Math Starters 5- to 10-Minute Activities Aligned with the Common Core Math Standards, Grades 6-12

Now updated with new math activities for computers and mobile devices—and now organized by the Common Core State Standards—this book includes more than 650 ready-to-use math starter activities that get kids quickly focused and working as soon as they enter the classroom. Ideally suited for any math curriculum, these high-interest problems spark involvement in the day's lesson, help students build skills, and allow teachers to handle daily management tasks without wasting valuable instructional time.

• A newly updated edition of a bestselling title
• Ideal for math teachers in grades six through twelve
• Includes more than 650 ready-to-use starter problems

Judith A. Muschla taught mathematics in South River, New Jersey, for over twenty-five years. Along with teaching and writing, she has been a member of the State Standards Review Panel for the Mathematics Core Curriculum Content Standards in New Jersey.

Gary Robert Muschla taught at Appleby School in Spotswood, New Jersey, for more than twenty-five years. His specialties include mathematics at the middle school level, reading, and writing. Judith and Gary have coauthored several very successful math activity books, including The Algebra Teacher's Activities Kit, Hands-On Math Projects with Real-Life Applications, and The Math Teacher's Book of Lists.

Erin Muschla-Berry teaches eighth grade math at Monroe Township Middle School in Monroe, New Jersey, and has collaborated with Judith and Gary on four previous math books, including Teaching the Common Core Math Standards with Hands-On Activities, Grades 6-8.

About the Authors

Acknowledgments

About This Book

Standards and Problems Chart

Part 1: Making Math Starters Part of Your Program

The Value of Math Starters

Starting Class with a Math Starter

Purpose and Value of a Math-Starter Notebook

Reproducible: Math-Starter Notebook Guidelines for Students

The Value of Written Explanations

Cooperative Problem Solving Using Math Starters

Organizing Groups for Problem Solving

How to Set Up Groups for Cooperative Math Starters

Reproducible: Rules for Students for Working in Groups on Math Starters

The Value of Sharing and Discussion

Using Problem-Solving Strategies

Reproducible Problem-Solving Strategies

Evaluation

Checklists

Point Systems

Quizzes That Include Math Starters

Review of Math-Starter Notebooks

Student Participation

Portfolios

A Final Word

Part 2: Math Starters

Section 1 Whole Numbers and Integers: Theory and Operations

1-1 Natural Numbers  H

1-2 Natural Numbers  HH

1-3 Whole Numbers H

1-4 Whole Numbers H G

1-5 Place Value with Whole Numbers H

1-6 Place Value with Whole Numbers HH

1-7 Numerical Operations H

1-8 Numerical Operations H G

1-9 Adding Whole Numbers H

1-10 Subtracting Whole Numbers H

1-11 Subtracting Whole Numbers HH

1-12 Multiplying Whole Numbers H

1-13 Multiplying Whole Numbers HH

1-14 Dividing Whole Numbers H (6.NS.2)

1-15 Dividing Whole Numbers H (6.NS.2)

1-16 Dividing Whole Numbers HH (6.NS.2)

1-17 Whole Numbers—Multistep Problem HH (7.EE.3)

1-18 Whole Numbers—Multistep Problem HH G (7.EE.3)

1-19 Estimation with Compatible Numbers H (7.EE.3)

1-20 Rounding Whole Numbers H

1-21 Divisibility by 2, 4, and 8 H

1-22 Divisibility by 3, 6, 9, and 12 H

1-23 Divisibility by 5 and 10 H

1-24 Factors H   

1-25 Factors HH

1-26 Greatest Common Factor H (6.NS.4)

1-27 Greatest Common Factor HH (6.NS.4)

1-28 Multiples H

1-29 Multiples HH

1-30 Least Common Multiple H (6.NS.4)

1-31 Least Common Multiple HH (6.NS.4)

1-32 Multiples and the Distributive Property HH (6.NS.4)

1-33 Prime Numbers H

1-34 Prime Numbers H

1-35 Composite Numbers H

1-36 Prime and Composite Numbers HH ?

1-37 Perfect Squares H

1-38 Perfect Squares and Prime Numbers HH

1-39 Order of Operations H

1-40 Order of Operations HH G

1-41 Powers of Numbers H (6.EE.1)

1-42 Simplifying Expressions with Exponents H (6.EE.1)

1-43 Simplifying Expressions with Exponents HH (6.EE.1)

1-44 Simplifying Expressions with Exponents HH (6.EE.1)

1-45 Writing Numerical Expressions HH

1-46 Identifying Parts of a Numerical Expression HH

1-47 Integers H (6.NS.5)

1-48 Integers HH (6.NS.5)

1-49 Opposites H (6.NS.5)

1-50 The Number Line H (6.NS.6)

1-51 The Number Line HH (6.NS.6)

1-52 Absolute Value H (6.NS.7)

1-53 Absolute Value HH G (6.NS.7)

1-54 Comparing Integers H

1-55 Inequality Symbols H

1-56 Ordering Integers on a Number Line H (6.NS.7)

1-57 Understanding Statements of Order HH (6.NS.7)

1-58 The Coordinate Plane HH (6.NS.6)

1-59 Graphing Points on the Coordinate Plane H (6.NS.6)

1-60 Solving Problems by Graphing Points on the Coordinate Plane HH (6.NS.8)

1-61 Adding Integers H (7.NS.1)

1-62 Adding Integers HH (7.NS.1)

1-63 Subtracting Integers H (7.NS.1)

1-64 Subtracting Integers HH (7.NS.1)

1-65 Adding and Subtracting Integers HH (7.NS.1)

1-66 Representing Addition and Subtraction on a Number Line HH (7.NS.1) ?

1-67 Multiplying Two Integers H (7.NS.2)

1-68 Multiplying More Than Two Integers HH (7.NS.2)

1-69 Multiplying More Than Two Integers HH (7.NS.2)

1-70 Dividing Two Integers H (7.NS.2)

1-71 Dividing Two Integers HH (7.NS.2)

1-72 Multiplying and Dividing Integers HH (7.NS.2)

1-73 Four Operations with Integers HH (7.NS.3)

1-74 Four Operations with Integers HH (7.NS.3)

1-75 Four Operations with Integers HHH G (7.NS.3)

1-76 Using Positive Exponents with Integers H (6.EE.1)

1-77 Using Scientific Notation to Express Large Numbers HH (8.EE.3)

1-78 Computing with Numbers Written in Scientific Notation HH (8.EE.3)

1-79 Changing Numbers in Scientific Notation to Standard Form HH (8.EE.4)

1-80 A Quotation Applicable to Mathematics H

Section 2 Rational Numbers: Fractions, Decimals, and Percents

2-1 Equivalent Fractions H

2-2 Simplifying Fractions H

2-3 Simplifying Fractions HH

2-4 Writing Improper Fractions as Mixed Numbers H

2-5 Writing Mixed Numbers as Improper Fractions H

2-6 Comparing Fractions HH ?

2-7 Ordering Fractions HH

2-8 Adding Fractions H

2-9 Adding Fractions H

2-10 Adding Mixed Numbers H

2-11 Adding Mixed Numbers HH

2-12 Subtracting Fractions H

2-13 Subtracting Fractions HH

2-14 Subtracting Mixed Numbers H

2-15 Subtracting Mixed Numbers HH

2-16 Subtracting Mixed Numbers HH

2-17 Multiplying Fractions H

2-18 Multiplying Fractions HH

2-19 Multiplying Fractions and Mixed Numbers H

2-20 Multiplying Mixed Numbers H

2-21 Estimating and Multiplying Mixed Numbers HH

2-22 Dividing Fractions H (6.NS.1)

2-23 Dividing Fractions H (6.NS.1)

2-24 Dividing Fractions HH G (6.NS.1)

2-25 Dividing Fractions and Mixed Numbers H (6.NS.1)

2-26 Dividing Mixed Numbers H (6.NS.1)

2-27 Dividing Mixed Numbers HH (6.NS.1)

2-28 Fractions—Multistep Problem HH (7.EE.3)

2-29 Fractions—Multistep Problem HH (7.EE.3)

2-30 Decimals H

2-31 Ordering Decimals H

2-32 Ordering Decimals H

2-33 Place Value with Decimals HH

2-34 Writing Fractions as Decimals H

2-35 Writing Decimals as Fractions H

2-36 Writing Decimals as Fractions HH

2-37 Repeating Decimals H (7.NS.2)

2-38 Repeating Decimals HH (7.NS.2)

2-39 Comparing Fractions and Decimals HH (7.EE.3)

2-40 Estimating with Decimals H (7.EE.3)

2-41 Rounding Decimals H

2-42 Rounding Decimals and Unit Pricing H (6.RP.2)

2-43 Adding Decimals H (6.NS.3)

2-44 Adding Decimals H (6.NS.3)

2-45 Subtracting Decimals H (6.NS.3)

2-46 Subtracting Decimals H (6.NS.3)

2-47 Multiplying Decimals H (6.NS.3)

2-48 Multiplying Decimals H (6.NS.3)

2-49 Dividing a Decimal by a Whole Number H (6.NS.3)

2-50 Dividing Decimals HH (6.NS.3)

2-51 Dividing Decimals HH (6.NS.3)

2-52 Decimals—Multistep Problem HH (6.NS.3)

2-53 Decimals—Multistep Problem HHH (6.RP.3)

2-54 Decimals—Multistep Problem HH (7.EE.3)

2-55 Decimals—Multistep Problem HH (7.EE.3)

2-56 Decimals—Multistep Problem HH (7.EE.3)

2-57 Decimals—Multistep Problem HH (7.EE.3)

2-58 Decimals—Multistep Problem HH (7.EE.3)

2-59 Order of Operations—Decimals H (6.NS.3)

2-60 Order of Operations—Decimals HH (6.NS.3)

2-61 Order of Operations—Decimals HH (6.NS.3)

2-62 Ratio H (6.RP.1)

2-63 Ratio HH (6.RP.1)

2-64 Ratio Reasoning HH (6.RP.3)

2-65 Proportional Relationships H (7.RP.2)

2-66 Proportional Relationships HH (7.RP.2)

2-67 Proportional Relationships and Scale HH (7.RP.1)

2-68 Ratio and Rate Reasoning HH (6.RP.3)

2-69 Equivalent Ratios and the Coordinate Plane H (6.RP.3)

2-70 Percents H

2-71 Percents HH

2-72 Equivalencies—Fractions, Decimals, and Percents H

2-73 Equivalencies—Fractions, Decimals, and Percents H

2-74 Equivalencies—Fractions, Decimals, and Percents HH

2-75 Equivalencies—Repeating Decimals HHH (7.NS.2)

2-76 Finding the Percent of a Number H (6.RP.3)

2-77 Finding the Percent of a Number H  (6.RP.3)

2-78 Finding the Percent of a Number HH  (6.RP.3)

2-79 Finding the Percent of a Number HH (6.RP.3)

2-80 Using Proportional Relationships to Find the Percent of a Number H (7.RP.2)

2-81 Finding a Number When a Percent of It Is Known HH (6.RP.3)

2-82 Using Proportional Relationships to Find a Number When a Percent of It Is Known H (7.RP.2)

2-83 Finding What Percent a Number Is of Another Number HH

2-84 Using Proportional Relationships to Find What Percent a Number Is of Another Number H (7.RP.2)

2-85 The Three Types of Percentage Problems HH ?

2-86 Percents and Sales Tax—Multistep Problem H (7.EE.2)

2-87 Percents and Discounts HH

2-88 Percents and Discounts—Multistep Problem HH (7.RP.3)

2-89 Percents and Sales Price—Multistep Problem HH (7.RP.3)

2-90 Percents and Tips—Multistep Problem HHH (7.RP.3)

2-91 Percent of Increase HH (7.RP.3)

2-92 Percent of Decrease HH (7.RP.3)

2-93 Adding Positive and Negative Fractions HH (7.NS.1)

2-94 Adding Positive and Negative Fractions HHH (7.NS.1)

2-95 Subtracting Positive and Negative Fractions HH (7.NS.1)

2-96 Subtracting Positive and Negative Fractions HH (7.NS.1)

2-97 Multiplying Positive and Negative Fractions HH (7.NS.2)

2-98 Multiplying Positive and Negative Fractions HH G (7.NS.2)

2-99 Dividing Positive and Negative Fractions HH (7.NS.2)

2-100 Dividing Positive and Negative Fractions HH G (7.NS.2)

2-101 Four Operations with Positive and Negative Fractions HHH (7.NS.3)

2-102 Simplifying Complex Fractions HH (7.NS.3)

2-103 Simplifying Complex Fractions HHH (7.NS.3)

2-104 Adding Positive and Negative Decimals HH (7.NS.1)

2-105 Subtracting Positive and Negative Decimals H (7.NS.1)

2-106 Multiplying Positive and Negative Decimals H (7.NS.2)

2-107 Dividing Positive and Negative Decimals H (7.NS.2)

2-108 Four Operations with Positive and Negative Decimals HH G (7.NS.3)

2-109 Classifying Numbers as Rational or Irrational HH (8.NS.1)

2-110 Changing Repeating Decimals to Rational Numbers HH G (8.NS.1)

2-111 Changing Repeating Decimals to Rational Numbers HHH (8.NS.1)

2-112 Rational Approximations of Irrational Numbers HH (8.NS.2)

2-113 Integer Exponents H (8.EE.1)

2-114 Integer Exponents HH (8.EE.1)

2-115 Square and Cube Roots HH (8.EE.2)

2-116 Using Scientific Notation to Express Small Numbers HH (8.EE.3)

2-117 Using Scientific Notation to Express Large and Small Numbers HH (8.EE.3)

2-118 Performing Operations with Numbers Expressed in Scientific Notation HH (8.EE.4)

2-119 Expressing Large and Small Numbers in Standard Form HH

2-120 A Quotation about to Mathematics HH

Section 3 Algebra and Beyond

3-1 Simplifying Numerical Expressions with Exponents H (6.EE.1)

3-2 Simplifying Numerical Expressions with Exponents HH (6.EE.1)

3-3 Simplifying Numerical Expressions with Exponents HHH (6.EE.1)

3-4 Words and Phrases as Mathematical Expressions H G (6.EE.2)

3-5 Writing Phrases as Algebraic Expressions H (6.EE.2)

3-6 Evaluating Expressions without Exponents H (6.EE.2)

3-7 Evaluating Expressions with Exponents H (6.EE.2)

3-8 Evaluating Expressions with Exponents HH (6.EE.2)

3-9 Generating Equivalent Expressions H (6.EE.3)

3-10 Generating Equivalent Expressions HH (6.EE.3)

3-11 Identifying Equivalent Expressions H (6.EE.4)

3-12 Identifying Equivalent Expressions HHH (6.EE.4)

3-13 Identifying the Solution of an Equation H (6.EE.5)

3-14 Identifying the Solutions of an Inequality H (6.EE.5)

3-15 Variables H (6.EE.6)

3-16 Using Variables to Represent Numbers H (6.EE.6)

3-17 Solving One-Step Equations—Addition H (6.EE.7)

3-18 Solving One-Step Equations—Subtraction H (6.EE.7)

3-19 Solving One-Step Equations—Addition and Subtraction HH (6.EE.7)

3-20 Solving One-Step Equations—Multiplication H (6.EE.7)

3-21 Solving One-Step Equations—Division H (6.EE.7)

3-22 Solving One-Step Equations—Multiplication and Division HH (6.EE.7)

3-23 Writing Inequalities H (6.EE.8)

3-24 Solving Inequalities HH (7.EE.4)

3-25 Representing Relationships between Dependent and Independent Variables HH G (6.EE.9)

3-26  Generating Equivalent Expressions HH (7.EE.1)

3-27 Rewriting Expressions in Different Forms HH (7.EE.2)

3-28 Solving Two-Step Equations HH (7.EE.3)

3-29 Solving Two-Step Equations HH G (7.EE.4)

3-30 Solving Two-Step Equations HH (7.EE.4)

3-31 Square Roots, Cube Roots, and Equations HH (8.EE.2)

3-32 Interpreting the Unit Rate HH G (8.EE.5)

3-33 Using Similar Triangles to Explain Slope HHH (8.EE.6)

3-34 Finding the Slope of a Line HH

3-35 Slopes of Horizontal and Vertical Lines H

3-36 Application of Finding the Slope HH

3-37 Identifying Like Terms H

3-38 Simplifying Expressions H

3-39 Simplifying Expressions HH

3-40 Simplifying and Evaluating Expressions H

3-41 Solving Equations Involving Several Steps with Variables on the Same Side H (8.EE.7)

3-42 Solving Equations involving Several Steps with Variables on the Same Side HH (8.EE.7)

3-43 Solving Equations involving Several Steps with Variables on Both Sides HH (8.EE.7)

3-44 Solving Equations involving Several Steps with Variables on Both Sides HH (8.EE.7)

3-45 Points of Intersection of Linear Equations H (8.EE.8)

3-46 Estimating Solutions to Systems of Linear Equations by Graphing HH (8.EE.8)

3-47 Using the Graphing Method to Solve Systems of Linear Equations H (8.EE.8)

3-48 Using the Substitution Method to Solve Systems of Linear Equations HH (8.EE.8)

3-49 Using the Addition-or-Subtraction Method to Solve Systems of Linear Equations HH (8.EE.8)

3-50 Using Multiplication with the Addition-or-Subtraction Method to Solve Systems of Linear Equations HH (8.EE.8)

3-51  Choosing Methods and Solving Systems of Linear Equations HH (A-REI.6)

3-52 Multiplying Monomials H

3-53 Multiplying Monomials HH G

3-54 Powers of Monomials HH

3-55 Powers of Monomials HH

3-56 Rewriting Monomials HH (A-SSE.2)

3-57 Dividing Monomials H

3-58 Dividing Monomials H

3-59 Dividing Monomials HH

3-60 Interpreting Algebraic Expressions H (A-SSE.1)

3-61 Finding the Greatest Common Factor (GCF) of Monomials H

3-62 Polynomials H G (A-APR.1)

3-63 Adding and Subtracting Polynomials H (A-APR.1)

3-64 Multiplying a Monomial by a Binomial H (A-APR.1)

3-65 Dividing a Polynomial by a Monomial H (A-APR.1)

3-66 Multiplying Binomials H (A-APR.1)

3-67 Multiplying Binomials H (A-APR.1)

3-68 Cubes of Binomials HH (A-APR.4)

3-69 Rewriting Differences of Squares HH (A-SSE.2)

3-70 Factoring Squares of Binomials HH (A-SSE.3)

3-71 Factoring Trinomials of the Form  Where c > 0 HH (A-SSE.3)

3-72 Factoring Trinomials of the Form  Where c < 0 HH (A-SSE.3)

3-73 Factoring Polynomials of the Form  Where a Is an Integer > 1 HHH

3-74 Factoring by Grouping HHH (A-SSE.3)

3-75 Sums and Differences of Cubes HHH

3-76 Completing the Square HH (A-SSE.3)

3-77 Arithmetic and Geometric Sequences H

3-78 Finding the Partial Sums of Infinite Series HH

3-79 Deriving the Formula for Finding the Sums of a Geometric Series HHH G (A-SSE.4)

3-80 Using the Remainder Theorem and the Factor Theorem HH (A-APR.2)

3-81 Identifying Zeros of Polynomials H (A-APR.3)

3-82 Using Zeros to Sketch Graphs of Functions Defined by Polynomials HH (A-APR.3)

3-83 Generating Pythagorean Triples HH (A-APR.4)

3-84 Pascal’s Triangle and the Binomial Theorem HHH G (A-APR.5)

3-85 Rewriting Rational Expressions H (A-APR.6)

3-86 Rewriting Rational Expressions HH (A-APR.6)

3-87 Rewriting Rational Expressions HHH (A-APR.6)

3-88 Simplifying Rational Expressions H (A-APR.6)

3-89 Multiplying and Dividing Rational Expressions HH (A-APR.7)

3-90 Multiplying and Dividing Rational Expressions HH (A-APR.7)

3-91 Adding and Subtracting Rational Expressions with the Same Denominator HH (A-APR.7)

3-92 Finding the Least Common Denominator of Rational Expressions HH (A-APR.7)

3-93 Adding and Subtracting Rational Expressions with Different Denominators HHH (A-APR.7)

3-94 Adding, Subtracting, Multiplying, and Dividing Rational Expressions HHH G (A-APR.7)

3-95 Explaining the Steps in Solving an Equation H (A-REI.1)

3-96 Explaining the Steps in Solving an Equation H (A-REI.1)

3-97 Solving Rational Equations HH (A-REI.2)

3-98 Solving Rational Equations—Extraneous Solutions HHH (A-REI.2)

3-99 Expressing Square Roots in Radical Form HH (A-REI.2)

3-100 Finding Square Roots H

3-101 Expressing Radical Expressions in Simplest Form HH (A-REI.2)

3-102 Adding and Subtracting Radicals HH (A-REI.2)

3-103 Multiplying Binomials Containing Radicals HHH (A.REI.2)

3-104 Rationalizing the Denominator That Contains Radicals HHH (A-REI.2)

3-105 Solving Radical Equations HH (A-REI.2)

3-106 Solving Simple Radical Equations—Extraneous Solutions HH (A-REI.2)

3-107 Transforming Equations HH G (A-CED.4)

3-108 Solving Linear Equations in One Variable—Coefficients Are Letters HH (A-REI.3)

3-109 Solving Two-Step Inequalities HH (A-REI.3)

3-110 Using Squares of Binomials and Perfect Squares HH (A-REI.4)

3-111 Using the ± Symbol HH

3-112 Solving Quadratic Equations by Completing the Square HHH (A-REI.4)

3-113 Deriving the Quadratic Formula HHH (A-REI.4)

3-114 Transforming Equations into the Form , a ? 0 HH (A-CED.4)

3-115 Solving Quadratic Equations Using the Quadratic Formula if  HH (A-REI.4)

3-116 Using the Zero-Product Property H (A-REI.4)

3-117 Solving Quadratic Equations by Factoring HH (A-REI.4)

3-118 Solving Quadratic Equations of the Form , a ? 0 HH (A-REI.4)

3-119 Sums and Products of Roots HH (A-REI.4)

3-120 Using the Discriminate HHH G (A-REI.4)

3-121 Producing Systems of Equations with the Same Solution H (A-REI.5)

3-122 Solving a System Consisting of a Linear Equation and a Quadratic Equation HHH (A-REI.7)

3-123 Representing a System of Linear Equations as a Matrix Equation H (A-REI.8)

3-124 Using the Inverse of a Matrix to Solve a Matrix Equation HH (A-REI.9)

3-125 Using the Inverse of a 3 × 3 Matrix to Solve a Matrix Equation HH (A-REI.9)

3-126 Graphs and Solutions of Equations H (A-REI.10)

3-127 Finding the Point Where Two Graphs Intersect HH (A-REI.11) ?

3-128 Graphing Solutions to a System of Linear Inequalities HHH (A-REI.12) ?

3-129 Writing and Solving Equations and Inequalities HH (A-CED.1)

3-130 Creating and Graphing Equations HH G (A-CED.2)

3-131 Interpreting Solutions as Viable Options HH (A-CED.3)

3-132 A Quotation about Algebra HH

Section 4 Functions

4-1 Domain and Range H (8.F.1)

4-2 Describing Graphs of Linear Functions HH (8.F.1)

4-3 Finding and Comparing Rates of Change HH (8.F.2)

4-4 Identifying Linear Functions H (8.F.3)

4-5 Identifying Linear Functions HH (8.F.3)

4-6 Interpreting the Initial Value of a Function H (8.F.4)

4-7 Functions and Graphs HH (8.F.5)

4-8 Increasing and Decreasing Functions HH G (8.F.5)

4-9 Understanding the Concept of a Function HH (F-IF.1)

4-10 Evaluating Functions H (F-IF.2)

4-11 Using Sequences Defined Recursively HH (F-IF.3)

4-12 Identifying Key Features of a Graph HH (F-IF.4)

4-13 Relating the Domain to the Relationships It Describes HH (F-IF.5)

4-14 Finding the Average Rate of Change HH (F-IF.6) ?

4-15 Graphs of Functions HH ((F-IF.7)

4-16 Step Graphs HH G (F-IF.7)

4-17 Using Factoring and Completing the Square in Quadratic Functions HH (F-IF.8)

4-18 Classifying Functions as Exponential Growth or Exponential Decay HHH (F-IF.8)

4-19 Comparing Properties of Functions HH (F-IF.9)

4-20 Writing Functions H (F-BF.1)

4-21 Writing Sequences HHH (F-BF.2)

4-22 Translations and Dilations of Graphs HH (F-BF.3)

4-23 Odd and Even Functions HH (F-BF.3)

4-24 Finding the Inverse of a Function HH (F-BF.4)

4-25 Determining if Two Functions Are Inverses HH (F-BF.4)

4-26 Using Exponential and Logarithmic Function HH (F-BF.5)

4-27 Linear and Exponential Models H (F-LE.1)

4-28 Constructing Linear and Exponential Functions HHH (F-LE.2)

4-29 Comparing Exponential, Linear, and Polynomial Functions HHH (F-LE.3) ?

4-30 Solving Exponential Equations H (F-LE.4)

4-31 Interpreting Parameters in the Compound Interest Formula HH (F-LE.5)

4-32 Understanding Radian Measures H (F-TF.1)

4-33  Extending Trigonometric Functions to All Real Numbers HH (F-TF.2)

4-34 Using Special Right Triangles H (F-TF.3)

4-35 Using the Unit Circle to Explain the Symmetry and Periodicity of the Trigonometric Functions HHH (F-TF.4) ?

4-36 Choosing Trigonometric Functions to Model Periodic Phenomena HHH (F-TF.5)

4-37 Restricting the Domain of a Trigonometric Function to Find Its Inverse HHH G (F-TF.6)

4-38 Using Inverse Trigonometric Functions HH (F-TF.7)

4-39 Proving a Pythagorean Identity HH (F-TF.8)

4-40 Proving the Addition Formula for the Sine Function HHH (F-TF.9)

4-41 A Quotation Applicable to Functions H

Section 5 Geometry

5-1 Naming Lines, Rays, and Segments H

5-2 Intersection of Lines, Segments, and Rays H

5-3 Unions of Lines, Segments, and Rays HH

5-4 Naming Angles H

5-5 Types of Angles H

5-6 Complementary and Supplementary Angles H

5-7 Pairs of Angles—Adjacent, Vertical, Complementary, and Supplementary Angles H

5-8 Angles Formed by a Transversal HH

5-9 Parallel Lines and Transversals H (8.G.5)

5-10 Perpendicular Lines and Unknown Angle Measurements H (7.G.5)

5-11 Identifying and Sketching Common Polygons H

5-12 Drawing Polygons in the Coordinate Plane HH  (6.G.3)

5-13 Diagonals of Polygons H

5-14 Sum of the Angles of a Polygon H

5-15 The Measure of Each Interior Angle of a Regular Polygon HH

5-16 The Measure of Each Exterior Angle of a Regular Polygon HH

5-17 The Sum of the Measures of Each Exterior Angle of a Polygon HH

5-18 Classifying Triangles by the Lengths of Their Sides H

5-19 Classifying Triangles by the Measures of Their Angles H

5-20 Included Sides and Angles of a Triangle HH

5-21 Opposite Sides and Angles of a Triangle H

5-22 Finding the Measures of the Angles in a Triangle HH G

5-23 Using the Triangle Inequality Theorem HH

5-24 Drawing Triangles with Given Conditions HH G (7.G.2)

5-25 Using the Pythagorean Theorem to Find the Length of the Hypotenuse H (8.G.7)

5-26 Explaining a Proof of the Pythagorean Theorem HH (8.G.6) ?

5-27 Using the Pythagorean Theorem to Find the Length of a Leg HH (8.G.7)

5-28 Applying the Pythagorean Theorem to Find the Distance between Two Points HH (8.G.8)

5-29 Testing for Acute and Obtuse Triangles HH

5-30 Finding the Length of the Hypotenuse in a 45?-45?-90? Triangle HH

5-31 Finding the Length of a Leg in a 45?-45?-90? Triangle HH

5-32 Finding the Length of the Hypotenuse in a 30?-60?-90? Triangle HH

5-33 Finding the Lengths of the Legs in a 30?-60?-90? Triangle HH

5-34 Finding the Missing Lengths of the Sides of a 45?-45 -90? and a 30?- 60?-90? Triangle HHH

5-35 Properties of Rotations, Reflections, and Translations H (8.G.1)

5-36 Translations, Rotations, and Reflections H (8.G.2)

5-37 Identifying Congruent Triangles H (8.G.2)

5-38 Rotations, Translations, and Reflections of a Right Triangle HH (8.G.2)

5-39 Using Undefined Terms H (G-CO.1)

5-40 Describing Transformations as Functions HH (G-CO.2)

5-41 Describing Dilations HH (G-CO.2)

5-42 Rotations and Reflections of Regular Polygons HH (G-CO.3)

5-43 Defining Rotations, Reflections, and Translations in Terms of Line Segments HHH G (G-CO.4)

5-44 Specifying a Sequence of Transformations That Will Carry a Given Figure onto Another HH (G-CO.5)

5-45 Predicting the Effects of a Rigid Motion HH (G-CO.6)

5-46 Writing a Statement of Congruence and Identifying Corresponding Parts HH (G-CO.7)

5-47 Identifying Corresponding Parts in Overlapping Triangles HH

5-48 Using SSS, SAS, and ASA to Verify Congruent Triangles HH

5-49 Explaining the Criteria for Triangle Congruence HH (G-CO.8)

5-50 Proving Vertical Angles Are Congruent H (G-CO.9)

5-51 Proving the Isosceles Triangle Theorem HH (G-CO.10)

5-52 Proving the Diagonals of a Parallelogram Bisect Each Other HH (G-CO.11)

5-53  Constructing the Perpendicular Bisector of a Segment HH (G-CO.12)

5-54  Constructing a Regular Hexagon Inscribed in a Circle HH (G-CO.13) ?

5-55 Describing the Effects of Dilations, Translations, Rotations, and Reflections HH (8.G.3)

5-56 Describing a Sequence That Exhibits Similarity between Two Figures HHH (8.G.4)

5-57  Verifying the Properties of Dilations HH (G-SRT.1)

5-58  Using the Definition of Similarity to Decide If Two Figures Are Similar H  (G-SRT.2)

5-59 Establishing the AA Criterion for Similar Triangles HH   (G-SRT.3)

5-60 Using AA, SSS, and SAS to Prove That Triangles Are Similar HH

5-61 Writing a Similarity Statement and Finding the Scale Factor HH

5-62 Proving the Triangle Proportionality Theorem HHH (G-SRT.4)

5-63 Finding the Lengths of the Sides of Similar Triangles HHH (G-SRT.5)

5-64 Working with Scale Drawings of Geometric Figures HH (7.G.1)

5-65 Finding the Area of a Triangle by Using a Rectangle H (6.G.1)

5-66 Finding the Area of a Triangle H

5-67 Finding the Area of a Triangle HHH

5-68 Definitions of Trigonometric Ratios for Acute Angles of a Right Triangle H (G-SRT.6)

5-69 Using the Sine and Cosine of Complementary Angles H (G-SRT.7)

5-70 Using Trigonometric Ratios and the Pythagorean Theorem to Solve Problems HHH G (G-SRT.8)

5-71 Deriving the Formula  to Find the Area of a Triangle HH (G-SRT.9)

5-72 Proving the Law of Sines HH (G-SRT.10)

5-73 Using the Law of Sines HH (G-SRT.11)

5-74 Applying the Law of Cosines HH (G-SRT.11)

5-75 Identifying Types of Quadrilaterals H

5-76 Classifying Quadrilaterals HH

5-77 Classifying Quadrilaterals in the Coordinate Plane H (G-GPE.4)

5-78 Parallelograms and Kites HH

5-79 Properties of Quadrilaterals HH

5-80 Properties of Diagonals of Quadrilaterals HH

5-81 Finding the Equations of Parallel and Perpendicular Lines H (G-GPE.5)

5-82 Partitioning Line Segments HH (G-GPE.6)

5-83 Finding the Area of a Square H

5-84 Area and Perimeter of Squares HHH G

5-85 Finding the Area of a Rectangle H

5-86 Finding the Area of a Rectangle HH

5-87 Finding the Area of a Rectangle by Using Other Figures HH (6.G.1)

5-88 Finding the Area and Perimeter of a Rectangle HH G

5-89 Finding the Area of an Irregular Figure HH (7.G.6)

5-90 Finding the Area of an Irregular Figure HH G (7.G.6)

5-91 The Area of a Parallelogram HH (7.G.6)

5-92 Finding the Area of a Trapezoid HH (7.G.6)

5-93 Using Coordinates to Compute Perimeters and Areas of Figures HHH (G-GPE.7)

5-94 Circles H G

5-95  Finding the Diameter and Radius of a Circle H

5-96 Finding the Circumference of a Circle H (7.G.4)

5-97 Diameter and Circumference HH (7.G.4)

5-98 Finding the Area of a Circle H (7.G.4)

5-99 Finding the Area of a Circle HH (7.G.4)

5-100 Comparing the Areas of a Square and a Circle HH (7.G.4)

5-101 Proving All Circles Are Similar HH (G-C.1)

5-102 Types of Arcs HH G

5-103 Central and Inscribed Angles HH (G-C.2)

5-104 Arcs and Angles of Circles HH (G-C.2)

5-105 Secants and Tangents H

5-106 Measures of Angles—Chord-Tangent Angle Theorem and Chord-Chord Angle Theorem HHH (G-C.2)

5-107 Measures of Angles Formed by Secants and Tangents Drawn from a Point outside the Circle HHH

5-108 Lengths of Segments—Chords Intersecting in the Interior of a Circle HH (G-C.2)

5-109 Length of Segments—Secant and Tangent Segments HHH

5-110 Proving Opposite Angles of a Quadrilateral Inscribed in a Circle Are Supplementary HH (G-C.3)

5-111 Constructing Tangent Lines to a Circle HH (G-C.4) ?

5-112 Arc Lengths HH

5-113 Area of a Sector HH (G-C.5)

5-114 Deriving the Formula for Finding the Area of a Sector HH (G-C.5)

5-115 Deriving the Equation of a Circle HH (G-GPE.1)

5-116 Deriving the Equation of a Parabola HHH (G-GPE.2)

5-117 Deriving the Equation of an Ellipse HHH (G-GPE.3)

5-118 Slicing Three-Dimensional Figures HH (7.G.3) ?

5-119 Identifying Three-Dimensional Objects Generated by Rotations of Two-Dimensional Objects HHH G (G-GMD.4)

5-120 Using Geometric Shapes to Describe Objects HH G (G-MG.1)

5-121 Finding the Volume of a Rectangular Prism HH (6.G.2)

5-122 Finding the Volume of a Rectangular Prism HHH G (6.G.2)

5-123 Using Nets to Find the Surface Area of a Three-Dimensional Figure HH (6.G.4)

5-124 Finding the Surface Area of a Rectangular Prism HH (7.G.6)

5-125 Finding the Surface Area of a Rectangular Prism HHH (7.G.6)

5-126 Finding the Volume and Surface Area of Pyramids HHH (7.G.6)

5-127 Finding the Volume of Cones HH (8.G.9)

5-128 Finding the Volume of Spheres HHH (8.G.9)

5-129 Using Various Volume Formulas HH (G-GMD.3)

5-130 Providing an Informal Argument for the Area of a Circle HH (G-GMD.1)

5-131 Cavalieri’s Principle and the Volume of a Sphere HHH (G-GMD.2) ?

5-132 Density in Modeling HHH (G-MG.2)

5-133 Solving Design Problems HH (G-MG.3)

5-134 A Quotation about Geometry HH

Section 6 Statistics, Probability, and Data Analysis

6-1 Statistical and Nonstatistical Questions H G (6.SP.1)

6-2 Distribution of Data H (6.SP.2)

6-3 Finding the Mean of a Set of Numbers H

6-4 Finding the Weighted Mean HH

6-5 Finding the Mode H

6-6 The Median H

6-7 Finding the Median and the Mode HH

6-8 Finding the Mean, Median, and Mode HH (6.SP.3)

6-9 Using the Measures of Center and Measure of Variation HH (6.SP.3)

6-10 Making a Histogram HH (6.SP.4)

6-11 Making a Bar Graph H

6-12 Using Stem-and-Leaf Plots HH

6-13 Completing a Circle Graph H

6-14 Summarizing Numerical Data HH (6.SP.5)

6-15 Obtaining Information about a Population H (7.SP.1)

6-16 Using Data from Random Samples to Draw Inferences about a Population HHH (7.SP.2)

6-17 Assessing Numerical Data Distributions HH (7.SP.3)

6-18 Drawing Comparative Inferences about Two Populations HH (7.SP.4)

6-19  The Probability of Impossible and Certain Events HH (7.SP.5)

6-20 Finding Simple Probability H G

6-21 Approximating the Probability of a Chance Event  HH (7.SP.6)

6-22 Predicting Relative Frequency HHH (7.SP.6)

6-23 Developing a Probability Model H G (7.SP.7)

6-24 Spinners as Probability Models H (7.SP.7)

6-25 Representing the Sample Spaces of Compound Events HH (7.SP.8)

6-26 Constructing a Scatter Plot HH G (8.SP.1)

6-27 Using Scatter Plots HH (8.SP.2)

6-28 Positive, Negative, and No Relationship HH

6-29 Interpreting the Slope and Y-Intercept H (8.SP.3)

6-30 Using Two-Way Tables H (8.SP.4)

6-31 Representing Data with a Box-and-Whisker Plot H (S-ID.1)

6-32 Comparing the Center and Spread of Two Sets of Data HH (S-ID.2)

6-33 Accounting for Outliers H (S-ID.3)

6-34 Using the Mean and Standard Deviation of a Data Set H (S-ID.4)

6-35 Summarizing Categorical Data H (S-ID.5)

6-36 Describing How Variables Are Related HH (S-ID.6)

6-37 Interpreting the Slope and Y-Intercept HH (S-ID.7)

6-38 Interpreting the Correlation Coefficient of a Linear Fit H  (S-ID.8)

6-39 Distinguishing between Correlation and Causation H  (S-ID.9)

6-40 Understanding the Value of Statistics H  G (S-IC.1)

6-41 Deciding If Results Are Consistent H  (S-IC.2)

6-42 Recognizing Sample Surveys, Observational Studies, and Experiments HH  (S-IC.3)

6-43 Using Data from a Sample Survey HH  (S-IC.4)

6-44 Data and Simulations HH  (S-IC.5)

6-45 Evaluating Reports Based on Data HH (S-IC.6)

6-46 Describing Events as Subsets of a Sample Space H (S-CP.1)

6-47 The Probability of Independent Events H (S-CP.2)

6-48 The Probability of Independent Events HH G (S-CP.2)

6-49 Understanding Conditional Probability HH (S-CP.3)

6-50 Interpreting a Two-Way Frequency Table H (S-CP.4)

6-51 Conditional Probability HH G (S-CP.5)

6-52 Finding Conditional Probability HH (S-CP.6)

6-53 Applying the Addition Rule for Finding Probability H (S-CP.7)

6-54 Applying the General Multiplication Rule H (S-CP.8)

6-55 Using the Factorial Counting Rule H

6-56 Using the Permutations Rule HH (S-CP.9)

6-57 Using the Combinations Rule HH (S-CP.9)

6-58 Defining a Random Variable H (S-MD.1)

6-59 Calculating the Expected Value of a Random Variable H (S-MD.2)

6-60 Developing a Probability Distribution HH (S-MD.3)

6-61 Developing a Probability Distribution Using Empirical Data HH (S-MD.4)

6-62 Evaluating a Flood Insurance Plan HHH G (S-MD.5)

6-63 Using Probabilities to Make Fair Decisions HH G (S-MD.6)

6-64 Basing Decisions on Probability HHH G (S-MD.7)

6-65 A Quotation about Statistics HH

Section 7 Numbers and Quantity

7-1 Using Rational Exponents H (N-RN.1)

7-2 Rewriting Expressions Using Radicals and Rational Exponents HH (N-RN.2)

7-3 Explaining Products and Sums H (N-RN.3)

7-4 Using Units as a Way to Understand Problems HH (N-Q.1) ?

7-5 Defining Appropriate Quantities HH (N-Q.2)

7-6 Levels of Accuracy HH (N-Q.3)

7-7 Using Imaginary Numbers HHH (N-CN.1)

7-8 Using Powers of i HHH

7-9 Adding, Subtracting, and Multiplying Complex Numbers HH (N-CN.2)

7-10 Finding Quotients of Complex Numbers H (N-CN.3)

7-11 Using an Argand Diagram H (N-CN.4)

7-12 Representing Operations with Complex Numbers in the Complex Plane HH (N-CN.5)

7-13 Finding the Distance between Numbers in the Complex Plane HH (N-CN.6)

7-14 Solving Quadratic Equations by Using the Quadratic Formula—Complex Solutions HH (N-CN.7)

7-15 Extending Polynomial Identities to the Complex Numbers HH (N-CN.8)

7-16 The Fundamental Theorem of Algebra HHH (N-CN.9)

7-17 Vector Quantities H (N-VM.1)

7-18 The Components of Vectors H (N-VM.2)

7-19 Using Vectors to Find a Plane’s Ground Speed and True Course HHH (N-VM.3)

7-20 Using the Parallelogram Rule H (N-VM.4)

7-21 Multiplying a Vector by a Scalar H (N-VM.5)

7-22 Using Matrices to Represent Data H (N-VM.6)

7-23 Multiplying Matrices by a Scalar H (N-VM.7)

7-24 Adding and Subtracting Matrices H (N-VN.8)

7-25 Multiplying Matrices HH (N-VM.8)

7-26 Proving the Properties of Matrix Multiplication for Square Matrices HHH (N-VM.9)

7-27 Using the Zero and Identity Matrix HHH (N-VM.10)

7-28 Translations and Vectors H

7-29 Using Transformation Matrices: Reflection HH (N-VM.11)

7-30 Using Transformation Matrices: Enlargement HH (N-VM.11)

7-31 Using the Determinate to Find Area HH (N-VM.12)

7-32 A Quotation about the Boundaries of Mathematics

Section 8 Potpourri

8-1 Emirps H

8-2 Deficient Numbers H

8-3 Perfect Numbers H

8-4 Abundant Numbers H

8-5 Deficient, Abundant, and Perfect Numbers HH G

8-6 Linear Measurement—The Customary System H

8-7 Linear Measurement—The Customary System HH

8-8 Linear Measurement—The Metric System HH

8-9 Linear Measurement—The Customary and Metric Systems HH

8-10 Linear Measurement—Obsolete Units HH

8-11 Linear Measurement—Obsolete Units HH

8-12 Linear Measurement—Quotation HH

8-13 Weight—The Customary System H

8-14 Weight—The Metric System HH

8-15 Weight—Using Balances H

8-16 Capacity—The Customary System HH

8-17 Capacity—The Metric System H

8-18 Time and the Calculation of Pi H

8-19 Interpreting Time HH

8-20 Time—A Tricky Problem HH

8-21 Temperature H

8-22 Converting Temperatures—Fahrenheit and Celsius HH

8-23 Measurement—Light-Years H

8-24 Babylonians and Angles in a Circle H

8-25 Platonic Solids and Euler’s Formula HH

8-26 Squares on a Checkerboard HH G

8-27 Rectangles on a Checkerboard HH G

8-28 Finding the Area of a Rectangular Chicken Coop H

8-29 Edward I and the Area of a Rectangle HH

8-30 Finding the Area of a Triangle Using Hero’s Formula HHH

8-31 An Ancient Palestinian Formula for Finding the Area of a Circle HHH

8-32 Palindromes H

8-33 Palindromes HH G

8-34 Using Cryptarithms HH

8-35 Number Ciphers HH G

8-36 Number Ciphers HHH

8-37 Using Number-Box Ciphers H

8-38 Roman Numerals HH G

8-39 Symbols (Infinity) HH

8-40 Figural Analogies HH

8-41 Fractals H

8-42 Fractals—Using the Sierpinski Triangle HH

8-43 Figurate Numbers—Square Numbers H

8-44 Figurate Numbers—Square Numbers HH

8-45 Figurate Numbers—Rectangular Numbers H

8-46 Figurate Numbers—Rectangular Numbers HH

8-47 Numerical Patterns H

8-48 Numerical Patterns HH G

8-49 Line Symmetry H

8-50 Lines of Symmetry HH

8-51 Networks H

8-52 Traceable Networks HH G

8-53 Using Digraphs H

8-54 Using Digraphs HH

8-55 Using Digraphs HH G

8-56 Symbols and Letters in Math HH

8-57 A Quotation about Mathematics HH

8-58 A Personal Quotation about Mathematics H

Answer Key

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