L i n d a C o o p e r Fo r e m a n a n d A l b e r t B . B e n n e t t , J r .

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

ContentsINTRODUCTION vii

LESSON 1 Surface Area and Volume 1

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 451

LESSON 30 Similarity and Scaling in 2-D and 3-D 469

APPENDIX Materials Appendix–1

INDEX Index–1

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Visual Mathematics, Course II / Appendix–1

NECESSARY MANIPULATIVES AND MATERIALS

MAKE FROM BLACKLINE MASTERS OR PURCHASE FROM MLC

ADDITIONAL VISUAL MATHEMATICS TEXTS

Visual Mathematics, Course II Student Activities PacketVisual Mathematics, Course II Student Activity GridsVisual Mathematics Student Journal

VIDEOS FROM MLC

Math and the Mind’s Eye VideoA Change of Course: Implementing Visual Mathematics in the Classroom Video

MATERIALS NOT AVAILABLE FROM MLC

INSTRUCTIONAL MATERIALS

Visual Mathematics, Course II (Lessons 1-30)Starting Points for Implementing Visual MathematicsVisual Mathematics, Course II Blackline Masters

Blackline Masters include Student Activities Grids.

Segment Strips Print Masters

Algebra Pieces 1 set per 4 students

Algebra Pieces, Overhead1 set per teacher

Bicolored Counting Pieces, Overhead1 set per teacher

Base Ten Area Pieces 1 sheet per student

Base Ten Linear Pieces 1 set per 36 students

Base Ten Area/Linear Pieces, Overhead1 sheet per teacher

Segment Strips1 set per 36 students

Segment Strips, Overhead1 set per teacher

MATERIALS AVAILABLE FROM MLC

Cubes, Wood (3⁄4" or 2-cm)30 per student

Dice, 6-sided2 dice per student

Linear Pieces, 2-cm 30 per student

Game Markers1 bag per 15 students

Geoboard, Clear1 per student / 1 per teacher

Calculators1 per student

Modeling Clay1 box per 16 students

Coffee Stirrers15 per student

Mirrors, Rigid 1 set per 5 students

Toothpicks1 box

Rulers1 per student

Lunch Bags1 per student

Overhead Pens1 set per teacher

Blank TransparenciesYarn or StringPoster PaperTape, Glue, Glue Sticks

Colored MarkersScissors

Materials

OPTIONAL MATERIALS

Visit catalog.mathlearningcenter.org to order these and other materials.

MATERIALS AVAILABILITY AS OF NOVEMBER 2016

Weather PagesConsecutive days of weather information, local and regional or national, 1 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.