Real Numbers and the Coordinate Plane
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- Meryl Armstrong
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1 1 Real Numbers and the Coordinate Plane Check Your Readiness Rational Numbers 8.NS b Activity Lab Repeating Decimals 8.NS In this chapter, you will develop an understanding of irrational numbers and approximate them using rational numbers. You will use square roots and cube roots to express solutions to equations. Additionally, you will apply the Pythagorean Theorem and its converse to solve real-world and mathematical problems involving unknown side lengths of right triangles. The Number System 8.NS.1 8.NS.2 8.EE.2 Geometry 8.G.6 8.G.7 8.G Irrational Numbers and Square Roots 8.NS.1, 8.NS.2, 8.EE Cube Roots 8.EE Checkpoint Quiz a Activity Lab Hands On: Exploring the Pythagorean Theorem 8.G The Pythagorean Theorem 8.G b Activity Lab Algebra Thinking: Proving the Pythagorean Theorem 8.G Guided Problem Solving: Squares and Square Roots, Using the Pythagorean Theorem 8.G Converse of the Pythagorean Theorem 8.G b Activity Lab Algebra Thinking: Proving the Converse of the Pythagorean Theorem 8.G Checkpoint Quiz Distance in the Coordinate Plane 8.G.7, 8.G Test-Taking Strategies: Writing Gridded Responses, 41 Chapter Review, 42 Chapter Test, 44 Test Prep: Reading Comprehension, 45 x _C3_TOC_px-ix.indd 10 9/5/12 1:59 PM
2 2 Solving Linear Equations Check Your Readiness a Activity Lab Hands On: Modeling Multi-Step Equations 8.EE.7, 8.EE.7.b In this chapter, you will solve linear equations with rational number coefficients. You will also simplify equations to identify the different types of solutions of linear equations, such as having no solutions, one solution, or infinitely many solutions. 8.EE.7 8.EE.7.a 8.EE.7.b 2-1 Solving Two-Step Equations 8.EE.7, 8.EE.7.b a Activity Lab Hands On: Modeling Expressions 8.EE Simplifying Algebraic Expressions 8.EE.7.b Checkpoint Quiz Solving Multi-Step Equations 8.EE.7, 8.EE.7.b Vocabulary Builder: High-Use Academic Words, Solving Equations With Variables on Both Sides 8.EE.7, 8.EE.7.b Guided Problem Solving: Writing Equations, 68 Checkpoint Quiz Types of Solutions of Linear Equations 8.EE.7, 8.EE.7.a, 8.EE.7.b Test-Taking Strategies: Reading for Understanding, 75 Chapter Review, 76 Chapter Test, 78 Test Prep: Cumulative Review, 79 xi _C3_TOC_px-ix.indd 11 9/5/12 1:59 PM
3 3 Introduction to Functions Check Your Readiness Relating Graphs to Events 8.F b Activity Lab Data Collection: Changing Graphs 8.F In this chapter, you will define and evaluate functions, and use functions to model relationships between quantities. You will also analyze linear graphs to express qualitative relationships between two quantities. In addition, you will understand and interpret linear functions, and give examples of nonlinear functions. 8.EE.5 Functions 8.F.1 8.F.3 8.F Functions 8.F Checkpoint Quiz Proportional Relationships 8.EE b Activity Lab Proportional Relationships in Graphs Guided Problem Solving: Using Data and Graphs, Linear Functions 8.F Vocabulary Builder: Making Word Cards, Nonlinear Functions 8.F b Activity Lab Data Analysis: Using Linear and Nonlinear Graphs Test-Taking Strategies: Using a Variable, 109 Chapter Review, 110 Chapter Test, 112 Test Prep: Reading Comprehension, 113 xii _C3_TOC_px-ix.indd 12 9/5/12 1:59 PM
4 4 Graphing Functions Check Your Readiness a Activity Lab Rate of Change 8.EE.5, 8.F Understanding Slope 8.EE.6, 8.F In this chapter, you will graph proportional relationships and interpret the unit rate as the slope of the graph. You will also write and graph functions to model linear relationships and compare two functions represented in different ways. 8.EE.5 8.EE.6 Functions 8.F.1 8.F.2 8.F.3 8.F.4 4-1b Activity Lab Slope of Parallel and Perpendicular Lines a Activity Lab Technology: Graphing Equations 8.F Graphing Linear Functions 8.EE.6, 8.F.1, 8.F.3, 8.F Writing Rules for Linear Functions 8.F b Activity Lab Data Analysis: Changing Representations 8.F Checkpoint Quiz Comparing Functions 8.F.2, 8.EE Guided Problem Solving: Writing Rules for Linear Functions, 139 Test-Taking Strategies: Working Backwards, 141 Chapter Review, 142 Chapter Test, 144 Test Prep: Cumulative Review, 145 xiii _C3_TOC_px-ix.indd 13 9/5/12 1:59 PM
5 5 Systems of Linear Equations Check Your Readiness Solving Systems by Graphing 8.EE.8.a, 8.EE.8.b, 8.EE.8.c In this chapter, you will analyze and solve systems of linear equations algebraically, and estimate solutions by graphing the equations. You will also model and solve real-world problems using two linear equations. 8.EE.8.a 8.EE.8.b 8.EE.8.c 5-1b Activity Lab Systems with Infinitely Many Solutions or No Solution 8.EE.8.b Solving Systems by Substitution 8.EE.8.b, 8.EE.8.c Solving Systems by Elimination 8.EE.8.b, 8.EE.8.c b Activity Lab Solving Systems by Inspection 8.EE.8.b Guided Problem Solving: Solving Systems of Equations, 163 Checkpoint Quiz Vocabulary Builder: Learning Vocabulary, Systems in the Real World 8.EE.8.b, 8.EE.8.c Test-Taking Strategies: Writing Short Responses, 171 Chapter Review, 172 Chapter Test, 174 Test Prep: Reading Comprehension, 175 xiv _C3_TOC_px-ix.indd 14 9/5/12 1:59 PM
6 6 Exponents Check Your Readiness Scientific Notation 8.EE b Activity Lab Data Analysis: Writing Measurements 8.EE In this chapter, you will develop and apply properties of integer exponents, and use numbers expressed as a single digit times an integer power of 10 to estimate very large or very small quantities. You will also perform operations with numbers expressed in scientific notation. 8.EE.1 8.EE.3 8.EE.4 6-2a Activity Lab Exploring Exponents 8.EE Exponents and Multiplication 8.EE Multiplying with Scientific Notation 8.EE b Activity Lab Technology: Calculations with Scientific Notation 8.EE Checkpoint Quiz Exponents and Division 8.EE b Activity Lab Power Rules 8.EE Guided Problem Solving: Solving Equations, Dividing with Scientific Notation 8.EE.3, 8.EE Test-Taking Strategies: Working Backward, 207 Chapter Review, 208 Chapter Test, 210 Test Prep: Cumulative Review, 211 xv _C3_TOC_px-xix.indd 15 9/19/12 11:51 AM
7 7 An Introduction to Geometry Check Your Readiness Pairs of Angles Angles and Parallel Lines 8.G In this chapter, you will develop an understanding of the congruence and similarity of two-dimensional figures. You will also use informal arguments to establish facts about the sum of the angles of a triangle, the exterior angle of triangles, and the angles created when parallel lines are cut by a transversal. 8.EE.6 Geometry 8.G.2 8.G.4 8.G Congruent Figures 8.G Checkpoint Quiz Similar Figures 8.G Proving Triangles Similar 8.G b Activity Lab Slope and Similar Triangles 8.EE Checkpoint Quiz a Activity Lab Angle Sums 8.G Angles and Polygons 8.G Vocabulary Builder: Using Concept Maps, 244 Guided Problem Solving: Finding Angles, 245 Test-Taking Strategies: Drawing a Picture, 247 Chapter Review, 248 Chapter Test, 250 Test Prep: Cumulative Review, 251 xvi _C3_TOC_px-ix.indd 16 9/5/12 2:00 PM
8 8 Transformations Check Your Readiness Translations 8.G.1.a, 8.G.1.b, 8.G.1.c, 8.G In this chapter, you will explore the behavior of two-dimensional shapes under translations, rotations, reflections, and dilations. You will then apply the understandings to concepts of congruence and similarity and their relationship to transformations. Geometry 8.G.1.a 8.G.1.b 8.G.1.c 8.G.3 8.G.4 8-2a Activity Lab Hands On: Exploring Reflections 8.G.1.a, 8.G.1.b, 8.G.1.c Reflections and Symmetry 8.G.1.a, 8.G.1.b, 8.G.1.c, 8.G Checkpoint Quiz a Activity Lab Hands On: Exploring Rotations 8.G.1.a, 8.G.1.b, 8.G.1.c Rotations 8.G.1.a, 8.G.1.b, 8.G.1.c, 8.G Transformations and Congruence 8.G Vocabulary Builder: High-Use Academic Words, 274 Checkpoint Quiz a Activity Lab Exploring Dilations 8.G.3, 8.G Dilations 8.G.3, 8.G b Activity Lab Hands On: Technology: Geometry Software and Dilations 8.G.3, 8.G Transformations and Similarity 8.G Guided Problem Solving: Transformations, 287 Test-Taking Strategies: Answering the Question Asked, 289 Chapter Review, 290 Chapter Test, 292 Test Prep: Reading Comprehension, 293 xvii _C3_TOC_px-xix.indd 17 9/19/12 11:51 AM
9 Geometry and Measurement CHA P T E R 9 Check Your Readiness Solids a Activity Lab Hands On: Modeling Volume 8.G In this chapter, you will solve real-world and mathematical problems involving the volume of cylinders, cones, and spheres. You will also apply your understanding of the Pythagorean Theorem to find unknown side lengths of right triangles when determining the volume of three-dimensional figures. 9-2 Checkpoint Quiz a Activity Lab Finding Volume Using Models 8.G Volumes of Pyramids and Cones 8.G Spheres 8.G Checkpoint Quiz a Activity Lab Changing Dimensions 8.G Geometry 8.G.7 8.G.9 Volumes of Prisms and Cylinders 8.G.7, 8.G Guided Problem Solving: Using Formulas, Exploring Similar Solids 8.G xviii _C3_TOC_px-xix.indd 18 Test-Taking Strategies: Eliminating Answers, 323 Chapter Review, 324 Chapter Test, 326 Test Prep: Reading Comprehension, 327 9/19/12 11:51 AM
10 CHAPTER 10 Data Analysis Check Your Readiness a Activity Lab Data Collection: Scatter Plots 8.SP Scatter Plots 8.SP.1, 8.SP In this chapter, you will construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantitative variables. You will also construct and interpret a two-way table summarizing data on two categorical variables collected on the same subjects. Statistics and Probability 8.SP.1 8.SP.2 8.SP.3 8.SP Analyzing Scatter Plots 8.SP Checkpoint Quiz Modeling Data With Lines 8.SP.2, 8.SP Guided Problem Solving: Equations and Graphs, Two-Way Tables 8.SP Test-Taking Strategies: Measuring to Solve, 351 Chapter Review, 352 Chapter Test, 354 Test Prep: Cumulative Review, _C3_TOC_px-ix.indd 19 xix 9/5/12 2:00 PM
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