Math Series Course 3 (Grade 8)

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1 Common Core State Standards Math Series Course 3 (Grade 8) The Carnegie Learning Math Series Course 3 is all new and written specifically for the CCSS for Grade 8. This course contains complete alignment, coverage, and support for the Standards for Mathematical Content and Practice. Course 3 focuses on algebraic thinking, geometry, and statistical thinking and probability, and revisits algebraic thinking and geometry. Textbook Chapters MATHia Software Sections 1. Linear Equations 2. Linear Functions Pan Balances and Linear Functions Using Pan Balances with Shapes Representing Variables and Constants Translating Between Pan Balances and Equations Using Pan Balances to Solve Equations Solving Equations Displayed as Pan Balances Linear Equations and the Distributive Property Solving Linear Equations Using Multiplication and Integers (no type in and type in) Using Multiplication and Decimals (no type in and type in) Using Division (no type in and type in) Using Division with Addition Variable Term (no type in and type in) Modeling with Integer Rates of Change Modeling with Fractional Rates of Change Modeling using the Distributive Property over Division Relations and Functions Recognizing Non-Numeric Functions Recognizing Numeric Functions Recognizing Graphs of Functions Classifying Relations and Functions Graphs of Functions Identifying Key Characteristics of Graphs of Functions 3. Analyzing Linear Equations 4. Multiple Representations of Linear Functions Linear Models and Slope-Intercept Graphs Graphing Given an Integer, Slope, and Y-Intercept Graphing Given a Decimal, Slope, and Y-Intercept Linear Models in General Form Modeling with Linear Inequalities Modeling Linear Equations in General Form Graphs of Linear Equations in Two Variables Graphing Linear Equations using Given Method Graphing Linear Equations using Chosen Method Finding Equations of a Line Modeling Given Slope and a Point Finding Slopes Modeling Given Two Points Modeling Given an Initial Point Linear Models and Multiple Representations Modeling Linear Functions 5. The Real Number System 6. Pythagorean Theorem Approximations of Square and Cube Roots Approximating Square Roots Approximating Cube Roots Simplification and Operations with Radicals Simplifying Radicals Adding and Subtracting Radicals Multiplying Radicals Rational and Irrational Numbers Creating Number Line Models Ordering Rational and Irrational Numbers Pythagorean Theorem Using the Pythagorean Theorem Calculating the Lengths of Sides of Special Right Triangles Distance in the Coordinate Plane Finding Distance Using Pythagorean Theorem Finding Distance Using the Distance Formula 20

2 Textbook Chapters 7. Translations, Reflections, and Rotations 8. Congruence of Triangles 9. Similarity Translations of Plane Figures Identifying Translations Rotations of Plane Figures Rotating Plane Figures Reflections of Plane Figures Reflecting Plane Figures Dilations of Plane Figures MATHia Software Sections Dilating Plane Figures Geometric Transformations Performing One Transformation Performing Multiple Transformations Similar Triangles Finding Corresponding Parts of Similiar Triangles 10. Line and Angle Relationships 11. Systems of Equations 12. More with Systems of Equations Lines Cut by a Transversal Classifying Angles Formed by Transversals Calculating Angles Formed by Transversals Calculating Angles Formed by Multiple Transversals Parallel and Perpendicular Lines Modeling Parallel and Perpendicular Lines Angles and Triangles Calculating and Justifying Angle Measures Calculating Angle Meaures Linear Equations with Variables on Both Sides Checking Solutions to Linear Equations Solving Linear Equations (type in) Solving with Integers (no type in and type in) Solving Linear Equations with No Solutions and Infinite Solutions (no type in) Solving with Decimals (no type in and type in) Systems of Linear Equations Modeling Modeling Systems of Linear Equations Linear System Solving using Substitution Solving Linear Systems using Substitution Linear System Solving using Elimination Solving Linear Systems using Elimination 13. Properties of Exponents 14. Volume Properties of Exponents Using the Product Rule Using the Quotient Rule Using the Power to a Power Rule Using the Product to a Power Rule Using the Quotient to a Power Rule Using Properties of Exponents with Whole Number Powers Zero and Negative Exponents Simplifying Expressions with Negative Exponents Using Properties of Exponents with Integer Powers Scientific Notation Using Scientific Notation with Whole Number and Positive Exponents Using Scientific Notation with Decimals and Positive Exponents Using Scientific Notation with Whole Number and Negative Exponents Using Scientific Notation with Decimals and Negative Exponents Using Scientific Notation Comparing Numbers using Scientific Notation Volume & Surface Area of Cylinders, Cones, & Spheres Finding Volume of Cylinders Finding Surface Area of Cylinders Finding Volume of Cones Finding Surface Area of Cones Finding Volume of Spheres Finding Surface Area of Spheres 15. Data Displays and Analysis 16. Lines of Best Fit 17. Non-Linear Data Representations Scatter Plots Reading Scatter Plots Lines of Best Fit Estimating Line of Best Fit Using Lines of Best Fit Frequency and Relative Frequency Reading Visual Displays of Frequency Tables 21

3 Carnegie Learning Math Series: Course 3 is composed of 17 chapters. In the pages that follow, you will see a scope & sequence that includes information on each chapter as well as each lesson contained within those chapters. Course 3 Chapter Sequence 1. Linear Equations 2. Linear Functions 3. Analyzing Linear Equations 4. Multiple Representations of Linear Functions 5. The Real Number System 6. Pythagorean Theorem 7. Translations, Reflections, and Rotations 8. Congruence of Triangles 9. Similarity 10. Line and Angle Relationships 11. Systems of Equations 12. More with Systems of Equations 13. Properties of Exponents 14. Volume 15. Data Displays and Analysis 16. Lines of Best Fit 17. Non-Linear Data Representations 22

4 The Middle School Math Series: Course 3 scope & sequence gives you information about each lesson. Lesson title Key math objective The Common Core State Standard that is addressed in that lesson Key terms that are introduced within the lesson Problem types that will be found within the lesson (see page 30 for more information on problem types) Chapter Lesson Title Key Math Objectives CCSS 1 Linear Equations This chapter focuses on strategies to solve linear equations in one variable with one solution, infinitely many solutions, and no solutions. Equations include rational number coefficients and require the use of the Distributive Properties. 1.1 A Park Ranger's Work Is Never Done Solving Problems Using Equations inverse operations, two- step equation, solution, coefficient, constant, Properties of Equality 1.2 Why Doesn't This Work? Equations with Infinite or No Solutions 1.3 Who has the Most? Solving Linear Equations 1.4 Games and Practice Solving More Linear Equations 2 Linear Functions This chapter develops the understanding that a function is a rule that assigns to each input exactly one output. Real- world problems, tables, graphs, and equations are used to model linear function relationships. Non- linear functions are introduced to contrast with linear functions. 2.1 Patterns, Patterns, Patterns Developing Sequences of Numbers from Diagrams and Contexts sequence, term, ellipsis 2.2 Every Graph Tells a Story Describing Characteristics of Graphs discrete graph, continuous graph, linear graph, collinear points, non- linear graph 2.3 To Be or Not to Be a Function? Defining and Recognizing Functions 2.4 Scaling a Cliff Linear Functions 2.5 U.S. Shirts Using Tables, Graphs, and Equations, Part 1 mapping, set, relation, input, output, function, domain, range, scatter plot, vertical line test linear function 2.6 Hot Shirts Using Tables, Graph, and Equations, Part 2 estimation, point of intersection 2.7 What, Not Lines? Introduction to Non- Linear Functions absolute value function, square or quadratic function, cube or cubic function 3 Analyzing Linear Equations This chapter focuses on the rate of change of linear functions that are represented in graphical displays, tables, and in real- world problem situations. Slope is defined and the slope- intercept form of a linear equation is introduced. 3.1 Hitting the Slopes Determining Rate of Change from a Graph 8.EE.5 rate, rate of change, per, unit rate, rise, run, rise/run 3.2 At the Arcade Determining Rate of Change from a Table first differences 3.3 To Put It in Context Determining Rate of Change from a Context 3.4 All Together Now! 3.5 Where It Crosses Determining Rate of Change from an Equation Determining y- intercepts from Various Representations 8.EE.5 slope, slope- intercept form y- intercept, direct variation 3.6 Slope- Intercept Form Determining the Rate of Change and y- intercept point- slope form, standard form 23

5 Chapter Lesson Title Key Math Objectives CCSS 4 Multiple Representations of Linear Functions This chapter focuses on using the multiple representations of functions to solve real- world problems. 4.1 Willie Catchem Analyzing Problem Situations Using Multiple Representations 8.EE Pony Express Interpreting the Standard Form of a Linear Equation 4.3 Slopes, Forms, Graphs, and Intercepts Connecting the Standard Form with the Slope- Intercept Form of Linear Functions 4.4 The Journey Starts with a Single Step But There Are Many Steps after That! Intervals of Increase, Decrease, and No Change increasing function, constant function, decreasing function, interval of increase, interval of decrease, constant interval 4.5 Piecewise Functions Developing the Graph of a Piecewise Function piecewise function 5 The Real Number System This chapter extends the understanding of properties of numbers and number systems to include irrational and real numbers. 5.1 Is It a Bird or a Plane? Rational Numbers 7.NS.3 natural numbers (counting numbers), whole numbers, integers, closed, rational numbers 5.2 Sew What? Irrational Numbers 8.NS.1 8.NS.2 irrational numbers, terminating decimal, repeating decimal, bar notation 5.3 Worth 1000 Words Real Numbers and Their Properties 8.NS.1 real number, Venn diagram, closure 6 Pythagorean Theorem This chapter develops the Pythagorean Theorem and the Converse of the Pythagorean Theorem. These theorems are then applied to solve real- world problems in two and three dimensions. 6.1 Soon You Will Determine the Right Triangle Connection The Pythagorean Theorem 8.NS.2 8.G.6 right triangle, right angle, leg, hypotenuse, diagonal of a square, Pythagorean Theorem, theorem, postulate, proof 6.2 Can That Be Right? The Converse of the Pythagorean Theorem 8.G.6 converse, Converse of the Pythagorean Theorem, Pythagorean triple 6.3 Pythagoras to the Rescue Solving for Unknown Lengths 6.4 Meeting Friends The Distance between Two Points in a Coordinate System 6.5 Diagonally Diagonals in Two Dimensions 6.6 Two Dimensions Meet Three Dimensions Diagonals in Three Dimensions 7 Translations, Reflections, and Rotations The chapter focuses on translations, rotations, and reflections of geometric figures on a coordinate plane. 7.1 Sliding Right, Left, Up, Down, and Diagonally Translations Using Geometric Figures transformation, translation, image, pre- image 7.2 Sliding Lines Translations of Linear Functions 7.3 Round and Round We Go! Rotations of Geometric Figures on the Coordinate Plane rotation, angle of rotation, point of rotation 7.4 Mirror, Mirror Reflections of Geometric Figures on the Coordinate Plane reflection, reflection line 8 Congruence of Triangles This chapter focuses on the effect of translations, rotations, and reflections of triangles using coordinates. 8.1 Slide, Flip, Turn! Translations, Rotations, and Reflections of Triangles 8.2 All the Same to You Congruent Triangles congruent line segments, congruent angles, corresponding sides, corresponding angles 24

6 Chapter Lesson Title Key Math Objectives CCSS 8.3 Two Ways to Tell SSS and SAS Congruence SSS Congruence Theorem, included angle, SAS Congruence Theorem 8.4 And Here's Two More! ASA and AAS Congruence included side, ASA Congruence Theorem, AAS Congruence Theorem 9 Similarity This chapter explores dilations of triangles to develop the concept of similarity. The Angle- Angle Similarity Theorem, Side- Angle- Side Similarity Theorem, and the Side- Side- Side Similarity Theorem are developed as efficient methods to demonstrate that two triangles are similar. 9.1 Expanding Your Mind Dilations of Triangles dilation, center of dilation, scale factor, enlargement, reduction 9.2 Look- Alikes Similar Triangles 9.3 Prove It! AA, SAS, and SSS Simliarity Theorems 9.4 Back on the Grid Similar Triangles on the Coordinate Plane 10 Line and Angle Relationships similar triangles AA Similarity Theorem, SAS Similarity Theorem, SSS Similarity Theorem This chapter focuses on line and angle characteristics and relationships. It begins with the relationships that can exist between two lines, then moves to the relationships between angles when intersected by a line, and finally concludes with transformations related to parallel and perpendicular lines Location, Location, Location! Line Relationships intersecting lines, planes, perpendicular lines, parallel lines, coplanar lines, skew lines, coincidental lines 10.2 When Lines Come Together Angle Relationships Formed by Two Intersecting Lines 7.G.5 supplementary angles, linear pair of angles 10.3 Crisscross Applesauce Angle Relationships Formed by Two Lines Intersected by a Transversal transversal, alternate interior angles, alternate exterior angles, same- side interior angles, same- side exterior angles 10.4 Parallel or Perpendicular? Slopes of Parallel and Perpendicular Lines 10.5 Up, Down, and All Around Line Transformations 8.G.1.c 8.EE.6 8.G.1.c reciprocal, negative reciprocal Triangle Sum Theorem 11 Systems of Equations This chapter introduces linear systems of equations. The focus is to understand that a solution to a system of two linear equations in two variables corresponds to the point of intersection of their graphs, and that there is no solution if the equations are parallel and the lines will never intersect. The substitution method is introduced as an algebraic strategy to determine a solution to a linear system of equations Producing and Selling T- Shirts Using a Graph to Solve a Linear System profit, income, point of intersection, break- even point 11.2 Saving Money Graphs and Solutions of Linear Systems 11.3 The County Fair Using Substitution to Solve a Linear System, Part 1 system of linear equations, solution of a linear system, consistent system, inconsistent system, independent system, dependent system substitution method 11.4 Tickets, Please Using Substitution to Solve a Linear System, Part 2 12 More with Systems of Equations This chapter continues to develop strategies to solve linear systems of equations. The linear combination method and graphing calculators are introduced as strategies to determine solutions to systems Systems of Equations Using Linear Combinations to Solve a Linear System linear combinations method (elimination) 12.2 What's for Lunch? Solving More Systems 12.3 Making Decisions Using the Best Method to Solve a Linear System 12.4 Going Green Using a Graphing Calculate to Solve Linear Systems 12.5 Beyond the Point of Intersection Using the Graphing Calculator to Analyze the System 25

7 Chapter Lesson Title Key Math Objectives CCSS 13 Properties of Exponents This chapter develops the properties of exponents and includes scientific notation Exponentially Speaking Powers and Exponents 8.EE.1 power, base, exponent 13.2 Digital Storage Multiplying and Dividing Powers 8.EE Extending the Rules Zero and Negative Exponents 8.EE Let's Get Scientific! Scientific Notation 13.5 Are We There Yet? What Is the Distance? Operations with Scientific Notation 13.6 Watch Your Step! Identifying the Properties of Powers 8.EE.1 8.EE.3 8.EE.4 8.EE.1 8.EE.3 8.EE.4 8.EE.1 8.EE.3 8.EE.4 scientific notation, order of magnitude, mantissa, characteristic 14 Volume This chapter develops formulas for the volumes of cones, right circular cylinders, and spheres. Volume formulas are used to solve real- world problems Drum Roll, Please! Volume of a Cylinder 8.G.9 cylinder, right circular cylinder, radius of a cylinder, height of a cylinder, circumference, pi 14.2 Piling On! Volume of Cone 8.G.9 cone, height of a cone 14.3 All Bubbly Volume of a Sphere 8.G.9 sphere, center of a sphere, radius of a sphere, diameter of a sphere, antipodes, great circle, hemisphere 14.4 Practice Makes Perfect Volume Problems 8.G.9 15 Data Displays and Analysis This chapter develops an understanding for constructing and interpreting scatter plots and investigating patterns of association between two quantities School Spirit and Scatter Plots Using Scatter Plots to Display and Analyze Two- Variable Relationships two- variable data set 15.2 Jump In! The Water's Fine! Interpreting Patterns in Scatter Plots independent variable (explanatory variable), dependent variable (response variable), association, linear association, cluster, positive association, negative association, outlier 15.3 How Fast Are Your Nerve Impulses? Connecting Tables and Scatter Plots of Collected Data 16 Lines of Best Fit This chapter explores real- world bivariate data and the concept of line of best fit. Class experiments will be conducted with the data recorded and plotted in a scatter plot. The line of best fit is then calculated and used to make predictions Where Do You Buy Your Books? Drawing Lines of Best Fit line of best fit, model, trend line, interpolating, extrapolating 16.2 Mia Is Growing Like a Weed Analyzing the Line of Best Fit 16.3 Stroop Test Performing an Experiment 16.4 Human Chain: Shoulder Experiment Using Technology to Determine a Linear Regression Equation linear regression, linear regression equation 16.5 Jumping Correlation 17 Non- Linear Data Representations This chapter focuses on the representations of data in scatter plots and bar graphs. Categorical data is first organized in a two- way table, and then displayed in either a frequency bar graph or a relative frequency bar graph Making a Quilt Scatter Plots and Non- Linear Data 8.SP.4 non- linear association (non- linear relationship) 17.2 What Do You Like to Play? Using Two- Way Tables to Display Two- Variable Data Sets 8.SP.4 categorical data, two- way table, frequency, relative frequencies 17.3 Got the Data, Show the Data Using Bar Graphs to Display Frequencies and Relative Frequencies for Two- Variable Categorical Data 8.SP.4 26

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