Volume 1 Contents Common Core State Standards for Mathematics........................................ xlv 1 Rates, Ratios, and Proportions Overview................................................................................ 1A The Learning Community: Beginning the Year.......................................... 1HH Multiplication and Rates Common Core Standards CC.6.RP.2, CC.6.RP.3, CC.6.RP.3a, CC.6.RP.3b 1 Factor Puzzles and the Multiplication Table.................... 1 ACTIVITIES Rows and Columns in the Multiplication Table Solving Factor Puzzles 2 Solving Factor Puzzles................. 11 ACTIVITIES Introduce Unit 1 Quick Practice Solving and Making Factor Puzzles 4 Rate Situations and Unit Rate Language.. 29 Rates and Multiplication 5 Unit Rates, Products, and Rate Tables..... 35 Discuss Rate Situations Quick Quiz 1 for Lessons 1, 2, 3, 4, 5 3 Rate Situations and Rate Tables.......... 19 Noreen s Story Record in a Rate Table Special Rate Situations and Graphing Common Core Standards CC.6.RP.2, CC.6.RP.3, CC.6.RP.3a, CC.6.RP.3b, CC.6.EE.6, CC.6.EE.9 6 Unit Pricing........................... 41 Unit Price Tables and Graphs Discuss Patterns in Rate Tables, Equations, and Graphs 7 Constant Speed....................... 53 Constant Speed Situations Quick Quiz 2 for Lessons 6, 7 Volume 1 Contents xxxi 6_MNLAETE567556_FMTOC.indd 31 6/10/11 8:17:20 PM
Volume 1 Contents (continued) Solve Problems with Ratio and Proportion Common Core Standards CC.6.RP.1, CC.6.RP.2, CC.6.RP.3, CC.6.RP.3a 8 Ratio as Linked Rates.................. 61 Ratios as Linked Rates 9 Finding Linked Values in Ratio Tables.... 67 Finding Linked Values in a Ratio Table 10 Seeing Proportions in Ratio Tables...... 75 Proportions Within a Ratio Table 11 Identify and Solve Proportion Situations.................. 83 Is It a Proportion Situation? New Quick Practice Routine Quick Quiz 3 for Lessons 8, 9, 10, 11 Identify, Solve, and Write Proportion Situations Common Core Standards CC.6.RP.1, CC.6.RP.2, CC.6.RP.3, CC.6.RP.3a, CC.6.NS.4 12 Solve Numeric Proportion Problems...... 93 Numeric Proportions and Proportion Problems 13 Basic Ratio Solution Strategies......... 101 Basic Ratio Strategies Quick Quiz 4 for Lessons 12, 13, 14 15 Focus on Mathematical Practices....... 111 ACTIVITIES Math and Hobbies Use Reasoning Establish a Position 14 Write and Solve Proportion Problems... 107 Solve Student Proportion Problems 1 Review and Test............................................................. 117 xxxii Volume 1 Contents 6_MNLAETE567556_FMTOC.indd 32 6/10/11 8:17:28 PM
2 Area of Polygons Overview............................................................................... 123A Derive Area Formulas and Solve Problems: Parallelograms and Triangles Common Core Standards CC.6.G.1, CC.6.EE.2, CC.6.EE.2c 1 Units of Area........................ 123 ACTIVITIES Visualize Perimeter and Area Identify and Correct Errors Real World Problems 2 Area of Any Right Triangle............ 131 Explore Right Triangles Real World Problems 3 Area of Any Parallelogram............. 139 Area of a Parallelogram Area of a Rhombus Solve Problems 4 Area of Any Triangle.................. 149 Compose Parallelograms with Triangles Triangles and Parallelograms Area of Triangles 5 Select the Needed Measurements....... 157 Appropriate Measurements Choosing a Base Which Measurements? Quick Quiz 1 for Lessons 1, 2, 3, 4, 5 Derive Area Formulas and Solve Problems: Trapezoids and Other Polygons Common Core Standards CC.6.G.1, CC.6.G.3, CC.6.EE.2, CC.6.EE.2c, CC.6.EE.3, CC.6.EE.6 6 Area of Any Trapezoid................ 165 Decompose and Compose with Trapezoids Equivalent Formulas Areas of Trapezoids 7 Area of a Complex Figure.............. 173 Area and Perimeter of Complex Figures 8 Area of Any Regular Polygon.......... 181 Area of Regular Polygons Generalize a Formula 9 Graph Polygons in the Coordinate Plane..................... 187 Graph Polygons Find Side Lengths Solve Real World Problems Quick Quiz 2 for Lessons 6, 7, 8, 9 10 Focus on Mathematical Practices....... 197 ACTIVITIES Math and Tiling Look for a Pattern Establish a Position 2 Review and Test............................................................. 203 Volume 1 Contents xxxiii 6_MNLAETE567556_FMTOC.indd 33 6/10/11 8:17:34 PM
Volume 1 Contents (continued) 3 Operations with Whole Numbers, Fractions, and Decimals Overview............................................................................... 209A Multiplication and Division of Whole Numbers and Decimals Common Core Standards CC.6.NS.2, CC.6.NS.3 1 Place Value and Whole Number Division..................... 209 ACTIVITIES Place Value Meanings Understand Multidigit Division 2 Estimated Multipliers in Division....... 221 Estimate the Multiplier Learning the Quick Practice 4 Decimal Divisors...................... 239 Dividing by Decimals 5 Multiplication or Division.............. 249 Review Decimal Multiplication and Division Quick Quiz 1 for Lessons 1, 2, 3, 4, 5 3 Multiplying by a Decimal.............. 229 Multiply by Decimals Relating, Composing, and Decomposing Decimals and Fractions Common Core Standards CC.6.NS.3, CC.6.NS.4 6 Comparing, Adding, and Subtracting with the Same Unit........ 257 Visualize Fractions and Decimals Adding and Subtracting 7 Equivalent Fractions or Decimals....... 267 Equivalent Fractions 8 Finding a Common Unit Fraction........ 275 Equivalent Fractions 9 Mixed Problem Solving................ 281 Mixed Practice Quick Quiz 2 for Lessons 6, 7, 8, 9 xxxiv Volume 1 Contents 6_MNLAETE567556_FMTOC.indd 34 6/10/11 8:17:41 PM
Multiplying Fractions and Dividing with Fractions and Whole Numbers Common Core Standards CC.6.NS.1, CC.6.NS.3, CC.6.NS.4 10 Multiplying with Fractions............. 289 Multiplying Fractions Introducing a New Quick Practice Routine 11 Dividing with Fractions and Whole Numbers...................... 301 Divide Whole Numbers and Unit Fractions 12 Is It Multiplying or Dividing?........... 309 Mixed Practice Quick Quiz 3 for Lessons 10, 11, 12 Dividing a Fraction by a Fraction Common Core Standards CC.6.NS.1, CC.6.NS.3 13 Dividing Numerators and Denominators....................... 317 Relating Multiplication and Division Learning the New Quick Practice Routine 14 Dividing by Unsimplifying............. 325 Two Division Methods 15 Dividing by Multiplying by the Reciprocal........................... 333 Review and Practice Division Methods 17 Mixed Practice with Decimals and Fractions........................ 349 Fraction and Decimal Review Quick Quiz 4 for Lessons 13, 14, 15, 16, 17 18 Focus on Mathematical Practices....... 355 ACTIVITIES Math and the Stock Market Use Reasoning Establish a Position 16 Is It Multiplying or Dividing?........... 341 Fractions as Factors and Divisors 3 Review and Test............................................................. 361 Volume 1 Contents xxxv 6_MNLAETE567556_FMTOC.indd 35 6/10/11 8:17:47 PM
Volume 1 Contents (continued) 4 Surface Area of Prisms and Pyramids Overview............................................................................... 365A Nets and Surface Area of Prisms Common Core Standards CC.6.G.1, CC.6.G.4, CC.6.EE.2, CC.6.EE.2c 1 Nets and Surface Area for Rectangular Prisms................... 365 ACTIVITIES Model Rectangular Prisms Surface Area of Rectangular Prisms Surface Area of Cubes 3 Surface Area of Prisms................ 387 Solve Problems Quick Quiz 1 for Lessons 1, 2, 3 2 Nets and Surface Area for Nonrectangular Prisms................ 377 Model Nonrectangular Prisms Surface Area of Nonrectangular Prisms Nets and Surface Area of Pyramids Common Core Standards CC.6.G.1, CC.6.G.4, CC.6.EE.2, CC.6.EE.2c, CC.6.EE.6 4 Nets for Pyramids.................... 393 Model Pyramids Construct Other Types of Pyramids 5 Surface Area of Pyramids.............. 401 Surface Area and Pyramids Quick Quiz 2 for Lessons 4 and 5 6 Focus on Mathematical Practices........ 407 ACTIVITIES Math and Packaging Look for a Pattern Establish a Position 4 Review and Test............................................................. 413 xxxvi Volume 1 Contents 6_MNLAETE567556_FMTOC.indd 36 6/10/11 8:17:54 PM
Volume 2 Contents 5 Expressions and Equations Overview................................................................................ 417A Writing, Interpreting, and Analyzing Expressions Common Core Standards CC.6.EE.1, CC.6.EE.2, CC.6.EE.2a, CC.6.EE.2b, CC.6.EE.2c, CC.6.EE.4, CC.6.G.1, CC.6.G.4 1 Expressions and Order of Operations... 417 ACTIVITIES The Language of Algebra Simplifying and Evaluating Expressions 2 Expressions with Exponents........... 425 Exponents Expressions That Represent Designs 3 Interpreting and Analyzing Expressions.. 435 Describe Expressions Analyze Expressions 4 Modeling and Simplifying Expressions......................... 445 Expressions for Dot Diagrams 5 Expressions for Area and Surface Area... 455 Different Expressions for the Same Area Surface Areas of Prisms Seeing Area in Different Ways (Optional) Quick Quiz 1 for Lessons 1, 2, 3, 4, 5 Equivalent Expressions Common Core Standards CC.6.EE.1, CC.6.EE.2, CC.6.EE.2a, CC.6.EE.2b, CC.6.EE.2c, CC.6.EE.3, CC.6.EE.4, CC.6.NS.4 6 Equivalent Expressions............... 465 Modeling Expressions 7 The Commutative and Associative Properties........................... 477 Commutative and Associative Properties of Addition Commutative and Associative Properties of Multiplication 8 The Distributive Property.............. 491 Understand and Apply the Distributive Property Equivalent Expressions 9 Practice with Expressions.............. 503 Introduce the New Quick Practice Routine Work with Expressions Quick Quiz 2 for Lessons 6, 7, 8, 9 Volume 2 Contents xxxvii 6_MNLAETE567440_FMTOC.indd 37 6/10/11 8:14:56 PM
Volume 2 Contents (continued) Representing and Describing Quantitative Relationships Common Core Standards CC.6.EE.6, CC.6.EE.9 10 Relating Two Quantities.............. 513 Quantities That Vary Together Equations for Quantities That Vary Together 11 Motion at a Constant Speed........... 523 Representations of Motion at a Constant Speed 13 Writing Equations.................... 545 Writing and Using Cost Equations Quick Quiz 3 for Lessons 10, 11, 12, 13 12 Relating Equations, Tables, and Graphs.......................... 535 Making a Table and Graph from an Equation Relating Equations to Rates and Graphs Solving Equations and Inequalities Common Core Standards CC.6.EE.2, CC.6.EE.2a, CC.6.EE.3, CC.6.EE.5, CC.6.EE.6, CC.6.EE.7, CC.6.EE.8, CC.6.EE.9 14 Inequalities.......................... 553 Writing Inequalities Graphing Inequalities 15 Solutions of Equations and Inequalities.......................... 565 Identify Solutions Use Reasoning to Solve Equations 16 Addition and Subtraction Equations.... 575 Addition and Subtraction Equations 17 Multiplication and Division Equations... 585 Multiplication and Division Equations Quick Quiz 4 for Lessons 14, 15, 16, 17 18 Focus on Mathematical Practices....... 597 ACTIVITIES Math and Transportation Use Reasoning Establish a Position 5 Review and Test............................................................. 603 xxxviii Volume 2 Contents 6_MNLAETE567440_FMTOC.indd 38 6/10/11 8:15:07 PM
6 Volume of a Rectangular Prism Overview................................................................................609A Volume Formulas for Rectangular Prisms Common Core Standards CC.6.G.1, CC.6.G.2, CC.6.G.4, CC.6.EE.2, CC.6.EE.2c, CC.6.EE.6 1 What Is Volume?..................... 609 ACTIVITIES Review Volume How Is Volume Different from Surface Area? Choose a Measure 4 Volume of Prisms with Fractional Edge Lengths........................ 641 Practice Finding Volume of Prisms Solve Real World Problems 5 Write and Solve Equations About Volume....................... 647 Relate Volume to Dimensions of the Prism Write and Solve Equations Problems Involving Surface Area and Volume 2 Fractional Unit Cubes................. 619 Prisms with Fractional Edge Lengths Packing a Prism with Unit Cubes of Appropriate Unit Fraction Edge Lengths 3 Compose Rectangular Prisms with Fractional Edge Lengths.......... 629 Build Rectangular Prisms Prisms with Fractional Base Dimensions Use Formulas to Express Volume and Find Unknown Dimensions Quick Quiz 1 for Lessons 1, 2, 3, 4, 5 6 Focus on Mathematical Practices....... 655 ACTIVITIES Math and Construction Look for a Pattern Establish a Position 6 Review and Test............................................................. 661 Volume 2 Contents xxxix 6_MNLAETE567440_FMTOC.indd 39 6/10/11 8:15:11 PM
Volume 2 Contents (continued) 7 Ratios and Rates with Fractions, Decimals, and Percents Overview................................................................................665A Ratios, Fractions, Unit Rates, and Cross-Multiplying Common Core Standards CC.6.RP.1, CC.6.RP.2, CC.6.RP.3, CC.6.RP.3a, CC.6.RP.3b, CC.6.EE.6, CC.6.EE.7 1 Comparing Ratios.................... 665 ACTIVITIES Review Ratio and Proportion from Unit 1 Use Tables to Compare Ratios Use Graphs to Compare Ratios 2 3 Ratios, Fractions, and Fraction Notation............................ 687 Ratios in Fraction Notation 4 Understanding Cross-Multiplication..... 695 Understanding Cross-Multiplication Unit Rates.......................... 675 Unit Rates for Ratios New Quick Practice Routine Solving Proportion Problems Using Unit Rates Quick Quiz 1 for Lessons 1, 2, 3, 4 Ratios with Tape Diagrams and Equations Common Core Standards CC.6.RP.1, CC.6.RP.2, CC.6.RP.3, CC.6.RP.3a, CC.6.RP.3b, CC.6.EE.6, CC.6.EE.7 5 Describing Ratios with Tape Diagrams.. 701 Using Tape Diagrams Ratios Involving the Whole 6 Ratios and Multiplicative Comparisons.. 709 Relating Quantities in Different Ways 7 Solve Ratio and Rate Problems......... 717 Solve Rate and Ratio Problems Quick Quiz 2 for Lessons 5, 6, 7 xl Volume 2 Contents 6_MNLAETE567440_FMTOC.indd 40 6/10/11 8:15:18 PM
Percent Common Core Standards CC.6.RP.3, CC.6.RP.3c, CC.6.EE.6, CC.6.EE.7 8 The Meaning of Percent............... 723 Understand Percent 9 Percent of a Number.................. 733 Finding Percent of a Number 10 Percent Calculations.................. 743 Finding the Portion Finding the Whole 11 Solve Percent Problems............... 753 Compare Using Percents Practice Solving Percent Problems Quick Quiz 3 for Lessons 8, 9, 10, 11 Relate Different Measurement Units Common Core Standards CC.6.RP.1, CC.6.RP.3, CC.6.RP.3c, CC.6.RP.3d, CC.6.EE.6, CC.6.EE.7, CC.6.EE.9, CC.6.G.1, CC.6.G.4 12 13 Convert Units of Length............... 759 Length Conversions Convert Units to Find Area Convert Units of Liquid Volume, Mass, and Weight.................... 769 Convert Units of Liquid Volume Convert Units of Mass and Weight Quick Quiz 4 for Lessons 12, 13 14 Focus on Mathematical Practices....... 779 ACTIVITIES Math and Collections Use Reasoning Establish a Position 7 Review and Test............................................................. 785 Volume 2 Contents xli 6_MNLAETE567440_FMTOC.indd 41 6/10/11 8:15:23 PM
Volume 2 Contents (continued) 8 Analyzing Statistics Overview................................................................................791A Displaying Data Common Core Standards CC.6.SP.1, CC.6.SP.4, CC.6.SP.5, CC.6.SP.5a 1 Making Sense of Data................ 791 ACTIVITIES Why Do We Study Statistics? Analyzing Numerical Data in a Dot Plot 2 Dot Plots and Histograms............. 799 Making and Reading Dot Plots Making and Reading Histograms Quick Quiz 1 for Lessons 1, 2 Summarizing Data: The Mean, the Median Common Core Standards CC.6.SP.2, CC.6.SP.3, CC.6.SP.4, CC.6.SP.5, CC.6.SP.5c, CC.6.SP.5d 3 Making Data Groups Equal............ 809 What Is the Mean of a Data Set? What s the Error? 4 Use the Mean........................ 817 Use the Mean to Summarize and Compare Data 5 The Mean as a Balance Point........... 823 Dot Plots with the Same Mean Calculate the Mean Using a Dot Plot 6 Find and Use the Median.............. 831 Find the Median The Shape of Data Quick Quiz 2 for Lessons 3, 4, 5, 6 xlii Volume 2 Contents 6_MNLAETE567440_FMTOC.indd 42 6/10/11 8:15:32 PM
Describing Variability in Data Common Core Standards CC.6.SP.1, CC.6.SP.2, CC.6.SP.3, CC.6.SP.4, CC.6.SP.5, CC.6.SP.5a, CC.6.SP.5b, CC.6.SP.5c, CC.6.SP.5d 7 Variability in Data.................... 841 The Range of Data Find Quartiles 8 Box Plots............................ 851 Box Plots Interpret Box Plots Interquartile Range 9 Mean Absolute Deviation.............. 861 Distance from the Mean Mean Absolute Deviation Interpret Mean Absolute Deviation 11 Collect, Display, and Interpret Data..... 875 Investigate Paper Airplanes Quick Quiz 3 for Lessons 7, 8, 9, 10, 11 12 Focus on Mathematical Practices....... 883 ACTIVITIES Math and Handprints Informal Units of Measure Use Reasoning Establish a Position 10 Clusters, Peaks, Gaps, and Outliers..... 869 The Overall Shape of Data Summarize and Describe Data 8 Review and Test............................................................. 889 9 Rational Numbers and the Coordinate Plane Overview................................................................................895A Discuss, Compare, and Graph Integers Common Core Standards CC.6.NS.5, CC.6.NS.6, CC.6.NS.6a, CC.6.NS.6b, CC.6.NS.6c, CC.6.NS.7, CC.6.NS.7a, CC.6.NS.7b, CC.6.NS.7c, CC.6.NS.7d, CC.6.NS.8 1 Negative Numbers in the Real World.... 895 ACTIVITIES Discuss Situations Involving Negative Numbers Identify Opposites 3 Compare and Order Integers........... 911 Compare and Order Integers Using a Number Line Use Absolute Value Compare and Order Integers in Real World Situations 4 Integers and the Coordinate Plane...... 923 Coordinate Plane Graphing Quadrants Real World Situations 2 Integers on a Number Line............ 901 Lengths on a Number Line Distance and Points on a Number Line Introduce the Quick Practice for Unit 9 The Number Line Game Quick Quiz 1 for Lessons 1, 2, 3, 4 Volume 2 Contents xliii 6_MNLAETE567440_FMTOC.indd 43 6/10/11 8:15:38 PM
Volume 2 Contents (continued) Discuss, Compare, and Graph Rational Numbers Common Core Standards CC.6.NS.5, CC.6.NS.6, CC.6.NS.6a, CC.6.NS.6b, CC.6.NS.6c, CC.6.NS.7, CC.6.NS.7a, CC.6.NS.7b, CC.6.NS.7c, CC.6.NS.7d, CC.6.NS.8, CC.6.G.3 5 Rational Numbers on a Number Line.... 935 Fractions on a Number Line Decimals on a Number Line The Number Line Game 6 Compare and Order Rational Numbers.. 945 Use a Number Line to Compare Rational Numbers Rational Numbers in Real World Situations 7 Rational Numbers and the Coordinate Plane..................... 953 Distance and Reflections in the Coordinate Plane Absolute Value and Distance Real World Situations Quick Quiz 2 for Lessons 5, 6, 7 8 Focus on Mathematical Practices........ 965 ACTIVITIES Math and Global Positioning Draw a Model Establish a Position 9 Review and Test............................................................. 971 Grade 6 Posters............................................................................ T1 Student Resources......................................................................... T5 Teacher Glossary.......................................................................... T13 Recommended Books..................................................................... T29 Index.................................................................................... T30 xliv Volume 2 Contents 6_MNLAETE567440_FMTOC.indd 44 6/10/11 8:15:41 PM