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Number Power Addition, Subtraction, Multiplication, and Division Correlations to the Common Core State Standards

Lesson Common Core State Standards

Place Value

Understanding Place Value pp. 6–8

CCSS.Math.Content.1.NBT.2 Understand that the two digits of a two‐digit number represent amounts of tens and ones.

CCSS.Math.Content.2.NBT.2 Understand that the three digits of a three‐digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.

Zeros and Place Value pp. 9–10

CCSS.Math.Content.1.NBT.2 Understand that the two digits of a two‐digit number represent amounts of tens and ones.

CCSS.Math.Content.2.NBT.2 Understand that the three digits of a three‐digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.

CCSS.Math.Content.4.NBT.1 Recognize that in a multi‐digit whole number, a digit in one place represents ten times what it represents in the place to its right.

Rounding Whole Numbers pp. 11–12

CCSS.Math.Content.4.NBT.3 Use place value understanding to round multi‐digit whole numbers to any place.

Addition

Addition Skills Inventory pp. 13–14

Basic Addition Facts pp. 15–16

Adding Larger Numbers p. 17

Adding and Carrying pp. 18–20

Adding Numbers Written Horizontally p. 21

Addition Shortcuts p. 22

CCSS.Math.Content.4.NBT.4 Fluently add and subtract multi‐digit whole numbers using the standard algorithm.

Rounding and Estimating pp. 23–24


Applying Your Addition Skills pp. 25–28


Addition Review pp. 29–30

CCSS.Math.Content.4.NBT.3 Use place value understanding to round multi‐digit whole numbers to any place. CCSS.Math.Content.4.NBT.4 Fluently add and subtract multi‐digit whole numbers using the standard algorithm.

© McGraw-Hill Education Updated February 2013 1


Subtraction

Subtraction Skills Inventory pp. 31–32

Basic Subtraction Facts pp. 33–34

Subtracting Larger Numbers p. 35

Subtracting and Borrowing p. 36

Borrowing More Than Once pp. 37–38

Subtracting Numbers Written Horizontally p. 39

Subtracting from Zeros pp. 40–42

Subtraction Shortcuts p. 43


Rounding and Estimating p. 44


Applying Your Subtraction Skills pp. 45–48


Multistep Problems pp. 49–50

CCSS.Math.Content.3.OA.8 Solve two‐step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.


Subtraction Review pp. 51–53



Multiplication

Multiplication Skills Inventory pp. 54–55

Basic Multiplication Facts pp. 56–58

The Multiplication Table p. 59

Multiplying by One–Digit Numbers p. 60

Multiplying by Larger Numbers pp. 61–62

CCSS.Math.Content.5.NBT.5 Fluently multiply multi‐digit whole numbers using the standard algorithm.



Multiplying Numbers Written Horizontally pp. 63–64

Multiplying and Carrying pp. 65–67


Multiplying 10, 100, and 1,000 pp. 68–69

CCSS.Math.Content.5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole‐number exponents to denote powers of 10.



Applying Your Multiplication Skills pp. 73–76



CCSS.Math.Content.3.OA.8 Solve two‐step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.


Multiplication Review pp. 79–81


Division

Division Skills Inventory pp. 82–83

Basic Division Facts pp. 84–86

Dividing by One–Digit Numbers pp. 87–89

Dividing with Remainders pp. 90–92

CCSS.Math.Content.6.NS.2 Fluently divide multi‐digit numbers using the standard algorithm.

Properties of Numbers p. 93

CCSS.Math.Content.2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

CCSS.Math.Content.3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one‐digit numbers.

Dividing by Two–Digit Numbers pp. 94–97

Dividing by Three–Digit Numbers pp. 98–99






Two–Digit Accuracy pp. 102–103



Applying Your Division Skills pp. 104–108



CCSS.Math.Content.3.OA.8 Solve two‐step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.3


Division Review pp. 111–113


Using Number Power

Changing Units of Measurement pp. 120–121

CCSS.Math.Content.5.MD.1 Convert among different‐sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi‐step, real world problems.

Adding Measurements p. 122

Subtracting Measurements p. 123

Multiplying Measurements p. 124

Dividing Measurements p. 125

CCSS.Math.Content.4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Perimeter: Measuring the Distance Around a Rectangle pp. 126–127

Area: Measuring the Space Inside a Rectangle pp. 128–130

CCSS.Math.Content.3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Volume: Measuring the Space Inside a 3–Dimensional Object pp. 131–132

CCSS.Math.Content.7.G.6 Solve real‐world and mathematical problems involving area, volume and surface area of two‐ and three‐dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.



Pricing a Meal from a Menu p. 133

CCSS.Math.Content.5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

CCSS.Math.Content.7.EE.3 Solve multi‐step real‐life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

Reading Sales Tax Tables pp. 134–135

Checking Your Change with Sales Receipts pp. 136–137



Using a Calorie Chart pp. 138–139

Reading Paycheck Stubs pp. 140–141

Using a Table to Look Up Check Cashing Rates pp. 142–143

Understanding Tax Statements pp. 144–145

Figuring the Cost of Electricity pp. 146–147

Reading Time Schedules pp. 148–149

Using the Cost Formula pp. 150–151

Using the Distance Formula pp. 152–153

Renting a Car p. 154



Number Power Fractions, Decimals, and Percents Correlations to the Common Core State Standards


Fractions

Fraction Skills Inventory pp. 8–10

CCSS.Math.Content.7.NS.3 Solve real‐world and mathematical problems involving the four operations with rational numbers.

Understanding Fractions p. 11

Writing Fractions p. 12

CCSS.Math.Content.3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

Thinking About the Size of Fractions p. 14

CCSS.Math.Content.3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Reducing Fractions pp. 15–17

Raising Fractions to Higher Terms p. 18

CCSS.Math.Content.4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Changing Improper Fractions to Whole or Mixed Numbers pp. 19–20

CCSS.Math.Content.3.NF.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Adding Fractions with the Same Denominators pp. 22–24

CCSS.Math.Content.4.NF.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Adding Fractions with Different Denominators p. 25

Finding the Common Denominator pp. 26–28

CCSS.Math.Content.5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

Estimating Addition Answers p. 29

Applying Your Addition Skills p. 30

CCSS.Math.Content.5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

Subtracting Fractions with the Same Denominators p. 31


Subtracting Fractions with Different Denominators pp. 32–33

Borrowing and Subtracting Fractions pp. 34–36




Estimating Subtraction Answers p. 37



Multiplying Fractions p. 40

Canceling and Multiplying Fractions pp. 41–42

CCSS.Math.Content.5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Multiplying Fractions and Whole Numbers p. 43

CCSS.Math.Content.4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

Multiplying Mixed Numbers p. 44

Estimating Multiplication Problems p. 45



CCSS.Math.Content.4.NF.4c Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.

Dividing Fractions by Fractions pp. 48–49

Dividing Whole Numbers by Fractions pp. 50–51

Dividing Fractions by Whole Numbers pp. 52–53

Dividing with Mixed Numbers pp. 54–55

CCSS.Math.Content.5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

Finding a Number When a Fraction of It is Given p. 56

CCSS.Math.Content.6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

Estimating Division Answers p. 57

CCSS.Math.Content.5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.


CCSS.Math.Content.5.NF.7c Solve real world problems involving division of unit fractions by non‐zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.

Fraction Review pp. 60–61




Decimals

Decimal Skills Inventory pp. 62–63


Understanding Decimals pp. 64–65

Reading Decimals p. 66

Writing Decimals p. 67

Getting Rid of Unnecessary Zeros p. 68

CCSS.Math.Content.5.NBT.3 Read, write, and compare decimals to thousandths.

Changing Decimals to Fractions p. 69


Changing Fractions to Decimals p. 70

CCSS.Math.Content.7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Comparing Decimals p. 71


Rounding Decimals pp. 72–73

CCSS.Math.Content.5.NBT.4 Use place value understanding to round decimals to any place.

Adding Decimals p. 74

CCSS.Math.Content.6.NS.3 Fluently add, subtract, multiply, and divide multi‐digit decimals using the standard algorithm for each operation.

Estimating Addition Answers p. 75


Applying Your Addition Skills p. 76

Subtracting Decimals p. 77


Estimating Subtraction Answers p. 78





Multiplying Decimals pp. 81–83


Multiplying Decimals by 10, 100, and 1,000 p. 84


Estimating Multiplication Answers p. 85



Dividing Decimals by Whole Numbers p. 88

Dividing Decimals by Decimals pp. 89–90

Dividing Whole Numbers by Decimals p. 91


Dividing Decimals by 10, 100, and 1,000 p. 92


Dividing to Fixed–Place Accuracy p. 93


Estimating Division Answers p. 94



Cumulative Review pp. 97–98




Percents

Percent Skills Inventory pp. 99–100

CCSS.Math.Content.7.RP.3 Use proportional relationships to solve multistep ratio and percent problems.

Understanding Percents p. 101

CCSS.Math.Content.6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

Changing Decimals to Percents p. 102

Changing Percents to Decimals p. 103

Changing Fractions to Percents p. 104

Changing Percents to Fractions p. 105


Finding a Percent of a Number pp. 107–108

Using Shortcuts p. 109


Finding a Percent of a Number: Applying Your Skills p. 110

Solving Two–Step Problems p. 112


Finding What Percent One Number Is of Another pp. 113–114

Finding What Percent One Number Is of Another: Applying Your Skills pp. 115–116


Finding a Percent of Change pp. 117–118


Finding a Number When a Percent of It Is Given pp. 119–120

Finding a Number When a Percent of It Is Given: Applying Your Skills pp. 121–122


Recognizing Types of Percent Problems pp. 123–124




Cumulative Review pp. 125–126






Using Number Power

Finding the Perimeter of Rectangles and Squares pp. 136–137

Finding the Area of Rectangles and Squares pp. 138–139

CCSS.Math.Content.4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

Finding the Volume of a Rectangular Solid pp. 140–141

CCSS.Math.Content.5.MD.5a Find the volume of a right rectangular prism with whole‐number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole‐number products as volumes, e.g., to represent the associative property of multiplication.

Finding the Circumference of a Circle pp. 142–143

Finding the Area of a Circle pp. 144–145

CCSS.Math.Content.7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Changing a Recipe p. 146


Converting Units of Measurement pp. 147–149




Finding Interest for One Year pp. 150–151

Finding Interest for Less than One Year p. 152

Finding Interest for More than One Year p. 153

Finding Compound Interest pp. 154–155

Finding the Percent Saved at a Sale pp. 156–157

Buying Furniture on Sale p. 158


Calculating Rates p. 159

Comparing Food Prices: Unit Pricing pp. 160–161

CCSS.Math.Content.7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Using a Tax Rate Schedule pp. 162–163

Filling Out a Wage and Tax Statement pp. 164–165

Working with a Budget pp. 166–167

Buying on an Installment Plan pp. 168–169



Number Power Algebra Correlations to the Common Core State Standards


Signed Numbers

Introducing Signed Numbers pp. 10

CCSS.Math.Content.6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real‐world contexts, explaining the meaning of 0 in each situation.

The Number Line pp. 11

CCSS.Math.Content.6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

Adding Signed Numbers pp. 12–15

CCSS.Math.Content.7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

Subtracting Signed Numbers pp. 16–17

CCSS.Math.Content.7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real‐world contexts.

Multiplying Signed Numbers pp. 18–19

CCSS.Math.Content.7.NS.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real‐world contexts.

Dividing Signed Numbers pp. 20–21

CCSS.Math.Content.7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non‐zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real‐world contexts.

Applying Your Skills: Signed Numbers pp. 22–23

Signed Numbers Review pp. 24–25

CCSS.Math.Content.7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers.

CCSS.Math.Content.7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.



Powers and Roots

What Is a Power? pp. 26–28

CCSS.Math.Content.6.EE.1 Write and evaluate numerical expressions involving whole‐number exponents.

Multiplication and Division of Powers pp. 29

Simplifying Products and Quotients with Like Bases pp. 30–31

Negative Exponents pp. 32

CCSS.Math.Content.8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.

Scientific Notation pp. 33

CCSS.Math.Content.8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

What Is a Square Root? pp. 34–35

CCSS.Math.Content.8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x

3 = p, where p is a positive rational number. Evaluate square roots of small perfect

squares and cube roots of small perfect cubes. Know that √2 is irra onal.

Applying Your Skills: Powers and Roots pp. 38–39

Powers and Roots Review pp. 40–41





Algebraic Expressions and Formulas

Writing Algebraic Expressions pp. 42–43

Applying Your Skills: Algebraic Expressions pp. 44–45

CCSS.Math.Content.6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers.

Evaluating Algebraic Expressions pp. 46–48

Evaluating Formulas pp. 49–50

Applying Your Skills: Formulas pp. 51

CCSS.Math.Content.6.EE.2c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real‐world problems. Perform arithmetic operations, including those involving whole‐number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

Simplifying an Algebraic Expression pp. 52–53

CCSS.Math.Content.6.EE.3 Apply the properties of operations to generate equivalent expressions.



Algebraic Expression Review pp. 54–55


One Step Equations

What Is an Equation? pp. 56–57

Checking Unknowns pp. 58

CCSS.Math.Content.6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

Solving an Algebraic Equation pp. 59

Solving an Addition Equation pp. 60

Solving a Subtraction Equation pp. 61

Applying Your Skills: One–Step Equations (+ and –) pp. 62

Solving a Multiplication Equation pp. 63

Solving a Division Equation pp. 64

Applying Your Skills: One–Step Equations (x and ÷) pp. 65

CCSS.Math.Content.7.EE.4 Use variables to represent quantities in a real‐world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Solving an Equation with a Fraction Coefficient pp. 66

Applying Your Skills: One–Step Equations (with Fractions) pp. 67



One–Step Equations Review pp. 68–71




Multistep Equations

What Is a Multistep Equation? pp. 72–73

Learning a Shortcut to Solving Equations pp. 74–75

CCSS.Math.Content.7.EE.4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

Solving an Equation with Separated Variables pp. 76–77

Terms on Both Sides of an Equation pp. 78–79

CCSS.Math.Content.8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Applying Your Skills: Multistep Equations pp. 80–81



Solving an Equation with Parentheses pp. 82–83

Applying Your Skills: Solving an Equation with Parentheses pp. 84–85


Rearranging a Formula pp. 86

Applying Your Skills: Rearranging a Formula pp. 87

CCSS.Math.Content.9‐12.A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Multistep Equations Review pp. 88–91

CCSS.Math.Content.8.EE.7 Solve linear equations in one variable.

Special Equations

Understanding Ratios pp. 92

CCSS.Math.Content.6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.



Applying Your Skills: Using Equations to Solve Ratio Problems pp. 93

CCSS.Math.Content.6.RP.3 Use ratio and rate reasoning to solve real‐world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Understanding Proportions pp. 94–95

CCSS.Math.Content.7.RP.2 Recognize and represent proportional relationships between quantities.

Applying Your Skills: Using Proportions pp. 96–97


Solving a Linear Equation pp. 98–99


Solving a System of Equations pp. 100–101

CCSS.Math.Content.8.EE.8 Analyze and solve pairs of simultaneous linear equations.

Quadratic Equations pp. 102–103

CCSS.Math.Content.9‐12.A.REI.4 Solve quadratic equations in one variable.

Applying Your Skills: Special Equations pp. 104–105

Special Equations Review pp. 106–107

CCSS.Math.Content.8.EE.8 Analyze and solve pairs of simultaneous linear equations.


Becoming Familiar with a Coordinate Grid pp. 108–109

CCSS.Math.Content.5.G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x‐axis and x‐coordinate, y‐axis and y‐coordinate).

Graphing Equations

Plotting Points on a Grid pp. 110


Graphing a Line pp. 111

CCSS.Math.Content.5.G.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.



Finding the Slope of a Line pp. 112–113

CCSS.Math.Content.8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

CCSS.Math.Content.8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Graphing a Linear Equation pp. 114–115

Applying Your Skills: Graphing Circumference pp. 116

Applying Your Skills: Graphing Temperature pp. 117


Graphing a System of Equations pp. 118–119

CCSS.Math.Content.8.EE.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

Graphing a Quadratic Equation pp. 120–121

CCSS.Math.Content.9‐12.A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Graphing Equations Review pp. 122–123


CCSS.Math.Content.9‐12.A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Graphing Equations Review pp. 123

CCSS.Math.Content.8.EE.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.



Inequalities

What Is an Inequality? pp. 124

CCSS.Math.Content.6.NS.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

Graphing an Inequality pp. 125–126

Solving an Inequality pp. 127–129

Applying Your Skills: Inequalities pp. 130

CCSS.Math.Content.7.EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

Two–Part Inequalities pp. 131–132

Applying Your Skills: Two–Part Inequalities pp. 133


Inequalities Review pp. 134–135

CCSS.Math.Content.7.EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

Polynomials

Naming Polynomials pp. 136

Like Terms in Polynomials pp. 137

Adding Polynomials pp. 138–139

Subtracting Polynomials pp. 140–141

Multiplying Monomials pp. 142

Multiplying a Polynomial by a Monomial pp. 143

Multiplying a Binomial by a Binomial pp. 144–145

CCSS.Math.Content.9‐12.A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Dividing Monomials pp. 146

Dividing a Binomial or Trinomial by a Monomial pp. 147





Applying Your Skills: Polynomials pp. 148–149

Polynomial Review pp. 150–151


Factoring

Factors pp. 152

Prime Numbers and Prime Factors pp. 153

CCSS.Math.Content.4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one‐digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

Finding the Square Root of an Algebraic Term pp. 154

Simplifying a Square Root pp. 155




CCSS.Math.Content.9‐12.A.SSE.2 Use the structure of an expression to identify ways to rewrite it.

Factoring an Algebraic Expression pp.

Factoring and Dividing pp. 158–159

Factoring a Difference of Squares pp. 160–161

Factoring Review pp. 162–163

CCSS.Math.Content.9‐12.A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.



Using Number Power

Windchill pp. 172–173

CCSS.Math.Content.7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real‐world contexts.

Distance Formula pp. 174–175

Simple Interest Formula pp. 176–177

Simple Interest Formula: Parts of a Year pp. 178–179

Work Problems pp. 180–181

Mixture Problems pp. 182–183

Temperature: Finding Fahrenheit from Celsius pp. 184–185

Using Algebra in Geometry pp. 186–187


Right Triangles and the Pythagorean Theorem pp. 188–189

Using Algebra in Trigonometry pp. 190–191

Finding the Distance Between Points on a Grid pp. 192–193

CCSS.Math.Content.9‐12.G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Absolute Value pp. 194–195

CCSS.Math.Content.6.NS.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real‐world situation.


Number Power Geometry Correlations to the Common Core State Standards


Angles

Introducing Angles pp. 10–11

CCSS.Math.Content.4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand the concepts of angle measurement.

Measuring an Angle pp. 12–13

CCSS.Math.Content.4.MD.5a An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one‐degree angle,” and can be used to measure angles.

CCSS.Math.Content.4.MD.6 Measure angles in whole‐number degrees using a protractor. Sketch angles of specified measure.

Types of Angles pp. 14–15

Labeling Angles p. 16

CCSS.Math.Content.4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two‐dimensional figures.

Using a Protractor pp. 17–19

Drawing Angles pp. 20–21


Pairs of Angles pp. 22–23

Applying Your Skills: Pairs of Angles pp. 24–25

CCSS.Math.Content.7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi‐step problem to write and solve simple equations for an unknown angle in a figure.

Parallel Lines pp. 26–27



Applying Your Skills: Parallel Lines pp. 28–29


Angles Review pp. 30–33





Triangles

Introducing Triangles pp. 34–35

CCSS.Math.Content.2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Sum of Angles in a Triangle pp. 36–37

Applying Your Skills: Sum of Angles pp. 38–39

CCSS.Math.Content.9‐12.G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

Types of Triangles pp. 40–42

Applying Your Skills: Types of Triangles p. 43

CCSS.Math.Content.4.G.2 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. Recognize right triangles as a category, and identify right triangles.

Similar Triangles pp. 44–47

Applying Your Skills: Similar Triangles pp. 48–51

CCSS.Math.Content.8.G.4 Understand that a two‐dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two‐dimensional figures, describe a sequence that exhibits the similarity between them.



Squares and Square Roots pp. 52–53

CCSS.Math.Content.8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x

2 = p and x

3 =

p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irra onal.

Pythagorean Theorem pp. 54–57

Applying Your Skills: Pythagorean Theorem pp. 58–59

CCSS.Math.Content.8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real‐world and mathematical problems in two and three dimensions.

Triangles Review pp. 60–62

CCSS.Math.Content.4.G.2 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. Recognize right triangles as a category, and identify right triangles.




2 = p and x

3 =

p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irra onal.



Perimeter

Customary Length Units pp. 64–65

Metric Length Units pp. 66–67

Adding and Subtracting Length Units pp. 68–69

Multiplying and Dividing Length Units pp. 70–71


Applying Your Skills: Length Units pp. 72–73


Recognizing Polygons pp. 74–75


Introducing Perimeter pp. 76–77

Perimeter of a Square pp. 78–79


Perimeter of a Rectangle pp. 80–81


Perimeter of a Triangle pp. 82–83

Perimeter of a Parallelogram and a Trapezoid pp. 84–85


Circumference of a Circle pp. 86–87


Perimeter Review pp. 88–89





Area

Introducing Area pp. 90–91

CCSS.Math.Content.3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.

Area Units pp. 92–93

Area of a Rectangle pp. 94–95

Area of a Triangle pp. 96–97

Area of a Parallelogram and a Trapezoid pp. 98–99

CCSS.Math.Content.3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.


Area of a Circle pp. 100–101


Applying Your Skills: Perimeter and Area pp. 102–105




Solving Two–Step Area Problems: Part 1 pp. 106–107

Solving Two–Step Area Problems: Part II pp. 108–109


Area Review pp. 110–113


CCSS.Math.Content.5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.



Volume

Recognizing Solid Figures pp. 112–113

CCSS.Math.Content.K.G.2 Correctly name shapes regardless of their orientations or overall size.

Introducing Volume pp. 114–115


Volume of a Cube pp. 116–117



Volume of a Rectangular Solid pp. 118–119



Volume of a Cylinder p. 120

Volume of a Cone p. 121

CCSS.Math.Content.8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real‐world and mathematical problems.

Applying Your Skills: Volume pp. 122–123

Solving Two–Step Volume Problems: Part I pp. 124–125

Solving Two–Step Volume Problems: Part II pp. 126–127

Volume Review pp. 128–130



Using Number Power

Tiling a Room pp. 138–139

Building a Patio pp. 140–141

Carpeting a Room pp. 142–143

Surface Area pp. 144–145




Working in Your Yard pp. 146–147



Dimensions of a Sphere pp. 148–149


Accuracy in Measurement pp. 150–151

CCSS.Math.Content.9‐12.N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Changing Volume to Capacity pp. 152–153

CCSS.Math.Content.6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Design Work pp. 154–155


Tessellations pp. 156–157

CCSS.Math.Content.9‐12.G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

More Properties of a Circle pp. 160–161

CCSS.Math.Content.9‐12.G.C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Applying the Pythagorean Theorem pp. 162–163


Symmetry: Reflection and Rotation pp. 164–165

CCSS.Math.Content.4.G.3 Recognize a line of symmetry for a two‐dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line‐symmetric figures and draw lines of symmetry.

Similar Figures pp. 166–167



CCSS.Math.Content.9‐12.G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Scale Drawings and Scale Models pp. 168–169

CCSS.Math.Content.7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.




Trigonometry pp. 170–174


Coordinate Geometry pp. 175–178

CCSS.Math.Content.8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two‐dimensional figures using coordinates.


Number Power Graphs, Charts, Schedules, and Maps Correlations to the Common Core State Standards


Graphs

Pictographs pp. 20–21

Practice Graph I pp. 22–23

Practice Graph II pp. 24–25

Practice Graph III pp. 26–27

Pictographs: Applying Your Skills pp. 28–31

Bar Graphs pp. 44–45

Practice Graph I pp. 46–47

Practice Graph II pp. 48–49

Practice Graph III pp. 50–51

Bar Graphs: Applying Your Skills pp. 52–55

CCSS.Math.Content.3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one‐ and two‐step “how many more” and “how many less” problems using information presented in scaled bar graphs.

Schedules and Graphs

Graph Review pp. 68–76


Maps

Map Skills Inventory pp. 102–105

Using a Distance Scale pp. 114–115

Directional Maps pp. 124–125

Practice Directional Map pp. 126–127

Directional Maps: Applying Your Skills pp. 128–129

Map Review pp. 134–139




Using Number Power

Budgeting a Paycheck pp. 154–155

Cost of Housing: Buying a House pp. 156–157


Costs of Hospitalization pp. 166–167


Calculating Driving Distances and Times pp. 168–169


Reading a Directional Map pp. 170–171


Constructing Graphs pp. 174–176



Number Power Word Problems Correlations to the Common Core State Standards


Addition and Subtraction Word Problems: Whole Numbers

Solving Addition Word Problems with Key Words p. 19

Solving Subtraction Word Problems with Key Words p. 21

Solving Addition and Subtraction Problems with Key Words pp. 23–24


More Addition and Subtraction Word Problems: Whole Numbers

Using Pictures and Diagrams to Solve Word Problems pp. 31–33


Using Number Sentences to Solve Word Problems pp. 34–36


Addition and Subtraction Word Problems: Decimals and Fractions

Using Estimation pp. 40–41


Decimals: Drawings and Diagrams pp. 44–45


Decimals: Writing Number Sentences pp. 46–47




Fractions: Diagrams and Pictures p. 50


Fractions: Using Number Sentences p. 51


Using Algebra to Solve Word Problems pp. 52–53


Solving Addition and Subtraction Word Problems pp. 54–56


Multiplication and Division Word Problems: Whole Numbers

Solving Multiplication Word Problems with Key Words p. 59

Solving Division Word Problems with Key Words p. 61

Solving Multiplication and Division Problems with Key Words p. 63

Deciding When to Multiply and When to Divide pp. 64–66

Using Diagrams When Deciding to Multiply or Divide pp. 67–71




Addition and Subtraction Word Problems: Whole Numbers

Solving Decimal Multiplication and Division Word Problems pp. 72–74

Solving Fraction Multiplication Word Problems pp. 75–77

Solving Fraction Division Word Problems pp. 78–79

Solving Fraction Multiplication and Division Word Problems pp. 80–81

Solving Multiplication and Division Word Problems pp. 82–83


Using Proportions

What Are Ratios? p. 84


What Are Proportions? pp. 85–87


Using Proportions to Solve Word Problems pp. 88–90

Using Proportions to Solve Decimal Word Problems pp. 91–92

Using Proportions to Solve Fraction Word Problems p. 93


Solving Conversion Word Problems pp. 94–95

CCSS.Math.Content.6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Using Proportions with Fractions and Decimals p. 96

Using Proportions with Multiplication and Division p. 97




Strategies with Mixed Word Problems

Mixed Word Problems with Whole Numbers pp. 98–99


Using Labels to Solve Word Problmes pp. 100–103


Mixed Word Problems: Whole Numbers, Decimals, and Fractions pp. 109–111


Percent Word Problems

Solving Percent Word Problems pp. 115–119

The Percent Circle pp. 122–124

Solving Percent Word Problems with Decimals and Fractions pp. 125–127

Solving More Percent Word Problems pp. 128–129


Solving Combination Word Problems pp. 130–134

Solving Problems with Decimals, Fractions, and Percents pp. 135–137


Order of Operations pp. 138–139

Using Order of Operations in Combination with Word Problems pp. 140–141

Using Pictures or Diagrams to Set Up Multistep Word Problems pp. 145–147




Solving Combination Word Problems Involving Conversions pp. 148–149

Solving Word Problems Containing Unnecessary Information pp. 150–151

Solving Longer Combination Word Problems pp. 152–153

Solving Combination Word Problems pp. 154–155


Using Number Power

Using Information from a Chart for Health pp. 162–165

Using Number Power in a Landscaping Business pp. 166–167

Using Number Power in Retail pp. 168–169

Using Number Power in the Medical Field pp. 170–171

Using Number Power in the Trucking Industry pp. 172–173

Challenging Word Problems pp. 174–176



Number Power Problem‐Solving and Test‐Taking Strategies Correlations to the Common Core State Standards


Looking at Word Problems

What is Estimation? pp. 18–19


The Five‐Step Process

Step 4: Solve the Problem pp. 28–29

Step 5: Check Your Answer pp. 30–31


Understanding the Question

Read Carefully pp. 32–35

Some Tricky Questions pp. 36–37


Working with Set–Up Questions pp. 38–39

More on Set–Up Problems pp. 40–43


Mixed Review pp. 44–45




Finding the Information

Looking at Labels pp. 46–47

Finding Hidden Information pp. 48–51



Choosing the Operation pp. 72–73


Equations pp. 74–77


Equations with Two Operations pp. 78–81


Writing Equations for Word Problems pp. 82–85

Solving a Word Problem Equation pp. 86–89


Writing Proportions for Word Problems pp. 90–93

CCSS.Math.Content.7.RP.2c Represent proportional relationships by equations.

Solving Proportions pp. 94–95

When Can You Use a Proportion? pp. 96–98


Drawing a Picture pp. 99–101







Solving the Problem

Estimating the Answer pp. 108–109

Using Friendly Numbers to Estimate pp. 110–111

Estimating with Fractions pp. 112–113


Writing Answers in Set–Up Format pp. 116–117

Choosing the Correct Expression pp. 118–119


Comparing and Ordering Numbers pp. 120–123

CCSS.Math.Content.4.NBT.2 Read and write multi‐digit whole numbers using base‐ten numerals, number names, and expanded form. Compare two multi‐digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Making Good Use of Your Calculator pp. 124–125


What to Do with Remainders pp. 126–127

CCSS.Math.Content.4.OA.3 Solve multistep word problems posed with whole numbers and having whole‐number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.





Checking the Answer

Is the Answer Reasonable? pp. 134–137



Using Charts, Graphs, and Drawings

Reading a Picture pp. 141–144

Reading Graphs and Charts Carefully p. 148

Reading Graphs and Charts Carefully p. 150


Working Geometry Word Problems

Finding Information on Drawings pp. 154–157


Let Formulas Work for You pp. 158–161


Visualizing Geometry Problems pp. 162–164

Picturing a Geometry Problem pp. 165–168






Using Number Power

Smart Selling: Finding and Using Information pp. 178–179

Creating a Budget: Using the Numbers in Your Life pp. 180–181

Pricing on the Job: Using a Chart pp. 182–183

Quality Control: Is the Number Reasonable? pp. 186–187

Understanding Profit: Multistep Problems pp. 188–189


Using Proportions: Calculating Waste pp. 190–191


Measurement: Reading a Blueprint pp. 192–193



Number Power Analyzing Data Correlations to the Common Core State Standards


Understanding Data

Making Statements About Data pp. 11–12

CCSS.Math.Content.6.SP.5b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

What are Statistics? pp. 13–15

CCSS.Math.Content.7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

How Big is a Billion? pp. 19–21


Numbers vs. Rates pp. 22–25


Organizing Data

Bar Graphs pp. 30–33 Double Bar Graphs pp. 34–35 Pictographs pp. 42–43


Line Plots pp. 47–49

CCSS.Math.Content.6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Scatter Diagrams pp. 50–51

CCSS.Math.Content.8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.



Arithmetic Mean pp. 52–53 Median p. 54 Mode p. 55 Mean, Median, and Mode p. 56 Critical Thinking with Data p. 57

CCSS.Math.Content.6.SP.5c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

The Purpose of a Graph or Chart pp. 58–62

CCSS.Math.Content.6.SP.5b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

Using Probability and Statistics

What Are the Chances? pp. 86–87

CCSS.Math.Content.7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long‐run relative frequency, and predict the approximate relative frequency given the probability.

Probabilities Between 1 and 0 pp. 88–89

CCSS.Math.Content.7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Using Data to Estimate Probability pp. 90–92


An Introduction to Sampling pp. 93–95


Random Samples pp. 96–98


Introduction to Surveys pp. 99–102




Evaluating Data

Understanding Correlation pp. 119–123

CCSS.Math.Content.8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Using Number Power

A Look at the U.S. Census pp. 146–147 Writing a Newspaper Article pp. 154–155 Using Graphs to Track Productivity pp. 162–163



Number Power Measurement Correlations to the Common Core State Standards


Measurements

Reading Rulers and Straight–Line Scales pp. 10–11

CCSS.Math.Content.2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

Measuring Around the House pp. 14–15

CCSS.Math.Content.3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).Add, subtract, multiply, or divide to solve one‐step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.



Length and Angles

Estimating Length in Meters pp. 16–17

CCSS.Math.Content.2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters.

Metric Lengths and the Decimal Point pp. 18–19

CCSS.Math.Content.4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two‐column table.

Operations with Metric Measurements p. 20


Estimating Length Using Customary Units pp. 21–23

CCSS.Math.Content.2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters.

Changing Among Inches, Feet, Yards, and Miles pp. 24–25




Adding and Subtracting Lengths pp. 26–28

Multiplying and Dividing Lengths pp. 29–30


Comparing and Ordering Lengths pp. 32–33


Focus on Geometry: Measuring Angles pp. 34–35


Focus on Geometry: Kinds of Angles p. 36


Focus on Geometry: Angles and Parallel Lines p. 37

Focus on Geometry: Pairs of Angles pp. 38–39


Focus on Geometry: Area and Perimeter pp. 40–41



Focus on Geometry: Area and Perimeter p. 41


Section 2 Cumulative Review pp. 42–44






Weight and Temperature

Metric Units of Weight p. 49

CCSS.Math.Content.3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one‐step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

Estimating in Ounces, Pounds, and Tons pp. 50–51

CCSS.Math.Content.4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two‐column table.

Changing Among Ounces, Pounds, and Tons pp. 52–53


Estimating in Milligrams, Grams, and Kilograms p. 54


Changing Among Milligrams, Grams, and Kilograms pp. 55–57


Adding and Subtracting Weights pp. 58–59

Multiplying and Dividing Weights pp. 60–61


Comparing and Ordering Weights pp. 62–63


Section 3 Cumulative Review p. 73




Capacity and Volume

Estimating Capacity pp. 78–79


Changing Among Customary Units of Capacity pp. 80–83


Estimating with Metric Units of Capacity pp. 84–85


Changing Among Milliliters, Liters, and Kiloliters pp. 86–88


Adding and Subtracting with Capacity Measurements pp. 89–90

Multiplying and Dividing with Capacity Measurements pp. 91–92


Focus on Geometry: Volume pp. 94–97


Focus on Geometry: Volume of Cylinders and Cones pp. 98–101








Time and Velocity

Adding and Subtracting Measurements of Time pp. 114–115

Multiplying and Dividing Measurements of Time pp. 116–117


Focus on Algebra: Velocity pp. 120–121






Using Number Power

Home Remodeling pp. 128–129


Scale on Drawings and Maps pp. 130–131


Doctors' Offices pp. 134–135

Automotive Fluids p. 136

Recipes p. 137




Ice, Water, Gas pp. 138–139

Heating and Air Conditioning p. 140

Packing and Moving p. 141

CCSS.Math.Content.5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

Miles Per Gallon pp. 144–145


Trucking and Delivery Services pp. 148–149


Speed of Planes pp. 150–151



Number Power Pre‐Algebra Correlations to the Common Core State Standards


Number Skills

Reviewing Fractions, Decimals, and Percents pp. 10–15


Applying Your Skills: Fractions on an Inch Ruler p. 16


Applying Your Skills: Decimals on a Centimeter Ruler p. 17

Positive and Negative Numbers pp. 18–19


Comparing Numbers: Inequalities pp. 20–21

CCSS.Math.Content.6.NS.7b Write, interpret, and explain statements of order for rational numbers in real‐world contexts.

Graphing an Inequality pp. 22–23

CCSS.Math.Content.6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real‐world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Applying Your Skills: Operations with Numbers pp. 24–25


Rounding to a Chosen Place Value pp. 26–27


Terminating and Repeating Decimals pp. 28–29




Number Skills Review pp. 30–31




Word Problem Skills

Estimating pp. 32–37


Understanding Set–Up Questions pp. 38–39

Set–Up Questions in Multistep Problems pp. 40–41

Finding an Average p. 42


Understanding Ratios pp. 44–45


Applying Your Skills: Rate pp. 46–47


Understanding Proportions pp. 48–49

Applying Your Skills: Proportion pp. 50–51




Work Problem Skills Review pp. 52–53




Problem–Solving Strategies

Drawing a Picture pp. 54–55


Using a Number Pattern pp. 64–65

CCSS.Math.Content.5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

Data Analysis

Finding Typical Values pp. 72–73


Reading a Pictograph pp. 76–77

Reading a Bar Graph pp. 78–79

Applying Your Skills: Changing How Data are Displayed pp. 84–85

Data Analysis Review pp. 86–87




Probability

Introducing Probability pp. 88–89

Expressing Probability as a Number pp. 90–91


Probabilities from 0 to 1 pp. 92–93


Using Probability for Prediction pp. 94–95


Making a List to Predict Outcomes pp. 96–97

Using a Tree Diagram pp. 98–99

CCSS.Math.Content.7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

Basing Probability on Data pp. 100–101

CCSS.Math.Content.7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

Applying Your Skills: Probability of Two Events pp. 102–103

Probability Review pp. 104–105


Geometry and Measurement

Lines p. 106

Angles p. 107

CCSS.Math.Content.9‐12.G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Types of Angles p. 108


Pairs of Angles p. 109

Angles Formed by Intersecting Lines pp. 110–111




Properties of Triangles pp. 112–113


Perimeter p. 114


Circumference of a Circle p. 115


Area of Squares and Rectangles p. 116

Area of a Triangle p. 117


Area of a Circle p. 118


Applying Your Skills: Perimeter, Circumference, and Area p. 119




Volume of a Rectangular Solid p. 120


Volume of a Cylinder p. 121




Geometry and Measurement Review pp. 122–123





Spatial Sense and Patterns

Symmetry pp. 124–125

CCSS.Math.Content.4.G.3 Recognize a line of symmetry for a two‐dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line‐symmetric figures and draw lines of symmetry.

Congruent Figures and Similar Figures pp. 126

CCSS.Math.Content.8.G.2 Understand that a two‐dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.


Applying Your Skills: Map Coordinates pp. 128–129



Working with Figures on a Coordinate Grid pp. 132–133

CCSS.Math.Content.6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real‐world and mathematical problems.



Spatial Sense and Patterns Review pp. 138–139

CCSS.Math.Content.6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real‐world and mathematical problems.

CCSS.Math.Content.8.G.2 Understand that a two‐dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.


The Language of Algebra

Algebraic Expressions p. 140

Picturing Algebraic Expressions p. 141

Applying Your Skills: Algebraic Expressions pp. 142–143


Using Exponents p. 144

CCSS.Math.Content.6.EE.1 Write and evaluate numerical expressions involving whole‐number exponents.

Finding a Square Root p. 145


2 = p and x

3

= p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irra onal.

Evaluating Algebraic Expressions pp. 146–147

Becoming Familiar with Equations p. 148

Picturing an Equation p. 149

CCSS.Math.Content.6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.

Solving an Equation p. 150

CCSS.Math.Content.6.EE.7 Solve real‐world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

Checking a Solution p. 151

CCSS.Math.Content.6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.



Solving an Addition Equation p. 152

Solving a Subtraction Problem p. 153

Applying Your Skills: Word Problems [+ and –] p. 154

Solving a Multiplication Equation pp. 155

Solving a Division Equation pp. 156

Applying Your Skills: Word Problems [x and ÷] pp. 157

Reviewing One–Step Equations pp. 158–159


The Language of Algebra Review pp. 160–161

CCSS.Math.Content.6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.


Using Number Power

Prime Numbers and Composite Numbers pp. 172–173

CCSS.Math.Content.4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one‐digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

Using a Protractor pp. 174–175


Accuracy in Measurement pp. 176–177

CCSS.Math.Content.9‐12.N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Distance Formula pp. 178–179

Fahrenheit and Celsius Temperatures pp. 180–181


Surface Area of a Rectangular Solid pp. 182–183




Surface Area of a Cylinder p. 184



Dimensions of Part of a Circle p. 185

CCSS.Math.Content.9‐12.G.C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Similar Figures pp. 186–187



Scale Drawings and Scale Models pp. 188


Pythagorean Theorem pp. 190–191



Number Power Review Correlations to the Common Core State Standards


Number Sense

Writing Familiar Numbers p. 8

Writing Larger Numbers p. 9

Comparing and Ordering Numbers p. 10


Rounding Whole Numbers p. 12


Rounding Dollars and Cents p. 13


Estimating Sums p. 14

Using Clustering to Estimate a Large Sum p. 15

Estimating Differences p. 16

Estimating Products p. 17


Estimating Quotients pp. 18–19

Applying Estimation pp. 20–21


Understanding Negative Numbers pp. 24–25

CCSS.Math.Content.6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real‐world contexts, explaining the meaning of 0 in each situation.

More About Inequalities pp. 26–27


Showing an Inequality on a Number Line pp. 28–29

CCSS.Math.Content.6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real‐world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.



Number Sense Review pp. 30–31




Whole Numbers

Adding Whole Numbers pp. 32–33

Subtracting Whole Numbers pp. 34–35

Applying Addition and Subtraction pp. 36–37


Problem Solver: Understanding Set–Up Questions pp. 38–39


Multiplying Whole Numbers pp. 40–41


Dividing Whole Numbers pp. 42–45


Applying Multiplication and Division pp. 46–47



Problem Solver: Solving Multistep Problems pp. 48–49

Problem Solver: Choosing the Correct Expression pp. 50–51

Problem–Solving Strategy: Working Backward pp. 52–53




Data Highlight: Finding Typical Values pp. 54–55


Whole Numbers Review pp. 56–57


Numbers Less Than 1

Parts of a Whole pp. 58–59


Reading and Writing Decimals pp. 60–61


Comparing and Ordering Decimals p. 62

CCSS.Math.Content.5.NBT.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Writing Proper Fractions p. 64


Picturing Equal Fractions p. 65

CCSS.Math.Content.3.NF.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

Reducing Fractions p. 66

Writing an Amount as a Fraction of a Larger Unit p. 67

Raising Fractions to Higher Terms p. 68

CCSS.Math.Content.3.NF.3b Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

Comparing Proper Fractions p. 69

Finding the Lowest Common Denominator (LCD) pp. 70–71

CCSS.Math.Content.4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Writing Improper Fractions and Mixed Numbers p. 72

CCSS.Math.Content.3.NF.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.



Understanding Percent pp. 74–75


Relating Decimals, Fractions, and Percents pp. 76–77


Numbers Less than 1 Review pp. 80–81



Fractions

Building Confidence by Estimating pp. 82–85


Changing an Improper Fraction to a Mixed Number p. 86


Adding Like Fractions pp. 87–88

Subtracting Like Fractions p. 89

Subtracting Fractions from Whole Numbers p. 90

Subtracting Fractions by Regrouping p. 91




Adding and Subtracting Unlike Fractions pp. 92–93

Applying Your Skills pp. 94–95


Multiplying Fractions pp. 96–97

Multiplying Fractions, Whole Numbers, and Mixed Numbers pp. 98–99


Dividing Fractions pp. 100–101

Dividing Fractions, Whole Numbers, and Mixed Numbers pp. 102–103





Relating Fractions and Ratios pp. 106–107


Working with Rates pp. 108–109


Problem Solver: Recognizing and Comparing Patterns pp. 110–111

CCSS.Math.Content.3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

Data Highlight: Reading a Pictograph pp. 112–113

CCSS.Math.Content.2.MD.10 Draw a picture graph and a bar graph (with single‐unit scale) to represent a data set with up to four categories. Solve simple put‐together, take‐apart, and compare problems using information presented in a bar graph.

Fractions Review pp. 114–115




Decimals

Building Confidence by Estimating pp. 116–117

Rounding to Different Place Values pp. 118–119


Adding Decimals p. 120

Subtracting Decimals p. 121


Multiplying Decimals pp. 124–125

Dividing Decimals pp. 126–127

Using Placeholding Zeros When Dividing Whole Numbers p. 128


Multiplying or Dividing by 10, 100, or 1,000 p. 129



Using Drawings pp. 132–133

Decimals Review pp. 136–137


Percents

Identifying Numbers in a Percent Problem p. 138

The Percent Circle p. 139

Using the Percent Circle pp. 140–141


Changing a Percent to a Fraction or a Decimal pp. 142–143

Changing a Fraction or a Decimal to a Percent pp. 144–145




Finding the Part pp. 146–147

Finding the Percent pp. 148–149

Finding the Whole pp. 150–151

Problem Solver: Estimating with Easy Percents pp. 152–153

Applying Percent Skills: Mixed Practice pp. 154–155


Understanding Simple Interest pp. 156–157

Computing Interest for Part of a Year pp. 158–159


Data Highlight: Reading a Bar Graph pp. 160–161


Percents Review pp. 162–163


Data Analysis and Probability

Locating Data pp. 164–165

CCSS.Math.Content.2.MD.10 Draw a picture graph and a bar graph (with single‐unit scale) to represent a data set with up to four categories. Solve simple put‐together, take‐apart, and compare problems4 using information presented in a bar graph.

Using More than One Data Source pp. 166–168


Drawing Conclusions from Data pp. 169–171


Understanding Probability pp. 172–173




Problem Solver: Making a List to Predict Outcomes pp. 174–175


Finding Probability for Two Events pp. 176–177

CCSS.Math.Content.7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Problem Solver: Using Probability for Prediction pp. 178–179


Data Analysis and Probability Review pp. 180–181



Algebra

Solving Addition and Subtraction Equations pp. 182–183

Solving Multiplication and Division Equations pp. 184–185

CCSS.Math.Content.6.EE.7 Solve real‐world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

Solving Multistep Equations pp. 186–187



Combining Like Terms in an Equation pp. 190–191

Solving Equations with Terms on Both Sides pp. 192–193




Learning About Proportion pp. 196–197




Problem Solver: Using Proportions to Solve Word Problems pp. 198–199



Solving an Equation with Two Variables pp. 200–201

CCSS.Math.Content.8.EE.8c Solve real‐world and mathematical problems leading to two linear equations in two variables.



Graphing a Linear Equation pp. 204–205

Finding Slope pp. 206–207


Algebra Review pp. 208–209




Geometry

Measuring Angles p. 211


Angle Relationships pp. 212–213


Angles Formed by Intersecting Lines pp. 214–215


Working with Triangles pp. 216–217




Problem Solver: Working with Similar Triangles pp. 218–219

Working with Similar Figures pp. 220–221



Understanding Squares and Square Roots pp. 222–223


2 = p and x

3


The Pythagorean Theorem pp. 224–225


Finding the Perimeter p. 226


Finding the Circumference of a Circle p. 227


Finding the Area of a Square or a Rectangle pp. 228–229

Finding the Area of a Triangle p. 230


Finding the Area of a Circle p. 231


Finding Surface Area pp. 232–233

Finding the Volume of a Rectangular Solid p. 234


Finding the Volume of a Cylinder p. 235


Using Algebra in Geometry pp. 236–237




Introducing Trigonometry p. 238

Values of Trigonometric Functions Depend Only on Angle p. 239

Applying Trigonometry p. 240


Geometry Review pp. 241–242




Number Power Calculator Power Correlations to the Common Core State Standards


Adding Two Numbers p. 16

Adding Three or More Numbers pp. 19–20

Subtracting Two or More Numbers pp. 21–22


Calculators and Word Problems pp. 23–24

The Importance of Estimating pp. 25–26

Estimation with Addition and Subtraction pp. 27–28


Application: Balancing a Checkbook pp. 29–30

Multiplying Two or More Numbers pp. 31–32

Dividing One Number by Another pp. 33–34


Using Math Common Sense with Multiplication and Division pp. 35–36

Multistep Word Problems pp. 37–38


Calculator Division and Remainders p. 40

Finding the Value of a Remainder pp. 41–42


Puzzle Power p. 43


Introducing Decimals pp. 45–46

Rounding Decimals pp. 47–48


Terminating and Repeating Decimals pp. 49–50




Recognizing Key Words p. 52

Adding Two or More Decimals pp. 53–54

Subtracting Two or More Decimals pp. 55–56

Decimal Addition and Subtraction Problems pp. 57–58

Multiplying Two or More Decimals pp. 59–60

Dividing Decimals pp. 61–62


Estimating with Multiplication and Division pp. 63–64

Application: Comparing the Cost of Child Care p. 65


Reviewing Fractions pp. 66–67


Overview of Percent pp. 73–74

Finding Part of a Whole pp. 75–76

Finding the Percent pp. 77–78

Finding the Whole pp. 79–80


Percent Problems pp. 83–84



Application: Percent and a Family Budget pp. 85–86




Arithmetic Expressions pp. 91–92

Using a Calculator to Evaluate Expressions pp. 93–94


Multistep Word Problems pp. 97–99


Special Multistep Problem: Finding Percent Increase or Decrease pp. 100–101


Keeping a Mileage Record p. 114

Completing a Purchase Order p. 115

Interpreting a Paycheck Stub p. 116

Comparing Annual Car Costs p. 117

Completing Payroll Forms pp. 118–119

Ordering from a Menu p. 120


"Best Buy" Shopping pp. 121–122


Computing Distance, Rate, and Time pp. 123–124


Finding an Average p. 125


Computing Simple Interest pp. 126–127

Paying a Mortgage pp. 128–129




Using Measurement Formulas pp. 130–132


Square Roots pp. 133–134


2 = p and x

3


Right Triangles and the Pythagorean Theorem pp. 135–136


Calculator Application Review pp. 137–140



Number Power Financial Literacy Correlations to the Common Core State Standards


Unit 1 Managing Money

Lesson 1: Income pp. 11–20

Lesson 2: Banking pp. 21–30

Lesson 3: Shopping pp. 31–40


Lesson 4: Unit Pricing pp. 41–48


Lesson 5: Dining Out pp. 49–56



Lesson 6: Travel pp. 57–68


Lesson 7: Home Renovation pp. 69–78



Lesson 8: Investing pp. 79–90




Unit 2 Borrowing Money

Lesson 9: Interest pp. 93–100

Lesson 10: Loans pp. 101–110

Lesson 11: Installment Buying pp. 111–118


Lesson 12: Credit pp. 119–128


Lesson 13: Mortgages pp. 129–136


Unit 3 Unavoidable Expenses

Lesson 14: Utilities pp. 139–152


Lesson 15: Renting or Buying a Home pp. 153–162


Lesson 16: Car Expenses pp. 163–172


Lesson 17: Insurance pp. 173–186

Lesson 18: Taxes pp. 187–196

Lesson 19: Income Tax pp. 197–210


Unit 4 Budgeting

Lesson 20: Writing a Budget pp. 212–222




Unit 5 Math Skills Review

Place Value p. 224



Whole Number Operations: Addition p. 225

Subtraction p. 226


Multiplication p. 226


Rounding Whole Numbers p. 227


Division p. 227

CCSS.Math.Content.5.NBT.6 Find whole‐number quotients of whole numbers with up to four‐digit dividends and two‐digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Estimation p. 228


Finding an Average (or Mean) and a Median p. 228


Decimals

Rounding Decimals p. 229


Adding and Subtracting Decimals p. 230

Multiplying and Dividing Decimals p. 231–232




Fractions

Reducing Fractions p. 233


Fractions and Decimals pp. 233–234


Finding What Part One Number is of Another p. 234


Basic Operations with Fractions p. 235


Percent

Finding a Percent of a Number pp. 236–237


Interest

Finding What Percent One Number Is of Another p. 238


Interest pp. 238–239


Measurement

Measurement pp. 239–240


Perimeter and Area

Perimeter and Area pp. 241–242



Number Power Transitions Math Correlations to the Common Core State Standards


Rules and Properties

Numbers and Operations pp. 1–4


Working with Exponents pp. 5–8


Working with Radicals pp. 9–12




Rules and Properties Review pp. 13–14


Variables

Using Variables to Create Expressions pp. 15–16


Simplifying Expressions pp. 17–20


Working with Fractions in Expressions pp. 21–24

CCSS.Math.Content.7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Evaluating Expressions pp. 25–27


Variables Review pp. 28–29

CCSS.Math.Content.7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.



Equation and Inequality Basics

Beyond Expressions pp. 31–33


The Rules of Equality pp. 34–35


Solving an Equation pp. 36–41


Solving Word Problems pp. 42–43

Solving Geometry Problems pp. 44–45

Solving More Word Problems pp. 46–47

Inequalities pp. 48–51

CCSS.Math.Content.9‐12.A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Absolute Value Equations pp. 52–55

CCSS.Math.Content.6.NS.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real‐world situation.


Formulas: Solving for a Specific Variable pp. 56–58

CCSS.Math.Content.9‐12.A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Equation and Inequality Basics Review pp. 59–64

CCSS.Math.Content.9‐12.A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.



Linear Equations and Graphing

Graphing on the Coordinate Plane pp. 66–68

CCSS.Math.Content.5.G Graph points on the coordinate plane to solve real‐world and mathematical problems.

Slope and Intercepts pp. 69–74

CCSS.Math.Content.8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

CCSS.Math.Content.9‐12.F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input‐output pairs (include reading these from a table).

Finding the Equation of a Line pp. 75–82


Parallel and Perpendicular Lines pp. 83–86

CCSS.Math.Content.9‐12.G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Problem Solving on the Coordinate Plane pp. 87–92

CCSS.Math.Content.9‐12.N.CN.6 Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

Linear Equations and Graphing Review pp. 93–98

CCSS.Math.Content.5.G Graph points on the coordinate plane to solve real‐world and mathematical problems.




Problem Solving with Multiple Variables

Graphing a System of Equations pp. 99–101

Solving a System of Equations Using Algebra pp. 102–109

CCSS.Math.Content.9‐12.A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Solving Word Problems Using Systems pp. 110–113

Solving Rate Problems Using Systems pp. 114–116

Solving Mixture and Work Problems Using Systems pp. 117–122

Solving Rate–Time–Distance Problems pp. 123–127

Solving Geometry Applications pp. 128–132

Problem Solving with Multiple Variables Review pp. 133–138

CCSS.Math.Content.8.EE.8c Solve real‐world and mathematical problems leading to two linear equations in two variables.

Quadratic Equations

Basics of Quadratic Equations pp. 139–141

Solve Quadratic Equations by Factoring pp. 142–149

Special Factorizations pp. 150–152

Factoring by Grouping pp. 153–155

CCSS.Math.Content.9‐12.A.REI.4b Solve quadratic equations by inspection (e.g., for x

2 = 49), taking square roots, completing the

square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Simplifying Rational Expressions pp. 156–157

More About Radicals pp. 158–162

CCSS.Math.Content.9‐12.A.SSE.2 Use the structure of an expression to identify ways to rewrite it.

Completing the Square pp. 163–168

CCSS.Math.Content.9‐12.A.REI.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)

2 = q that has the same solutions. Derive the quadratic formula from this form.



The Quadratic Formula pp. 169–172




Quadratic Equations and Word Problems pp. 173–175


Quadratic Equations Review pp. 176–180




Graphing Quadratics

Graphing Parabolas pp. 181–185

Patterns in Graphing Equations pp. 186–189

CCSS.Math.Content.9‐12.F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

Transformations pp. 190–194

CCSS.Math.Content.9‐12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

Circles pp. 195–197

Graphing Quadratics Review pp. 198–203

CCSS.Math.Content.9‐12.F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

Extension Topics

Function Basics pp. 204–210

CCSS.Math.Content.9‐12.F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Graphing Linear and Quadratic Inequalities pp. 211–213

CCSS.Math.Content.9‐12.A.REI.12 Graph the solutions to a linear inequality in two variables as a half‐plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half‐planes.

Trigonometric Ratios pp. 214–220

CCSS.Math.Content.9‐12.G.SRT.10 Prove the Laws of Sines and Cosines and use them to solve problems.



Extension Topics Review pp. 221–223, 225

CCSS.Math.Content.9‐12.F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

CCSS.Math.Content.9‐12.G.SRT.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.


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