Math Series Course 2 (Grade 7)

Transcription

1 Common Core State Standards Math Series Course 2 (Grade 7) The Carnegie Learning Math Series Course 2 is all new and written specifically for the CCSS for Grade 7. This course contains complete alignment, coverage, and support for the Standards for Mathematical Content and Practice. Course 2 focuses on proportional reasoning, developing number sense, algebraic thinking, geometry, and statistical thinking and probability. Textbook Chapters MATHia Software Sections 1. Ratios and Rates 2. Direct Variation and Constant of Proportionality Problem Solving with Ratios and Rates Solving Problems using Tables Solving Problems using Double Number Lines Solving Problems using Graphs and Proportions Solving Proportions using Equivalent Fractions Solving Proportions using Means and Extremes Proportions and Direct Variation Writing Proportions in Two Variables Writing Direct Variations Equations Converting Between Proportions and Direct Variation Equations Linear and Ratios (with Grapher) Modeling Linear Functions with Ratios Graphs of Direct Variation Determining Characteristics of Direct Variation Graphs 3. Rates and Percents Fraction, Decimal, and Percent Conversions Converting Common Percents Converting with Percents Less Than 100 Converting with Percents Greater Than 100 Converting with Percents Less Than 1 Converting with Fractional Percents 4. Addition and Subtraction with Rational 5. Multiplication and Division with Rational Percents and Proportions Using Common Percents Finding the Percent of a Number Finding Percents Given Two Finding Totals Equal to 100% using Percents Percent Change Finding Percent Change Finding Final Amounts Given Percent Change Finding Percent Change and Final Amounts Integer Addition and Subtraction Using Number Lines to Add/Subtract Positive Integers Using Number Lines to Add/Subtract Negative Integers Using Number Lines to Add/Subtract Integers Using the Solver to Add/Subtract Integers Rational Number Addition and Subtraction Simplifying Numeric Expressions (no type in) Simplifying Numeric Expressions (type in) Integer Multiplication and Division Multiplying Integers Dividing Integers Multiplying and Dividing Integers Order of Operations with Rational Simplifying Numeric Expressions (no type in) Simplifying Numeric Expressions (type in) 12

2 Textbook Chapters MATHia Software Sections 6. Numerical and Algebraic Expressions and Equations 7. Solving Equations and Inequalities 8. Solving Problems with Equations and Inequalities Factoring Linear Expressions Modeling Distributive Property (algebra tiles) Modeling Factoring (algebra tiles) Order of Operations with Variable Expressions Combining Like Terms Using Using Properties to Simplify Variable Expressions Simplifying Variable Expressions (no type in) Simplifying Variable Expressions (type in) Patterns and Two-Step Equations Modeling Two-Step Equations Solving with Multiplication (no type in) Solving with Multiplication (type in) Solving with Division (no type in and type in) Solving Two-Step Equations Linear Inequalities Graphing Inequalities Solving Linear Inequalities Problem Solving with Linear Equations/Inequalities Solving Linear Problems Problem Solving with Two-Step Equations Solving Problems with Two-Step Equations Solving Problems with More Difficult Two-Step Equations Solving Problems with Decimal and Fraction Equations Linear and Four Quadrant Graphs Graphing with Positive Integer Rates of Change Graphing with Positive Fractional Rates of Change Graphing with Negative Rates of Change Linear Equations with Similar Terms Solving Two-Step Equations (type in) Solving by Combining Like Variable Terms and a Constant with Integers (type in and no type in) Solving by Combining Like Variable Terms with Decimals (type in and no type in) Solving by Combining Like Variable Terms and a Constant with Decimals (type in and no type in) 9. Using Geometry 10. Triangles Angles and Angle Pairs Measuring Angles Classifying Angles Classifying Angle Pairs Angle Properties Calculating and Justifying Angle Measures Calculating Angle Measures Triangle Properties Measuring Angles in a Triangle Calculating and Justifying Angle Measures Calculating Angle Measures 11. Scale Drawing and Scale Factors 12. Circles 13. Slicing Three-Dimensional Figures 14. Data Collection 15. Comparing Populations Scale Drawings Calculating Measures of Scale Figures Perimeter and Area Circumference and Area of Circles Samples Collecting Samples Determining How Sample Size Affects Representation of Data Sets Samples and Predictions Using Samples to Make Predictions about Samples Categorical Data Display Comparisons Volume and Surface Area of Right Prisms Finding Volume of Right Prisms Finding Surface Area of Right Prisms Finding Volume of Comparing Bar Graphs Comparing Pie Charts Comparing Stem-and-Leaf Plots Comparing Dot Plots Comparing Histograms Comparing Box-and-Whisker Plots 16. Introduction to Probability Single Event Probability Finding Simple Probabilities Finding Disjoint Probabilities 17. Probability of Compound Events Samples and Probability Using Samples to Calculate Probabilities Sample Spaces Finding the Sample Space for Independent Events using Tree Diagrams Finding the Sample Space for Dependent Events using Tree Diagrams 13

3 Carnegie Learning Math Series Course 2 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 2 Chapter Sequence 1. Ratios and Rates 2. Direct Variation and Constant of Proportionality 3. Rates and Percents 4. Addition and Subtraction with Rational 5. Multiplication and Division with Rational 6. Numerical and Algebraic Expressions and Equations 7. Solving Equations and Inequalities 8. Solving Problems with Equations and Inequalities 9. Using Geometry 10. Triangles 11. Scale Drawing and Scale Factors 12. Circles 13. Slicing Three-Dimensional Figures 14. Data Collection 15. Comparing Populations 16. Introduction to Probability 17. Probability of Compound Events 14

4 The Middle School Math Series: Course 2 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) Worked Examples Peer Analysis Talk the Talk 1 Ratios and Rates This chapter begins with a review of ratio and unit rate concepts, and scaling up and scaling down strategies to determine equivalent ratios. The means and extremes strategy for solving proportions is introduced and connected to the students previous understanding of equivalent ratios. 1.1 Show Someone You Care- Send Flowers! Introduction to Ratios and Rates 6.RP.1 ratio, rate, proportion, equivalent ratios, unit rate, scaling up, scaling down 1.2 Making Punch Ratios, Rates, and Mixture Problems 1.3 For the Birds Rates and Proportions convert 1.4 Tutor Time! Using Tables to Solve Problems 1.5 Looks Can Be Deceiving Using Proportions to Solve Problems 1.6 The Price Is Close 2 Using Unit Rates in Real World Applications Direct Variation and Constant of Proportionality variable, means and extremes, solve a proportion, inverse operations This chapter develops the representations of proportional relationships between quantities using words, tables, equations, and graphs. The constant of proportionality is introduced and used to solve various real-world problems What Makes You Tap Your Feet? Building Bird Feeders IS For the Birds! Kids Just Wanna Have Fun! Introduction to Direct Variation 7.RP.2.d direct variation (direct roportional), origin Determining Equivalent Ratios Determining and Applying the Constant of Proportionality constant of proportionality 2.4 Stop That Speeding Snail? Using the Constant of Proportionality to Solve Proportions 2.5 The Man Who Ran from Marathon to Athens Graphing Direct Proportions 7.RP.2.d Racing to the Finish Line! Connecting Representations of Proportional Relationships Using Direct Variation Interpreting Multiple Representations of Direct Proportions 7.RP.2.d 3 Rates and Percents This chapter extends the use of proportional reasoning to solve percent problems. 3.1 Give Me a Ballpark Figure of the Cost Estimating and Calculating with Percents and Rates 3.2 One Size Fits All? Solving Percent Problems 3.3 Mathematics and Nutrition Using Proportions and Percent Equations 3.4 Be Mindful of the Fees! Using Percents 3.5 Shoe Super Store Solving Percent Problems Involving Proportions percent equation interest, depreciate, principal, simple interest, percent increase, percent decrease commission 15

5 Worked Examples Peer Analysis Talk the Talk 4 Addition and Subtraction with Rational This chapter uses models to develop a conceptual understanding of addition and subtraction with respect to the set of integers. These strategies are formalized through questioning, and then extended to operations with respect to the set of rational numbers. 4.1 Math Football Using to Understand Integers 7.NS.1.a 4.2 Walk the Line Adding Integers, Part I 4.3 Two- Color Counters Adding Integers, Part II 7.NS.1.a 7.NS.1.c additive inverses 4.4 What's the Difference? Subtracting Integers 7.NS.1.a 7.NS.1.c zero pair 4.5 What Do We Do Now? Adding and Subtracting Rational 7.NS.1.c 5 Multiplication and Division with Rational This chapter use models to develop a conceptual understanding of multiplication and division with respect to the set of integers. These strategies are formalized, and then extended to operations with respect to the set of rational numbers. 5.1 Equal Groups Multiplying and Dividing Integers 7.NS.2.b 5.2 What's My Product or Quotient? Multiplying and Dividing Rational 7.NS.2.b 5.3 Properties Schmoperties Simplifying Arithmetic Expressions with Rational 5.4 Building a Wright Brothers' Flyer Evaluating Expressions with Rational 7.NS.2.b 7.NS Repeat or Not? That is the Question! Exact Decimal Representations of Fractions 7.NS.2.d terminating decimals, non-terminating decimals, repeating decimals, non-repeating decimals, bar notation 6 Numerical and Algebraic Expressions and Equations This chapter focuses on the use of properties to interpret, simplify, add, subtract, and factor linear expressions. 6.1 What's It Really Saying? Evaluating Algebraic Expression 6.EE.6 7.NS.3 variable, algebraic expression, evaluate an algebraic expression 6.2 Express Math Simplifying Expressions Using Distributive Properties 7.NS.3 Distributive Property of Multiplication over Addition, Distributive Property of Multiplication over Subtraction, Distributive Property of Division over Addition, Distributive Property of Division over Subtraction 6.3 Reverse Distribution Factoring Algebraic Expressions factor, common factor, greatest common factor (GCF), coefficient, like terms, combining like terms 6.4 Are They the Same or Different? Verifying that Expressions Are Equivalent 6.5 It is Time to Justify! Simplifying Algebraic Expressions Using Operations and Their Properties 7 Solving Equations and Inequalities This chapter uses models, properties of rational numbers, and operations to develop strategies for solving equations and inequalities. Algebraic reasoning is used to solve real-world problems. 7.1 Picture This Picture Algebra 7.2 Maintaining a Balance Solving Equations 7.3 Plamning a Graduation Party Solving Two-Step Equations 7.4 Solving in Big-Time Style Using Two-Step Equations equation Properties of Equality two-step equation 7.5 We're Shipping Out! Solving and Graphing Inequalities in One Variable 7.EE.4.b solve an inequality 16

6 Worked Peer Talk the Examples Analysis Talk Worked Peer Talk the Examples Analysis Talk This chapter focuses on the use of algebraic reasoning to solve real-world problems posed with positive and negative rational numbers. Tables, graphs, and 8 Solving Problems with Equations and Inequalities equations are used throughout. This chapter focuses on the use of algebraic reasoning to solve real-world problems posed with positive and negative rational numbers. Tables, graphs, and 8 Solving Problems with Equations and Inequalities equations are used throughout. Some Places are Mulitple Representations of Problem 8.1 Expensive; Some Places Some Places are Situations are More Affordable Mulitple Representations of Problem 8.1 Expensive; Some Places Situations are More Affordable 8.2 Plastic Containers Using Two- Step Equations 8.2 Plastic Containers Using Two- Step Equations 8.3 Just Another Saturday Solving More Complicated Equations multiplicative inverse, multiplying by the reciprocal 8.3 Just Another Saturday Solving More Complicated Equations multiplicative inverse, multiplying by the reciprocal 8.4 Climbing El Capitan Making Sense of Negative Solutions 8.4 Climbing El Capitan Making Sense of Negative Solutions 8.5 Flying in the Ocean Rate of Change unit rate of change 7.EE.4.b 8.5 Flying in the Ocean Rate of Change unit rate of change 7.EE.4.b Using Multiple Representations to 8.6 Emptying a Tank Solve Problems Using Multiple Representations to 8.6 Emptying a Tank Solve Problems This chapter introduces points, lines, and planes as the essential building blocks of geometry. Key terms and basic constructions are introduced that will 9 Using Geometry allow students to construct and compare triangles in the Chapter 10. This chapter introduces points, lines, and planes as the essential building blocks of geometry. Key terms and basic constructions are introduced that will 9 Using Geometry allow students to construct and compare triangles in the Chapter 10. geometry, protractor, compass, straightedge, sketch, draw, Introduction to Geometry and construct, geometric construction, point, line, plane, 9.1 Earth Measure geometry, protractor, compass, straightedge, sketch, draw, Geometric Constructions coplanar lines, skew lines, line segment, endpoints, arc, Introduction to Geometry and construct, geometric construction, point, line, plane, 9.1 Earth Measure congruent line, segments, congruent, intersection Geometric Constructions coplanar lines, skew lines, line segment, endpoints, arc, congruent line, segments, congruent, intersection ray, angle, sides of an angle, vertex, degrees, acute angle, 9.2 Angles and More Angles Measuring and Constructing Angles right angle, obtuse angle, straight angle, congruent angles, ray, angle, sides of an angle, vertex, degrees, acute angle, bisect, angle bisector 9.2 Angles and More Angles Measuring and Constructing Angles right angle, obtuse angle, straight angle, congruent angles, bisect, angle bisector supplementary angles, complementary angles, Complements, Supplements, perpendicular, midpoint of a segment, segment bisector, 9.3 Special Angles Midpoints, Perpendiculars, and supplementary angles, complementary angles, Complements, Supplements, 7.G.5 perpendicular bisector, adjacent angles, linear pair, vertical Perpendicular Bisectors perpendicular, midpoint of a segment, segment bisector, 9.3 Special Angles Midpoints, Perpendiculars, and angles 7.G.5 perpendicular bisector, adjacent angles, linear pair, vertical Perpendicular Bisectors angles 10 Triangles This chapter investigates the conditions that determine unique triangles. 10 Triangles This chapter investigates the conditions that determine unique triangles. Triangle Sum, Exterior Angle, and Triangle Sun Theorem, remote interior angles of a triangle, 10.1 Pulling a One-Eighty! Exterior Angle Inequality Theorems Exterior Angle Theorem, Exterior Angle Inequality Theorem Triangle Sum, Exterior Angle, and Triangle Sun Theorem, remote interior angles of a triangle, 10.1 Pulling a One-Eighty! Exterior Angle Inequality Theorems Exterior Angle Theorem, Exterior Angle Inequality Theorem 10.2 Triangle Construction I Constructing Triangles 10.2 Triangle Construction I Constructing Triangles geometric figures, congruent geometric figures, Congruent Figures and Constructing 10.3 Triangle Construction II corresponding sides, corresponding angles, included angle, geometric figures, congruent geometric figures, Congruent Triangles Congruent Figures and Constructing included side 10.3 Triangle Construction II corresponding sides, corresponding angles, included angle, Congruent Triangles 10.4 Pasta Anyone? Triangle Inequality Theorem Triangle Inequality included Theorem side 10.4 Pasta Anyone? Triangle Inequality Theorem Triangle Inequality Theorem 11 Scale Drawing and Scale Factors This chapter explores scale drawings, scale models, and scale factors through real-world problems. 11 Scale Drawing and Scale Factors This chapter explores scale drawings, scale models, and scale factors through real-world problems. Scale Drawings, Scale, and 11.1 Bigger and Smaller 7.G.1 scale factor Scale Factors Scale Drawings, Scale, and 11.1 Bigger and Smaller 7.G.1 scale factor 11.2 Say Cheese! Applications Scale Factors of Ratio 7.G.1 aspect ratio 11.2 No GPS? Say Better Cheese! Get The Applications of Ratio 7.G.1 aspect ratio 11.3 Exploring Scale Drawings 7.G.1 scale drawings Map Out! No GPS? Better Get The 11.3 Exploring Scale Drawings 7.G.1 scale drawings Houses Map for Out! Our 11.4 Creating Blueprints 7.G.1 Feathered Friends Houses for Our 11.4 Creating Blueprints 7.G.1 Feathered Friends 12 Circles This chapter develops the formula for the area of a circle. Problems are solved involving circles and circle formulas. 12 Circles This chapter develops the formula for the area of a circle. Problems are solved involving circles and circle formulas. circle, center of a circle, radius of a circle, diameter of a 12.1 Introduction to Circles Circle, Radius, and Diameter 7.G.4 circle circle, center of a circle, radius of a circle, diameter of a 12.1 Introduction to Circles Circle, Radius, and Diameter 7.G.4 circle But Most of All, I Like 12.2 Circumference of a Circle 7.G.4 pi Pi! But Most of All, I Like 12.2 Circumference of a Circle 7.G.4 pi Pi! 12.3 One Million Sides! Area of a Circle 7.G.4 inscribed circle 12.3 One Million Sides! Area of a Circle 7.G.4 inscribed circle 12.4 It's About Circles! Unknown Measurements 7.G It's About Circles! Unknown Measurements 7.G.4 This chapter explores planes intersected with three-dimensional geometric figures. Real-world problems are solved involving area, volume, and surface area 13 Slicing Three-Dimensional Figures of three-dimensional figures. This chapter explores planes intersected with three-dimensional geometric figures. Real-world problems are solved involving area, volume, and surface area 13 Slicing Three-Dimensional Figures of three-dimensional figures Slicing and Dicing Slicing Through a Cube 7.G.3 cross-section 13.1 Slicing and Dicing Slicing Through a Cube 7.G.3 cross-section Slicing Through Right Rectangular 13.2 The Right Stuff 7.G.3 Prisms 13.2 The Right Stuff 7.G.3 Slicing Through Right Rectangular Prisms And Now On To Soicing Through Right Rectangular 13.3 And Now On To Soicing Through Right Rectangular 13.3 Introduction to Volume and Surface 13.4 Backyard Barbecue Area Introduction to Volume and Surface 13.4 Backyard Barbecue Applying Volume Area and Surface Area 13.5 Famous Fomulas Applying Volume and Surface Area 13.5 Famous Fomulas pyramid, base of a pyramid, lateral faces of a pyramid, lateral edges of a pyramid, vertex of a pyramid, pyramid, base of pyramid, lateral faces of a height of a pyramid, regular pyramid, slant height of a pyramid, lateral edges of a pyramid, vertex of a pyramid, pyramid height of a pyramid, regular pyramid, slant height of a pyramid 7.G.3 7.G.3 7.G.6 volume, surface area 7.G.6 volume, surface area 7.G.6 7.G.6 17

7 Worked Examples Peer Analysis Talk the Talk 14 Data Collection This chapter emphasizes data collection, sampling, random samples, and frequencies We want to Hear from You! Formulating Questions and Collecting Data survey, data, population, census, sample, parameter, statistic 14.2 Dealing with Data: Selecting a Sample Collecting Data through Random Sampling 14.3 Floor Plans and Tiles Random Sampling 14.4 What Does the Data Mean? Using Samples, Centers, and Spreads to Describe Data 14.5 Taking a Survey Using a Sample Size random sample, random number generator, random number, table dot plot (line plot) variability, spread, range, mean absolute deviation, deviation from the mean sample size 15 Comparing Populations This chapter uses measures of variability to compare inferences across two populations Checking the Papers and the Blogs Comparing Measures of Center for Two Populations 7.SP Can Podcasts Effect Ratings? Comparing Measures of Center of Two Populations 7.SP Finding Your Spot to Live Drawing Conclusions about Two Populations 7.SP.3 16 Introduction to Probability This chapter investigates experimental and theoretical probabilities. Probability models are developed and used to calculate probabilities of events Rolling, Rolling, Rolling Defining and Representing Probability 7.SP.5 outcome, experiment, sample space, event, simple event, probability, equally likely 16.2 Toss the Cup Determining Experimental Probability 7.SP.5 experimental probability 16.3 Double Your Fun Determining Theoretical Probability 7.SP.5 theoretical probability 16.4 A Toss of a Coin Simulating Experiments 7.SP.5 simulation, trial 16.5 Roll the Cubes Again Using for Simulations spreadsheet 17 Probability of Compound Events This chapter focuses on probabilities of compound events. Simulations are used to generate frequencies for compound events Is It Better to Guess? Using for Probability probability model, uniform probability model, non-uniform probability model 17.2 Three Girls and No Boys? Creating and Using Probability 7.SP.8.a 7.SP.8.b tree diagram, complementary events 17.3 Pet Shop Probability Determining Compound Probability 7.SP.8.a 7.SP.8.b compound event 17.4 What Type of Blood Do You Have? Simulating Probability of Compound Events 7.SP.8.c 18