions are equivalent using a variety of methods

**Comparing Fractions with Different Numerators and Different Denominators**

4.3.D compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <

**Recognizing Valid Fraction Comparisons II**

4.3.D compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <

**Decomposing Fractions and Mixed Numbers**

4.3.A represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b > 0, including when a > b

4.3.B decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations

**Writing Fractions as Mixed Numbers and Mixed Numbers as Fractions**

4.3.A represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b > 0, including when a > b

**Adding and Subtracting Fractions with Like Denominators**

4.3.E represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations

**Adding and Subtracting Fractions with Like Denominators in Real-World Situations**

4.3.E represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations

4.3.F evaluate the reasonableness of sums and differences of fractions using benchmark fractions 0, 1/4, 1/2, 3/4, and 1, referring to the same whole

## Number and Operations in Base Ten

**Comparing Decimal Fractions**

4.2.G relate decimals to fractions that name tenths and hundredths

4.3.G represent fractions and decimals to the tenths or hundredths as distances from zero on a number line

**Comparing and Ordering Decimal Fractions**

4.2.F compare and order decimals using concrete and visual models to the hundredths

**Decimal Notation I**

4.2.E represent decimals, including tenths and hundredths, using concrete and visual models and money

4.2.H determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line

**Decimal Notation II**

4.2.B represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals

**Decimals to Hundredths**

4.2.B represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals

4.2.E represent decimals, including tenths and hundredths, using concrete and visual models and money

4.2.G relate decimals to fractions that name tenths and hundredths

4.3.G represent fractions and decimals to the tenths or hundredths as distances from zero on a number line

**Introduction to Comparing Decimals to Hundredths**

4.2.F compare and order decimals using concrete and visual models to the hundredths

**Comparing Decimals to Hundredths**

4.2.F compare and order decimals using concrete and visual models to the hundredths

**Recognizing Valid Decimal Comparisons**

4.2.F compare and order decimals using concrete and visual models to the hundredths

## Number and Operations - Fractions

**Understanding Fractions with Denominators of 10 and 100**

4.3.C determine if two given fractions are equivalent using a variety of methods

4.3.G represent fractions and decimals to the tenths or hundredths as distances from zero on a number line

## Measurement and Data

**Perimeter**

4.5.C use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l x w)

4.5.D solve problems related to perimeter and area of rectangles where dimensions are whole numbers

**Area and Perimeter of Rectangles**

4.5.C use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l x w)

4.5.D solve problems related to perimeter and area of rectangles where dimensions are whole numbers

4.8.C solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate

**Angles 0 to 180**

4.7.A illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is “cut out” by the rays of the angle. Angle measures are limited to whole numbers

4.7.B illustrate degrees as the units used to measure an angle, where 1/360 of any circle is one degree and an angle that “cuts” n/360 out of any circle whose center is at the angle’s vertex has a measure of n degrees. Angle measures are limited to whole numbers

4.7.C determine the approximate measures of angles in degrees to the nearest whole number using a protractor

4.7.D draw an angle with a given measure

4.7.E determine the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angle measures

## Geometry

**Classifying Triangles**

4.6.C apply knowledge of right angles to identify acute, right, and obtuse triangles

4.6.D classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size

**Classifying Quadrilaterals II**

4.6.A identify points, lines, line segments, rays, angles, and perpendicular and parallel lines

4.6.D classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size

**Symmetry**

4.6.B identify and draw one or more lines of symmetry, if they exist, for a two-dimensional figure

## Measurement and Data

**Units of Measure – Customary**

4.8.A identify relative sizes of measurement units within the customary and metric systems

4.8.B convert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table

**Units of Measure – Metric**

4.8.A identify relative sizes of measurement units within the customary and metric systems

4.8.B convert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table

**Line Plots**

4.9.A represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions

4.9.B solve one- and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot

## Operations and Algebraic Thinking

**Generating and Describing Number Patterns**

4.5.B represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence

## Financial Literacy

**Expenses and Profit**

4.10.A distinguish between fixed and variable expenses

4.10.B calculate profit in a given situation

**Saving Money**

4.10.C compare the advantages and disadvantages of various savings options

**Money Decisions**

4.10.D describe how to allocate a weekly allowance among spending; saving, including for college; and sharing

## Grade 5

## Texas Learning Pathway

## Number and Operations in Base Ten

**Multiplying Whole Numbers – Standard Algorithm**

5.3.B multiply with fluency a three-digit number by a two-digit number using the standard algorithm

**Dividing Whole Numbers – Two-Digit Divisors**

5.3.C solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm

**Operations with Whole Numbers – Mixed Practice**

5.3.B multiply with fluency a three-digit number by a two-digit number using the standard algorithm

5.3.C solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm

5.3.K add and subtract positive rational numbers fluently

5.4.B represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity

## Operations and Algebraic Thinking

**Relating Factors and Multiples I**

5.4.A identify prime and composite numbers

**Factors**

5.4.A identify prime and composite numbers

**Relating Factors and Multiples II**

5.4.A identify prime and composite numbers

## Number and Operations - Fractions

**Understanding Fractions – Relationship Between Numerator and Denominator**

5.3.I represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models

**Adding and Subtracting Mixed Numbers with Like Denominators – Conceptual Strategies**

5.3.K add and subtract positive rational numbers fluently

**Adding and Subtracting Mixed Numbers with Like Denominators**

5.3.K add and subtract positive rational numbers fluently

**Word Problems with Fractions and Mixed Numbers – Visual Models**

5.3.K add and subtract positive rational numbers fluently

**Word Problems with Fractions and Mixed Numbers – Estimation**

5.3.K add and subtract positive rational numbers fluently

**Multiplying Unit Fractions by Whole Numbers**

5.3.I represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models

**Multiplying Fractions by Whole Numbers**

5.3.I represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models

**Solving Word Problems with Multiplication of Fractions by Whole Numbers**

5.3.I represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models

**Adding Fractions with Denominators of 10 or 100**

5.3.H represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations

**Adding Fractions**

5.3.H represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations

**Adding Fractions – Estimation Strategies**

5.3.H represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations

**Subtracting Fractions**

5.3.H represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations

**Subtracting Fractions – Estimation Strategies**

5.3.H represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations

**Adding and Subtracting Fractions**

5.3.H represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations

**Adding and Subtracting Fractions – Multistep Word Problems**

5.3.H represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations

**Dividing Unit Fractions by Whole Numbers**

5.3.J represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ÷ 7 and 7 ÷ 1/3 using objects and pictorial models, including area models

5.3.L divide whole numbers by unit fractions and unit fractions by whole numbers

**Dividing Whole Numbers by Unit Fractions**

5.3.J represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ÷ 7 and 7 ÷ 1/3 using objects and pictorial models, including area models

5.3.L divide whole numbers by unit fractions and unit fractions by whole numbers

## Number and Operations in Base Ten

**Rounding Decimals to the Nearest Tenth and Hundredth**

5.2.C round decimals to tenths or hundredths

**Decimals to Thousandths**

5.2.A represent the value of the digit in decimals through the thousandths using expanded notation and numerals

**Comparing Decimals to Thousandths**

5.2.B compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =

**Adding and Subtracting Decimals**

5.3.K add and subtract positive rational numbers fluently

**Adding and Subtracting Decimals in Real-World Situations**

5.3.K add and subtract positive rational numbers fluently

**Multiplying Decimals to Hundredths**

5.3.D represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area models

5.3.E solve for products of decimals to the hundredths, including situations involving money, using strategies based on place-value understandings, properties of operations, and the relationship to the multiplication of whole numbers

**Dividing Decimals to Hundredths**

5.3.F represent quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using objects and pictorial models, including area models

5.3.G solve for quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using strategies and algorithms, including the standard algorithm

## Expressions and Equations

**Evaluating Simple Expressions**

5.4.E describe the meaning of parentheses and brackets in a numeric expression

5.4.F simplify numerical expressions that do not involve exponents, including up to two levels of grouping

## Operations and Algebraic Thinking

**Writing Simple Expressions**

5.4.B represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity

**Writing and Interpreting Simple Expressions**

5.4.B represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity

5.4.F simplify numerical expressions that do not involve exponents, including up to two levels of grouping

## Geometry

**Introduction to the Coordinate Plane**

5.8.A describe the key attributes of the coordinate plane, including perpendicular number lines (axes) where the intersection (origin) of the two lines coincides with zero on each number line and the given point (0, 0); the x-coordinate, the first number in an ordered pair, indicates movement parallel to the x-axis starting at the origin; and the y-coordinate, the second number, indicates movement parallel to the y-axis starting at the origin

5.8.B describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane

5.8.C graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and realworld problems, including those generated by number patterns or found in an input-output table

**Representing Real-World Quantities in the First Quadrant**

5.8.B describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane

5.8.C graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and realworld problems, including those generated by number patterns or found in an input-output table

**Introduction to Scatter Plots**

5.9.B represent discrete paired data on a scatterplot

**Perimeter**

5.4.H represent and solve problems related to perimeter and/or area and related to volume

**Area and Perimeter of Rectangles**

5.4.H represent and solve problems related to perimeter and/or area and related to volume

## Measurement and Data

**Volume of Rectangular Prisms I**

5.4.H represent and solve problems related to perimeter and/or area and related to volume

5.6.A recognize a cube with side length of one unit as a unit cube having one cubic unit of volume and the volume of a three-dimensional figure as the number of unit cubes (n cubic units) needed to fill it with no gaps or overlaps if possible

5.6.B determine the volume of a rectangular prism with whole number side lengths in problems related to the number of layers times the number of unit cubes in the area of the base

**Volume of Rectangular Prisms II**

5.4.G use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the special form for a cube (V = l x w x h, V = s x s x s, and V = Bh)

## Geometry

**Classifying 2-Dimensional Figures**

5.5 classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties

## Measurement and Data

**Units of Measure – Customary**

5.7 solve problems by calculating conversions within a measurement system, customary or metric

**Units of Measure – Metric**

5.7 solve problems by calculating conversions within a measurement system, customary or metric

## Statistics and Probability

**Bar Graphs and Histograms**

5.9.A represent categorical data with bar graphs or frequency tables and numerical data, including data sets of measurements in fractions or decimals, with dot plots or stem-and-leaf plots

5.9.C solve one- and two-step problems using data from a frequency table, dot plot, bar graph, stem-and-leaf plot, or scatterplot

## Operations and Algebraic Thinking

**Additive and Multiplicative Patterns**

5.4.D recognize the difference between additive and multiplicative numerical patterns given in a table or graph

**Generating and Describing Number Patterns**

5.4.C generate a numerical pattern when given a rule in the form y = ax or y = x + a and graph

## Financial Literacy

**Methods of Payment**

5.10.C identify the advantages and disadvantages of different methods of payment, including check, credit card, debit card, and electronic payments

**Balancing a Budget**

5.10.D develop a system for keeping and using financial records

5.10.E describe actions that might be taken to balance a budget when expenses exceed income

5.10.F balance a simple budget

## Grade 6

## Texas Learning Pathway

## Number and Operations in Base Ten

**Multiplying by Powers of Ten**

6.3.E multiply and divide positive rational numbers fluently

6.7.A generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization

**Multiplying and Dividing by Powers of Ten**

6.3.E multiply and divide positive rational numbers fluently

6.7.A generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization

**Dividing Whole Numbers – Standard Algorithm**

6.3.E multiply and divide positive rational numbers fluently

## The Number System

**Greatest Common Factor**

6.7.A generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization

**Greatest Common Factor – Applications**

6.7.A generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization

**Least Common Multiple**

6.7.A generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization

## Number and Operations - Fractions

**Understanding Fractions as Division**

6.2.E extend representations for division to include fraction notation such as a/b represents the same number as a ÷ b where b ≠ 0

**Multiplying Unit Fractions by Whole Numbers**

6.3.B determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one

**Multiplying Fractions by Whole Numbers**

6.3.B determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one

**Solving Word Problems with Multiplication of Fractions by Whole Numbers**

6.3.B determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one

## The Number System

**Using the Relationship Between Multiplication and Division to Divide Fractions**

6.3.A recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values

6.3.B determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one

6.3.E multiply and divide positive rational numbers fluently

**Dividing Fractions by Fractions**

6.3.E multiply and divide positive rational numbers fluently

**Using Division of Fractions to Represent and Solve Problems**

6.3.E multiply and divide positive rational numbers fluently

## Number and Operations in Base Ten

**Fraction and Decimal Equivalents**

6.4.G generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money

**Comparing Fractions and Decimals**

6.4.G generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money

## Ratios and Proportional Relationships

**Identifying Ratios**

6.4.E represent ratios and percents with concrete models, fractions, and decimals

6.5.A represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions

**Ratios**

6.4.E represent ratios and percents with concrete models, fractions, and decimals

6.5.A represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions

**Concept of Ratios and Rates**

6.4.C give examples of ratios as multiplicative comparisons of two quantities describing the same attribute

6.4.D give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients

**Using Ratios to Solve Problems**

6.4.B apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates

**Identifying Unit Rates**

6.4.E represent ratios and percents with concrete models, fractions, and decimals

6.5.A represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions

**Interpreting Unit Rates on Graphs**

6.5.A represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions

**Proportion Concepts**

6.4.A compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships

**Converting Units of Measure I**

6.4.H convert units within a measurement system, including the use of proportions and unit rates

**Converting Units of Measure II**

6.4.H convert units within a measurement system, including the use of proportions and unit rates

## Expressions and Equations

**Fraction, Decimal, and Percent Equivalents**

6.2.E extend representations for division to include fraction notation such as a/b represents the same number as a ÷ b where b ≠ 0

6.4.E represent ratios and percents with concrete models, fractions, and decimals

6.4.F represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers

6.4.G generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money

6.5.C use equivalent fractions, decimals, and percents to show equal parts of the same whole

## Ratios and Proportional Relationships

**Percent Concepts**

6.4.E represent ratios and percents with concrete models, fractions, and decimals

6.4.F represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers

6.5.B solve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, inlcuding the use of concrete and pictorial models

**Reasoning with Percents**

6.4.E represent ratios and percents with concrete models, fractions, and decimals

6.4.F represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers

6.5.B solve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, inlcuding the use of concrete and pictorial models

## The Number System

**Integer Concepts**

6.2.B identify a number, its opposite, and its absolute value

6.2.C locate, compare, and order integers and rational numbers using a number line Integer

**Concepts with a Number Line**

6.2.B identify a number, its opposite, and its absolute value

6.2.C locate, compare, and order integers and rational numbers using a number line

**Absolute Value I**

6.2.B identify a number, its opposite, and its absolute value

**Absolute Value II**

6.2.B identify a number, its opposite, and its absolute value

**Comparing Rational Numbers I**

6.2.C locate, compare, and order integers and rational numbers using a number line

6.2.D order a set of rational numbers arising from mathematical and real-world contexts

**Comparing Rational Numbers II**

6.2.C locate, compare, and order integers and rational numbers using a number line

6.2.D order a set of rational numbers arising from mathematical and real-world contexts

**Adding and Subtracting Rational Numbers I**

6.3.C represent integer operations with concrete models and connect the actions with the models to standardized algorithms

6.3.D add, subtract, multiply, and divide integers fluently

**Adding and Subtracting Rational Numbers II**

6.3.C represent integer operations with concrete models and connect the actions with the models to standardized algorithms

6.3.D add, subtract, multiply, and divide integers fluently

**Multiplying and Dividing Rational Numbers**

6.3.C represent integer operations with concrete models and connect the actions with the models to standardized algorithms

6.3.D add, subtract, multiply, and divide integers fluently

**Classifying Rational Numbers**

6.2.A classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers

6.2.C locate, compare, and order integers and rational numbers using a number line

6.2.D order a set of rational numbers arising from mathematical and real-world contexts

## Expressions and Equations

**Reasoning About One-Step Equations**

6.10.B determine if the given value(s) make(s) one-variable, one-step equations or inequalities true

**Writing and Solving One-Step Equations**

6.9.A write one-variable, one-step equations and inequalities to represent constraints or conditions within problems

6.9.C write corresponding real-world problems given one-variable, one-step equations or inequalities

6.10.A model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts

**Evaluating Expressions with Two Operations**

6.7.A generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization

**Identifying and Generating Equivalent Expressions**

6.7.C determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations

6.7.D generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties

**Evaluating Expressions with the Distributive Property**

6.7.D generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties

**Using the Distributive Property to Represent Real-World Situations**

6.7.D generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties Independent and

**Dependent Quantities**

6.6.B write an equation that represents the relationship between independent and dependent quantities from a table

## Geometry

**Classifying Triangles**

4.6.C apply knowledge of right angles to identify acute, right, and obtuse triangles

4.6.D classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size

**Classifying Quadrilaterals II**

4.6.A identify points, lines, line segments, rays, angles, and perpendicular and parallel lines

**Area of Parallelograms**

6.8.B model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes

6.8.C write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers

6.8.D determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers

**Area of Triangles**

6.8.B model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes

6.8.C write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers

6.8.D determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers

**Area of Trapezoids and Composite Figures**

6.8.B model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes

6.8.C write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers

6.8.D determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers

**Volume of Rectangular Prisms II**

6.8.C write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers

**Angles in a Polygon**

6.8.A extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle

## The Number System

**Integers in the Coordinate Plane I**

6.11 graph points in all four quadrants using ordered pairs of rational numbers

**Integers in the Coordinate Plane II**

6.11 graph points in all four quadrants using ordered pairs of rational numbers

**Rational Numbers in the Coordinate Plane I**

6.11 graph points in all four quadrants using ordered pairs of rational numbers

**Rational Numbers in the Coordinate Plane II**

6.11 graph points in all four quadrants using ordered pairs of rational numbers

## Expressions and Equations

**Understanding Exponents**

6.7.A generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization

**Evaluating Expressions and Equations with Exponents**

6.7.A generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization

## Statistics and Probability

**Measures of Spread – Range**

6.12.C summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution

**Measures of Center – Median**

6.12.C summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution

**Measures of Center – Mean**

6.12.C summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution

**Summarizing Data**

6.12.B use the graphical representation of numeric data to describe the center, spread, and shape of the data distribution

6.12.D summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution

**Data Analysis**

6.13.B distinguish between situations that yield data with and without variability

## Measurement and Data

**Line Plots**

4.9.A represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions

4.9.B solve one- and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot

## Statistics and Probability

**Bar Graphs and Histograms**

6.12.A represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots

6.13.A interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots

**Stem-and-Leaf Plots**

6.12.A represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots

6.13.A interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots

**Quartiles**

6.12.C summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution

**Box Plots**

6.12.A represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots

6.13.A interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots

## Expressions and Equations

**Introduction to the Language of Algebra**

6.6.C represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b

6.7.B distinguish between expressions and equations verbally, numerically, and algebraically

6.9.A write one-variable, one-step equations and inequalities to represent constraints or conditions within problems

**Introduction to Solving Word Problems with Algebra**

6.6.C represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b

6.9.A write one-variable, one-step equations and inequalities to represent constraints or conditions within problems

**Concept of Inequalities I**

6.9.A write one-variable, one-step equations and inequalities to represent constraints or conditions within problems

6.9.B represent solutions for one-variable, one-step equations and inequalities on number lines

## Functions

**Interpreting Graphs of Real-World Situations**

6.6.A identify independent and dependent quantities from tables and graphs

6.6.C represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b

7.7 represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b

**Introduction to Sketching Graphs of Real-World Situations**

6.6.C represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b

## Financial Literacy

**Methods of Payment**

6.14.B distinguish between debit cards and credit cards

**Balancing a Budget**

6.14.C balance a check register that includes deposits, withdrawals, and transfers

**Credit Reports**

6.14.D explain why it is important to establish a positive credit history

6.14.E describe the information in a credit report and how long it is retained

6.14.F describe the value of credit reports to borrowers and to lenders

**Paying for College I**

6.14.G explain various methods to pay for college, including through savings, grants, scholarships, student loans, and workstudy

## Grade 7

## Texas Learning Pathway

## Expressions and Equations

**Evaluating Simple Expressions**

5.4.E describe the meaning of parentheses and brackets in a numeric expression

5.4.F simplify numerical expressions that do not involve exponents, including up to two levels of grouping

**Solving and Modeling Two-Step Problems**

7.10.A write one-variable, two-step equations and inequalities to represent constraints or conditions within problems

7.11.A model and solve one-variable, two-step equations and inequalities

**Solving Equations with the Distributive Property**

7.10.A write one-variable, two-step equations and inequalities to represent constraints or conditions within problems

7.11.A model and solve one-variable, two-step equations and inequalities

**Solving Equations with the Distributive Property in Context**

7.10.A write one-variable, two-step equations and inequalities to represent constraints or conditions within problems

7.11.A model and solve one-variable, two-step equations and inequalities

## Number and Operations - Fractions

**Multiplying Unit Fractions by Fractions and Understanding Multiplication as Scaling**

7.3.A add, subtract, multiply, and divide rational numbers fluently

**Multiplying Fractions by Fractions**

7.3.A add, subtract, multiply, and divide rational numbers fluently

**Multiplying Fractions by Whole Numbers to Solve Multistep Problems**

7.3.A add, subtract, multiply, and divide rational numbers fluently

**Dividing Unit Fractions by Whole Numbers**

5.3.J represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ÷ 7 and 7 ÷ 1/3 using objects and pictorial models, including area models

5.3.L divide whole numbers by unit fractions and unit fractions by whole numbers

**Dividing Whole Numbers by Unit Fractions**

5.3.J represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ÷ 7 and 7 ÷ 1/3 using objects and pictorial models, including area models

5.3.L divide whole numbers by unit fractions and unit fractions by whole numbers

## The Number System

**Operations with Fractions – Mixed Practice**

7.3.A add, subtract, multiply, and divide rational numbers fluently

7.3.B apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers

**Classifying Rational Numbers**

7.2 extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of rational numbers

## Number and Operations in Base Ten

**Using Reasoning and Estimation to Calculate with Decimals**

7.3.A add, subtract, multiply, and divide rational numbers fluently

7.3.B apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers

**Calculating with Decimals**

7.3.A add, subtract, multiply, and divide rational numbers fluently

7.3.B apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers

## Ratios and Proportional Reasoning

**Interpreting Unit Rates on Graphs**

7.4.A represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt

**Solving Problems with Unit Rates**

7.4.A represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt

7.4.B calculate unit rates from rates in mathematical and real-world problems

7.4.D solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems

**Distance, Rate, and Time**

7.4.A represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt

7.4.D solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems

**Proportion Concepts**

7.4.A represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt

7.4.C determine the constant of proportionality (k = y/x) within mathematical and real-world problems

**Proportional Relationships in Tables and Equations**

7.4.A represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt

**Using Proportions to Solve Problems**

7.4.A represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt

7.4.C determine the constant of proportionality (k = y/x) within mathematical and real-world problems

**Converting Units of Measure II**

7.4.E convert between measurement systems, including the use of proportions and the use of unit rates

**Proportions in Scale Drawings**

7.5.C solve mathematical and real-world problems involving similar shape and scale drawings

**Introduction to Similar Figures**

7.5.A generalize the critical attributes of similarity, including ratios within and between similar shapes

7.5.C solve mathematical and real-world problems involving similar shape and scale drawings

**Using Similar Figures to Solve Problems**

7.5.A generalize the critical attributes of similarity, including ratios within and between similar shapes

7.5.C solve mathematical and real-world problems involving similar shape and scale drawings

**Similarity**

7.5.A generalize the critical attributes of similarity, including ratios within and between similar shapes

**Calculations with Percent**

7.4.D solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems

7.13.A calculate the sales tax for a given purchase and calculate income tax for earned wages

**Percent and Percent Change**

7.4.D solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems

**Percent and Percent Error**

7.4.D solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems

**Simple Interest**

7.13.E calculate and compare simple interest and compound interest earnings

## The Number System

**Writing and Interpreting Expressions with Rational Numbers**

7.3.A add, subtract, multiply, and divide rational numbers fluently

**Operations with Rational Numbers I**

7.3.A add, subtract, multiply, and divide rational numbers fluently

**Operations with Rational Numbers II**

7.3.A add, subtract, multiply, and divide rational numbers fluently

## Geometry

**Circumference**

7.5.B describe π as the ratio of the circumference of a circle to its diameter

7.8.C use models to determine the approximate formulas for the circumference and area of a circle and connect the models to the actual formulas

7.9.B determine the circumference and area of circles

**Area of Circles**

7.8.C use models to determine the approximate formulas for the circumference and area of a circle and connect the models to the actual formulas

7.9.B determine the circumference and area of circles

**Area of Complex Composite Figures**

7.9.C determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles

**Surface Area and Volume of Rectangular Prisms**

7.9.A solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids

7.9.D solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid by determining the area of the shape’s net

**Surface Area of Pyramids**

7.9.D solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid by determining the area of the shape’s net

**Volume of Pyramids and Cones**

7.8.A model the relationship between the volume of a rectangular prism and a rectangular pyramid having both congruent bases and heights and connect that relationship to the formulas

7.8.B explain verbally and symbolically the relationship between the volume of a triangular prism and a triangular pyramid having both congruent bases and heights and connect that relationship to the formulas

7.9.A solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids

**Angle Pairs**

7.11.C write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships

**Parallel Lines and Transversals**

7.11.C write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships

**Angles in a Polygon**

7.11.C write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships

## Statistics and Probability

**Circle Graphs**

7.6.G solve problems using data represented in bar graphs, dot plots, and circle graphs, including part-to-whole and part-to-part comparisons and equivalents

**Bar Graphs and Histograms**

7.6.G solve problems using data represented in bar graphs, dot plots, and circle graphs, including part-to-whole and part-to-part comparisons and equivalents

**Sampling**

7.6.F use data from a random sample to make inferences about a population

7.12.B use data from a random sample to make inferences about a population

7.12.C compare two populations based on data in random samples from these populations, including informal comparative inferences about differences between the two populations

**Comparing Data**

7.12.A compare two groups of numeric data using comparative dot plots or box plots by comparing their shapes, centers, and spreads

**Simple Probability**

7.6.A represent sample spaces for simple and compound events using lists and tree diagrams

7.6.E find the probabilities of a simple event and its complement and describe the relationship between the two

7.6.I determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces

**Compound Probability**

7.6.A represent sample spaces for simple and compound events using lists and tree diagrams

7.6.E find the probabilities of a simple event and its complement and describe the relationship between the two

7.6.I determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces

**Making Predictions**

7.6.C make predictions and determine solutions using experimental data for simple and compound events

7.6.D make predictions and determine solutions using theoretical probability for simple and compound events

7.6.H solve problems using qualitative and quantitative predictions and comparisons from simple experiments

**Simulations of Simple and Compound Events**

7.6.B select and use different simulations to represent simple and compound events with and without technology

## Expressions and Equations

**Introduction to Solving Word Problems with Algebra**

7.10.C write a corresponding real-world problem given a one-variable, two-step equation or inequality

**Solving Word Problems with Algebra**

7.10.A write one-variable, two-step equations and inequalities to represent constraints or conditions within problems

**Concept of Inequalities I**

7.10.B represent solutions for one-variable, two-step equations and inequalities on number lines

7.11.B determine if the given value(s) make(s) one-variable, two-step equations and inequalities true

**Combining Like Terms**

7.10.A write one-variable, two-step equations and inequalities to represent constraints or conditions within problems

7.11.A model and solve one-variable, two-step equations and inequalities

## Financial Literacy

**Creating a Budget**

7.13.B identify the components of a personal budget, including income; planned savings for college, retirement, and emergencies; taxes; and fixed and variable expenses, and calculate what percentage each category comprises of the total budget

7.13.D use a family budget estimator to determine the minimum household budget and average hourly wage needed for a family to meet its basic needs in the student’s city or another large city nearby

## Grade 8

## Texas Learning Pathway

## Expressions and Equations

**Using the Distributive Property to Represent Real-World Situations**

6.7.D generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties

## Functions

**Interpreting Graphs of Real-World Situations**

8.4.C use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems

8.5.A represent linear proportional situations with tables, graphs, and equations in the form of y = kx

8.5.B represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0 8.5.G identify functions using sets of ordered pairs, tables, mappings, and graphs

8.5.I write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations

**Introduction to Sketching Graphs of Real-World Situations**

8.4.C use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems

8.5.A represent linear proportional situations with tables, graphs, and equations in the form of y = kx

8.5.B represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0

8.5.G identify functions using sets of ordered pairs, tables, mappings, and graphs

8.5.I write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations

## Ratios and Proportional Relationships

**Interpreting Unit Rates on Graphs**

8.4.B graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship

**Interpreting Points on Graphs of Proportional Relationships**

8.4.B graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship

**Similarity**

8.3.A generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation

**Simple Interest**

8.12.A solve real-world problems comparing how interest rate and loan length affect the cost of credit

8.12.D calculate and compare simple interest and compound interest earnings

## Expressions and Equations

**Interpreting Slope**

8.5.A represent linear proportional situations with tables, graphs, and equations in the form of y = kx

**Slope**

8.4.A use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y2 – y1) / (x2 – x1), is the same for any two points (x1, y1) and (x2, y2) on the same line

8.5.A represent linear proportional situations with tables, graphs, and equations in the form of y = kx

8.5.B represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0

8.5.G identify functions using sets of ordered pairs, tables, mappings, and graphs

8.5.I write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations

## Functions

**Slope-Intercept Form**

8.5.A represent linear proportional situations with tables, graphs, and equations in the form of y = kx

8.5.B represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0

8.5.G identify functions using sets of ordered pairs, tables, mappings, and graphs

**Point-Slope Form**

8.5.A represent linear proportional situations with tables, graphs, and equations in the form of y = kx

8.5.G identify functions using sets of ordered pairs, tables, mappings, and graphs

## Expressions and Equations

**Solving a System of Linear Equations Graphically**

8.9 identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations

## Building Functions

**Direct Variation**

8.5.A represent linear proportional situations with tables, graphs, and equations in the form of y = kx

8.5.E solve problems involving direct variation 8.5.F distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0

8.5.H identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems

## Statistics and Probability

**Comparing Linear and Nonlinear Functions**

8.5.C contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation

8.5.D use a trend line that approximates the linear relationship between bivariate sets of data to make predictions

8.11.A construct a scatterplot and describe the observed data to address questions of association such as linear, nonlinear, and no association between bivariate data

## Expressions and Equations

**Analyzing Solution Sets to Linear Equations with the Variable on Both Sides**

8.8.A write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants

8.8.B write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants

8.8.C model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants

**Solving Equations with the Variable on Both Sides**

8.8.A write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants

8.8.B write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants

8.8.C model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants

**Understanding Square and Cube Roots**

8.2.B approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line

**Approximating Values of Irrational Numbers**

8.2.B approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line Interpreting

**Numbers Written in Scientific Notation**

8.2.C convert between standard decimal notation and scientifice notation

## The Number System

**Classifying and Ordering Real Numbers**

8.2.A extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers

8.2.D order a set of real numbers arising from mathematical and real-world contexts

## Geometry

**Surface Area and Volume of Rectangular Prisms**

8.7.B use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders

**Surface Area of Cylinders**

8.7.B use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders

**Volume of Cylinders**

8.6.A describe the volume formula V = Bh of a cylinder in terms of its base area and its height

8.6.B model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas

8.7.A solve problems involving the volume of cylinders, cones, and spheres

**Volume of Pyramids and Cones**

8.6.B model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas

8.7.A solve problems involving the volume of cylinders, cones, and spheres

**Volume of Spheres**

8.7.A solve problems involving the volume of cylinders, cones, and spheres

**Volume of Composite Solids**

8.7.A solve problems involving the volume of cylinders, cones, and spheres

**Understanding the Pythagorean Theorem**

8.6.C use models and diagrams to explain the Pythagorean theorem

**Pythagorean Theorem – Hypotenuse**

8.7.C use the Pythagorean Theorem and its converse to solve problems

**Pythagorean Theorem – Legs**

8.7.C use the Pythagorean Theorem and its converse to solve problems

**Pythagorean Theorem – Mixed Problems**

8.7.C use the Pythagorean Theorem and its converse to solve problems

**Pythagorean Theorem – Distance Formula**

8.7.C use the Pythagorean Theorem and its converse to solve problems

8.7.D determine the distance between two points on a coordinate plane using the

**Pythagorean Theorem Parallel Lines and Transversals**

8.8.D use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles

**Translations**

8.10.A generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of twodimensional shapes on a coordinate plane

**Reflections**

8.10.A generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of twodimensional shapes on a coordinate plane

**Rotations**

8.10.A generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of twodimensional shapes on a coordinate plane

**Composition of Transformations**

8.10.C explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90°, 180°, 270°, and 360° as applied to two-dimensional shapes on a coordinate plane using an algebraic representation

**Dilations**

8.3.A generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation

8.3.B compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane

8.3.C use an algebraic representation to explain the effect of a given positive rational scale factor applied to twodimensional figures on a coordinate plane with the origin as the center of dilation

8.10.D model the effect on linear and area measurements of dilated two-dimensional shapes

**Congruence**

8.10.B differentiate between transformations that preserve congruence and those that do not

## Statistics and Probability

**Box Plots**

6.12.A represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots

**Deviation from the Mean**

8.11.B determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean using a data set of no more than 10 data points

**Sampling**

8.11.C simulate generating random samples of the same size from a population with known characteristics to develop the notion of a random sample being representative of the population from which it was selected

## Financial Literacy

**Cost of Loans**

8.12.B calculate the total cost of repaying a loan, including credit cards and easy access loans, under various rates of interest and over different periods using an online calculator

**Methods of Payment**

8.12.E identify and explain the advantages and disadvantages of different payment methods

**Paying for College II**

8.12.G estimate the cost of a two-year and four-year college education, including family contribution, and devise a periodic savings plan for accumulating the money needed to contribute to the total cost of attendance for at least the first year of college

## Algebra Readiness

## Texas Learning Pathway

## Expressions and Equations

**Using the Distributive Property to Represent Real-World Situations**

6.7.D generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties

## Functions

**Interpreting Graphs of Real-World Situations**

8.4.C use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems

8.5.G identify functions using sets of ordered pairs, tables, mappings, and graphs

**Introduction to Sketching Graphs of Real-World Situations**

8.4.C use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems

8.5.G identify functions using sets of ordered pairs, tables, mappings, and graphs

## Ratios and Proportional Relationships

**Interpreting Unit Rates on Graphs**

8.4.B graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship

**Interpreting Points on Graphs of Proportional Relationships**

8.4.B graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship

**Similarity**

8.3.A generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation

**Simple Interest**

8.12.A solve real-world problems comparing how interest rate and loan length affect the cost of credit

8.12.D calculate and compare simple interest and compound interest earnings

## Expressions and Equations

**Interpreting Slope**

8.5.A represent linear proportional situations with tables, graphs, and equations in the form of y = kx

**Slope**

8.4.A use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y2 – y1) / (x2 – x1), is the same for any two points (x1, y1) and (x2, y2) on the same line

8.5.G identify functions using sets of ordered pairs, tables, mappings, and graphs

## Functions

**Slope-Intercept Form**

8.5.A represent linear proportional situations with tables, graphs, and equations in the form of y = kx

8.5.G identify functions using sets of ordered pairs, tables, mappings, and graphs

**Point-Slope Form**

8.5.A represent linear proportional situations with tables, graphs, and equations in the form of y = kx

8.5.G identify functions using sets of ordered pairs, tables, mappings, and graphs

## Expressions and Equations

**Solving a System of Linear Equations Graphically**

8.9 identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations

## Building Fractions

**Direct Variation**

8.5.A represent linear proportional situations with tables, graphs, and equations in the form of y = kx

8.5.E solve problems involving direct variation

8.5.F distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0

8.5.H identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems

## Statistics and Probability

**Comparing Linear and Nonlinear Functions**

8.5.C contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation

8.5.D use a trend line that approximates the linear relationship between bivariate sets of data to make predictions

8.11.A construct a scatterplot and describe the observed data to address questions of association such as linear, nonlinear, and no association between bivariate data

## Expressions and Equations

**Analyzing Solution Sets to Linear Equations with the Variable on Both Sides**

8.8.A write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants

8.8.B write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants

8.8.C model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants

**Solving Equations with the Variable on Both Sides**

8.8.A write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants

**Understanding Square and Cube Roots**

8.2.B approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line

**Approximating Values of Irrational Numbers**

8.2.B approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line

**Interpreting Numbers Written in Scientific Notation**

8.2.C convert between standard decimal notation and scientifice notation

## The Number System

**Classifying and Ordering Real Numbers**

8.2.A extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers

8.2.D order a set of real numbers arising from mathematical and real-world contexts

## Geometry

**Surface Area and Volume of Rectangular Prisms**

8.7.B use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders

**Surface Area of Cylinders**

8.7.B use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders

**Volume of Cylinders**

8.6.A describe the volume formula V = Bh of a cylinder in terms of its base area and its height

8.6.B model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas

8.7.A solve problems involving the volume of cylinders, cones, and spheres

**Volume of Pyramids and Cones**

8.6.B model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas

8.7.A solve problems involving the volume of cylinders, cones, and spheres

**Volume of Spheres**

8.7.A solve problems involving the volume of cylinders, cones, and spheres

**Volume of Composite Solids**

8.7.A solve problems involving the volume of cylinders, cones, and spheres

**Pythagorean Theorem – Hypotenuse**

8.6.C use models and diagrams to explain the Pythagorean Theorem

8.7.C use the Pythagorean Theorem and its converse to solve problems

**Pythagorean Theorem – Legs**

8.6.C use models and diagrams to explain the Pythagorean Theorem

8.7.C use the Pythagorean Theorem and its converse to solve problems

**Pythagorean Theorem – Mixed Problems**

8.6.C use models and diagrams to explain the Pythagorean Theorem

8.7.C use the Pythagorean Theorem and its converse to solve problems

**Pythagorean Theorem – Distance Formula**

8.7.C use the Pythagorean Theorem and its converse to solve problems

8.7.D determine the distance between two points on a coordinate plane using the Pythagorean Theorem

**Parallel Lines and Transversals**

8.8.D use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles

**Translations**

8.10.A generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of twodimensional shapes on a coordinate plane

**Reflections**

8.10.A generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of twodimensional shapes on a coordinate plane

**Rotations**

8.10.A generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of twodimensional shapes on a coordinate plane

**Composition of Transformations**

8.10.C explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90°, 180°, 270°, and 360° as applied to two-dimensional shapes on a coordinate plane using an algebraic representation

**Dilations**

8.3.A generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation

8.3.B compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane

8.3.C use an algebraic representation to explain the effect of a given positive rational scale factor applied to twodimensional figures on a coordinate plane with the origin as the center of dilation

8.10.D model the effect on linear and area measurements of dilated two-dimensional shapes

**Congruence**

8.10.B differentiate between transformations that preserve congruence and those that do not

## Statistics and Probability

**Box Plots**

6.12.A represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots

**Deviation from the Mean**

8.11.B determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean using a data set of no more than 10 data points

**Sampling**

8.11.C simulate generating random samples of the same size from a population with known characteristics to develop the notion of a random sample being representative of the population from which it was selected

## Financial Literacy

**Cost of Loans**

8.12.B calculate the total cost of repaying a loan, including credit cards and easy access loans, under various rates of interest and over different periods using an online calculator

**Methods of Payment**

8.12.E identify and explain the advantages and disadvantages of different payment methods

**Paying for College II**

8.12.G estimate the cost of a two-year and four-year college education, including family contribution, and devise a periodic savings plan for accumulating the money needed to contribute to the total cost of attendance for at least the first year of college

## Algebra 1

## Texas Learning Pathway

## Expressions and Equations

**Solving Equations with the Distributive Property**

AI.5.A solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides

**Solving Equations with the Distributive Property in Context**

AI.5.A solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides

**Solving Equations with the Variable on Both Sides**

AI.5.A solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides

**Interpreting Slope**

AI.3.A determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y – y1 = m(x – x1)

AI.3.B calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems

**Slope**

AI.3.A determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y – y1 = m(x – x1)

AI.3.B calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems

## Functions

**Slope-Intercept Form**

AI.2.B write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y – y1 = m(x – x1), given one point and the slope and given two points

AI.3.A determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y – y1 = m(x – x1)

AI.3.B calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems

**Point-Slope Form**

AI.2.B write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y – y1 = m(x – x1), given one point and the slope and given two points

AI.3.A determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y – y1 = m(x – x1)

## Building Fractions

**Direct Variation**

AI.2.D write and solve equations involving direct variation

## Seeing Structure in Expressions

**Interpreting the Structure of Linear and Exponential Expressions**

AI.9.B interpret the meaning of the values of a and b in exponential functions of the form f(x) = ab^xx in real-world problems

## Creating Equations

**Writing and Graphing Linear Equations in Two or More Variables**

AI.2.C write linear equations in two variables given a table of values, a graph, and a verbal description

**Equations of Parallel and Perpendicular Lines**

AI.2.E write the equation of a line that contains a given point and is parallel to a given line

AI.2.F write the equation of a line that contains a given point and is perpendicular to a given line

AI.2.G write an equation of a line that is parallel or perpendicular to the X or Y axis and determine whether the slope of the line is zero or undefined

## Reasoning with Equations and Inequalities

**Solving Linear Inequalities in One Variable**

AI.5.B solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides

## Creating Equations

**Modeling Exponential Relationships with Equations, Inequalities, and Graphs**

AI.9.C write exponential functions in the form f(x) = ab^x (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay

AI.9.D graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems

**Solving Literal Equations**

AI.12.E solve mathematic and scientific formulas, and other literal equations, for a specified variable

## Reasoning with Equations and Inequalities

**Solving Systems of Linear Equations**

AI.2.I write systems of two linear equations given a table of values, a graph, and a verbal description

AI.3.F graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist

AI.3.G estimate graphically the solutions to systems of two linear equations with two variables in real-world problems

AI.5.C solve systems of two linear equations with two variables for mathematical and real-world problems

## Expressions and Equations

**Solving a System of Linear Equations Graphically**

AI.3.G estimate graphically the solutions to systems of two linear equations with two variables in real-world problems

## Reasoning with Equations and Inequalities

**Graphing Linear Inequalities and Systems of Linear Inequalities in Real-World Situations**

AI.2.H write linear inequalities in two variables given a table of values, a graph, and a verbal description

AI.3.D graph the solution set of linear inequalities in two variables on the coordinate plane

AI.3.H graph the solution set of systems of two linear inequalities in two variables on the coordinate plane

## Interpreting Functions

**Function Notation I**

AI.12.B evaluate functions, expressed in function notation, given one or more elements in their domains

**Function Notation II**

AI.12.A decide whether relations represented verbally, tabularly, graphically, and symbolically define a function

**Interpreting Graphs of Linear and Exponential Functions in Context**

AI.9.B interpret the meaning of the values of a and b in exponential functions of the form f(x) = ab^xx in real-world problems

**Sketching Graphs of Linear and Exponential Functions from a Context**

AI.3.C graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems

AI.9.D graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems

**Understanding the Domain of a Function**

AI.2.A determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities

AI.9.A determine the domain and range of exponential functions of the form f(x) = ab^x and represent the domain and range using inequalities

**Rate of Change for Linear and Exponential Functions**

AI.2.C write linear equations in two variables given a table of values, a graph, and a verbal description

## Building Functions

**Transformations of Graphs of Linear Functions**

AI.3.E determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by af(x), f(x) + d , f(x – c), f(bx) for specific values of a, b, c, and d

**Writing Linear and Exponential Functions from a Context**

AI.2.C write linear equations in two variables given a table of values, a graph, and a verbal description

AI.9.C write exponential functions in the form f(x) = ab^x (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay

## Linear. Quadratic, and Exponential Models

**Writing Linear and Exponential Functions Based on Different Representations**

AI.2.C write linear equations in two variables given a table of values, a graph, and a verbal description

AI.9.C write exponential functions in the form f(x) = ab^x (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay

## Building Functions

**Writing Arithmetic Sequences Explicitly and Recursively**

AI.12.C identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes

AI.12.D write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms

**Writing Geometric Sequences Using an Explicit Formula**

AI.12.D write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms

**Writing Geometric Sequences Recursively**

AI.12.C identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes

## Interpreting Functions

**Sequences as Functions**

AI.12.C identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes

AI.12.D write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms

## Interpreting Categorical and Quantitative Data

**Fitting Functions to Data**

AI.4.C write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems

AI.9.E write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems

**Correlation**

AI.4.B compare and contrast association and causation in real-world problems

AI.4.C write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems

## Arithmetic with Polynomials and Rational Expressions

**Adding and Subtracting Polynomials**

AI.10.A add and subtract polynomials of degree one and degree two

**Multiplying and Dividing Monomials**

AI.10.B multiply polynomials of degree one and degree two

AI.10.C determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend

**Multiplying Polynomials**

AI.10.B multiply polynomials of degree one and degree two

## Expressions and Equations

**Simplifying Monomials**

AI.10.D rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property

**Factoring Expressions**

AI.10.D rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property

AI.10.E factor, if possible, trinomials with real factors in the form ax² + bx + c, including perfect square trinomials of degree two

## The Real Number System

**Using Rational Exponents to Rewrite Expressions**

AI.11.B simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents

## Interpreting Functions

**Rewriting and Interpreting Exponential Functions in Terms of Context**

AI.9.B interpret the meaning of the values of a and b in exponential functions of the form f(x) = ab^xx in real-world problems

## Building Functions

**Writing Quadratic Functions from a Context**

AI.6.B write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x – h)² + k), and rewrite the equation from vertex form to standard form (f(x) = ax² + bx + c)

## Interpreting Functions

**Sketching Graphs of Quadratic Functions in Context**

AI.6.A determine the domain and range of quadratic functions and represent the domain and range using inequalities

AI.7.A graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry

## Seeing Structure in Expressions

**Factoring Quadratic Expressions**

AI.7.B describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions

AI.8.A solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

AI.10.E factor, if possible, trinomials with real factors in the form ax² + bx + c, including perfect square trinomials of degree two

AI.10.F decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial

## Reasoning with Equations and Inequalities

**Solving Quadratics – Completing the Square**

AI.8.A solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

## Interpreting Functions

**Rewriting Quadratics to Reveal Their Structure**

AI.6.B write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x – h)² + k), and rewrite the equation from vertex form to standard form (f(x) = ax² + bx + c)

## Reasoning with Equations and Inequalities

**Problem Solving with Quadratic Functions**

AI.8.A solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

AI.11.A simplify numerical radical expressions involving square roots

**Using the Quadratic Formula**

AI.8.A solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

## Geometry

## Texas Learning Pathway

## Geometry

**Angles in a Polygon**

G.6.D verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems

## Conguence

**Defining Transformations**

G.3.B determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane

G.3.C identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane

**Rotational and Reflectional Symmetry**

G.3.D identify and distinguish between reflectional and rotational symmetry in a plane figure

**Representing Transformations with Algebra**

G.3.A describe and perform transformations of figures in a plane using coordinate notation

G.3.C identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane

**Rigid Motion and Congruence**

G.6.C apply the definition of congruence, in terms of rigid transformations, to identify congruent figures and their corresponding sides and angles

**What is Proof?**

G.4.A distinguish between undefined terms, definitions, postulates, conjectures, and theorems

G.6 prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart

**Proving Theorems About Lines and Angles**

G.4.A distinguish between undefined terms, definitions, postulates, conjectures, and theorems

G.6.A verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points on its perpendicular bisector and apply these relationships to solve problems

**Proving Theorems About Congruent Triangles**

G.6 prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart

## Similarity, Right Triangles, and Trigonometry

**Problem Solving with Congruent Triangles**

G.6.B prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Side-Side-Side, AngleAngle-Side, and Hypotenuse-Leg congruence conditions

## Conguence

**Proving Theorems About Parallelograms**

G.5.A investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools

G.6.E prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides, opposite angles, or diagonals and apply these relationships to solve problems

**Constructing Angles and Special Line Segments**

G.5.B construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge

**Constructing Inscribed Figures**

G.5.B construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge

## Modeling with Geometry

**Modeling Objects with Geometric Figures**

G.11.B determine the area of composite two-dimensional figures comprised of a combination of triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve problems using appropriate units of measure

**Using Geometric Relationships to Solve Design Problems**

G.10.B determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change

## Similarity, Right Triangles, and Trigonometry

**Properties of Dilations I**

G.3 generate and describe rigid transformations (translation, reflection, and rotation) and non-rigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity)

**Properties of Dilations II**

G.3.B determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane

**Transformations and Similarity**

G.7.A apply the definition of similarity in terms of a dilation to identify similar figures and their proportional sides and the congruent corresponding angles

G.7.B apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides to solve problems

G.8.A prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve problems

**Problem Solving with Transformations and Similarity**

G.8.A prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve problems

## Geometry

**Pythagorean Theorem – Mixed Problems**

G.6.D verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems

G.9.B apply the relationships in special right triangles 30°-60°-90° and 45°-45°-90° and the Pythagorean Theorem, including Pythagorean triples, to solve problems

## Similarity, Right Triangles, and Trigonometry

**Proving Theorems About Similar Triangles**

G.8.A prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve problems

**Problem Solving with Similarity and Trigonometric Ratios**

G.9.A determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems

**Sine and Cosine of Complementary Angles**

G.9.A determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems

## Geometry

**Area of Parallelograms**

G.11.A apply the formula for the area of regular polygons to solve problems using appropriate units of measure

**Area of Triangles**

G.11.A apply the formula for the area of regular polygons to solve problems using appropriate units of measure

**Surface Area and Volume of Rectangular Prisms**

G.11.C apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure

G.11.D apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure

**Surface Area of Cylinders**

G.11.C apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure

**Surface Area of Pyramids**

G.11.C apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure

**Surface Area of Cones**

G.11.C apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure

**Surface Area of Spheres**

G.11.C apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure

**Surface Area of Composite Solids**

G.11.C apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure

**Volume of Cylinders**

G.11.D apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure

**Volume of Pyramids and Cones**

G.11.D apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure

**Volume of Spheres**

G.11.D apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure

**Volume of Composite Solids**

G.11.D apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure-=-

## Geometric Measurement and Dimension

**Understanding Formulas for Curved Figures**

G.11.C apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure

**Cross-Sections of 3-Dimensional Figures**

G.10.A identify the shapes of two-dimensional cross-sections of prisms, pyramids, cylinders, cones, and spheres and identify three-dimensional objects generated by rotations of two-dimensional shapes

## Expressing Geometric Properties with Equations

**Coordinates of Parallel and Perpendicular Lines**

G.2.B derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines

G.2.C determine an equation of a line parallel or perpendicular to a given line that passes through a given point

**Problem Solving with Coordinates of Parallel and Perpendicular Lines**

G.2.B derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines

G.2.C determine an equation of a line parallel or perpendicular to a given line that passes through a given point

## The Number System

**Distance on the Coordinate Plane II**

G.2.A determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint

## Expressing Geometric Properties with Equations

**Dividing a Segment Proportionally**

G.2.A determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint

**Using Coordinates to Find Perimeters and Areas**

G.2.B derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines

## Circles

**Tangents, Chords, Radii, and Angles in Circles**

G.12.A apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems

**Radians and Area of Sectors**

G.11.B determine the area of composite two-dimensional figures comprised of a combination of triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve problems using appropriate units of measure

G.12.B apply the proportional relationship between the measure of an arc length of a circle and the circumference of the circle to solve problems

G.12.C apply the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems

G.12.D describe radian measure of an angle as the ratio of the length of an arc intercepted by a central angle and the radius of the circle

## Expressing Geometric Properties with Equations

**Equation of a Circle**

G.12.E show that the equation of a circle with center at the origin and radius r is x² + y² = r² and determine the equation for the graph of a circle with radius r and center (h, k), (x – h)² + (y – k)² =r²

## Expressing Geometric Properties with Equations

**Using Area Models for Compound Probability**

G.13.A develop strategies to use permutations and combinations to solve contextual problems

G.13.D apply conditional probability in contextual problems

G.13.E apply independence in contextual problems

**Understanding Independent and Dependent Events**

G.13.C identify whether two events are independent and compute the probability of the two events occurring together with or without replacement