Linda Cooper Foreman and Alber t B Bennett, Jr COURSE II Visual Mathematics, Course II by Linda Cooper Foreman and Albert B Bennett Jr Visual Mathematics, Course II is preceded by Visual Mathematics, Course II and followed by Math Alive! Visual Mathematics, Course III Copyright ©1996 The Math Learning Center, PO Box 12929, Salem, Oregon 97309 Tel 503 370-8130 All rights reserved Produced for digital distribution November 2016 This document was developed from printed archival masters As a result, some PDF functionalities, such as editing, copying, and text search, are not available The Math Learning Center grants permission to classroom teachers to reproduce blackline masters and student activity pages (separate documents) in appropriate quantities for their classroom use This project was supported, in part, by the National Science Foundation Opinions expressed are those of the authors and not necessarily those of the Foundation Prepared for publication on Macintosh Desktop Publishing system Printed in the United States of America QPS032, QPS033, QPS034 0108 DIGITAL2016 ISBN 1-886131-42-2 Contents vii INTRODUCTION LESSON 1 Surface Area and Volume LESSON 2 Shape and Surface Area 17 LESSON 3 Variables and Formulas 29 LESSON 4 Cube Patterns 47 LESSON 5 Positive and Negative Integers 63 LESSON 6 Integer Addition and Subtraction 77 LESSON 7 Counting Piece Arrays 91 LESSON 8 Integer Multiplication and Division 103 LESSON 9 Tile Patterns and Graphing 117 LESSON 10 Counting Piece Patterns and Graphing 133 LESSON 11 Classifying Geoboard Triangles 147 LESSON 12 Angle Measurement 161 LESSON 13 Paperfolding 177 LESSON 14 Mirrors and Shapes 197 LESSON 15 Areas of Silhouettes 211 LESSON 16 Probability and Fair Games 227 LESSON 17 Data Centers, Spreads and Plots 241 LESSON 18 Investigating Relationships in Data 261 LESSON 19 Decimal and Fraction Operations 279 LESSON 20 Operations Using Rectangles 303 LESSON 21 Modeling Percentages 323 LESSON 22 Picturing Percentage Problems 337 LESSON 23 Ratio and Proportion 355 LESSON 24 Getting Information by Sampling 373 LESSON 25 Data Collection and Analysis 383 LESSON 26 Modeling Algebraic Expressions 399 LESSON 27 Seeing and Solving Equations 417 LESSON 28 Squares and Square Roots 433 LESSON 29 Sorting and Classifying Solids LESSON 30 Similarity and Scaling in 2-D and 3-D 451 469 APPENDIX Materials Appendix–1 INDEX Index–1 Materials NECESSARY MANIPULATIVES AND MATERIALS INSTRUCTIONAL MATERIALS Visual Mathematics, Course II (Lessons 1-30) Starting Points for Implementing Visual Mathematics Visual Mathematics, Course II Blackline Masters Blackline Masters include Student Activities Grids Segment Strips Print Masters MAKE FROM BLACKLINE MASTERS OR PURCHASE FROM MLC Algebra Pieces Base Ten Linear Pieces set per students set per 36 students Algebra Pieces, Overhead Base Ten Area/Linear Pieces, Overhead set per teacher sheet per teacher Bicolored Counting Pieces, Overhead Segment Strips set per teacher set per 36 students Base Ten Area Pieces Segment Strips, Overhead sheet per student set per teacher MATERIALS AVAILABLE FROM MLC Cubes, Wood (3⁄4" or 2-cm) Coffee Stirrers 30 per student 15 per student Dice, 6-sided Mirrors, Rigid dice per student set per students Linear Pieces, 2-cm Toothpicks 30 per student box Game Markers Rulers bag per 15 students per student Geoboard, Clear Lunch Bags per student / per teacher per student Calculators Overhead Pens per student set per teacher Modeling Clay box per 16 students Visit catalog.mathlearningcenter.org to order these and other materials MATERIALS NOT AVAILABLE FROM MLC Blank Transparencies Yarn or String Poster Paper Tape, Glue, Glue Sticks Colored Markers Scissors Weather Pages Consecutive days of weather information, local and regional or national, day per student Consecutive pages from a local newspaper or consecutive daily reports from an online weather service work well See Lesson 18 for details OPTIONAL MATERIALS ADDITIONAL VISUAL MATHEMATICS TEXTS Visual Mathematics, Course II Student Activities Packet Visual Mathematics, Course II Student Activity Grids Visual Mathematics Student Journal VIDEOS FROM MLC Math and the Mind’s Eye Video A Change of Course: Implementing Visual Mathematics in the Classroom Video MATERIALS AVAILABILITY AS OF NOVEMBER 2016 Visual Mathematics, Course II / Appendix–1 .. .Visual Mathematics, Course II by Linda Cooper Foreman and Albert B Bennett Jr Visual Mathematics, Course II is preceded by Visual Mathematics, Course II and followed by Math Alive! Visual Mathematics, ... Plots 24 1 LESSON 18 Investigating Relationships in Data 26 1 LESSON 19 Decimal and Fraction Operations 27 9 LESSON 20 Operations Using Rectangles 303 LESSON 21 Modeling Percentages 323 LESSON 22 Picturing... 337 LESSON 23 Ratio and Proportion 355 LESSON 24 Getting Information by Sampling 373 LESSON 25 Data Collection and Analysis 383 LESSON 26 Modeling Algebraic Expressions 399 LESSON 27 Seeing