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 I

Visual Mathematics, Course I by Linda Cooper Foreman and Albert B. Bennett Jr.

Visual Mathematics, Course I is followed by: Visual Mathematics, Course II Math Alive! Visual Mathematics, Course III

Copyright ©1995 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.

QP235, QP236, QP237 P1002 DIGITAL2016

ISBN 1-886131-27-9

ContentsINTRODUCTION vii

LESSON 1 Introduction to Visual Mathematics 1

LESSON 2 Basic Operations 11

LESSON 3 Visualizing Number Relationships 27

LESSON 4 Communicating Mathematics 39

LESSON 5 Visual Reasoning 49

LESSON 6 Odd & Even Numbers 59

LESSON 7 Factors & Primes 71

LESSON 8 Fraction Concepts with Egg Cartons 87

LESSON 9 Building Intuitions About Fraction Operations 101

LESSON 10 Averaging Two Numbers 113

LESSON 11 Averaging Several Numbers 123

LESSON 12 Probability 135

LESSON 13 Base Five Grouping & Numeration 145

LESSON 14 Place Value & Numeration 155

LESSON 15 Geoboard Figures 165

LESSON 16 Congruence & Symmetry 175

LESSON 17 Pattern Block Trains 189

LESSON 18 Pattern Block Perimeters 199

LESSON 19 Geoboard Area I 209

LESSON 20 Diagrams & Sketches 223

LESSON 21 Linear Measure 239

LESSON 22 Dimension & Area I 249

LESSON 23 Addition & Subtraction Concepts 261

LESSON 24 Multiplication & Division Concepts 271

LESSON 25 Whole Number & Decimal Numeration 281

LESSON 26 Whole Number & Decimal Addition & Subtraction 297

LESSON 27 Inventing Addition & Subtraction Algorithms 311

LESSON 28 Division Concept of a Fraction 325

LESSON 29 Relationships Between Decimals & Fractions 339

LESSON 30 Rounding & Ordering Numbers 353

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(Continues on next page)

LESSON 31 Estimating Sums & Differences 367

LESSON 32 Angle Measurement 383

LESSON 33 Graphing 397

LESSON 34 Graphing & Decision Making 411

LESSON 35 Geoboard Area II 423

LESSON 36 Dimension & Area II 435

LESSON 37 Whole Number & Decimal Multiplication 449

LESSON 38 Whole Number & Decimal Division 467

LESSON 39 Modeling Percent 483

LESSON 40 Linear Model for Fractions 497

LESSON 41 Area Model for Fractions 509

LESSON 42 Modeling Fraction Operations 519

LESSON 43 Linear & Area Measure 531

LESSON 44 Inventing Algorithms for Fraction Operations 543

LESSON 45 Sampling, Confidence, & Probability 551

MATERIALS

INDEX

Contents (continued)

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Visual Mathematics, Course I / Appendix–1

NECESSARY MANIPULATIVES AND MATERIALS

MANIPULATIVES—MAKE FROM BLACKLINE MASTERS OR PURCHASE FROM MLC

ADDITIONAL VISUAL MATHEMATICS TEXTS

Visual Mathematics, Course I Student Activities PacketVisual 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 I (Lessons 1-45)Starting Points for Implementing Visual MathematicsVisual Mathematics, Course I Blackline Masters

Blackline Masters include Student Activities Grids.

Segment Strips Print Masters

Base Five Area Pieces 1 sheet per student

Base Five Linear Pieces 1 set per 36 students

Base Ten Area Pieces 1 sheet per student

Base Ten Linear Pieces 1 set per 36 students

MANIPULATIVES AVAILABLE FROM MLC

Cubes, Wood (3⁄4" or 2-cm)120 cubes

Dice, 6-sided8 dice

Linear Pieces (1-inch red)About 120 pieces

Large Linear Unit Pieces (2-cm black)1 set per teacher

Game Markers1 bag per 15 students

Pattern BlocksStandard set of 250 blocks

Colored TileAbout 1,200 1-inch tiles in 4 colors

Geoboards, Clear1 per student and teacher

Coffee StirrersAbout 60 stirrers

Overhead Pens1 set per teacher

Rulers1 per student

Blank TransparenciesScissorsYarn or String

Poster PaperTape, Glue, Glue SticksColored Markers

Pom-Poms About 48 small pom-poms

Materials

OPTIONAL MATERIALS

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

OVERHEAD ITEMS—MAKE FROM BLACKLINE MASTERS OR PURCHASE FROM MLC

Base Five Area/Linear Pieces, Overhead1 set of each per teacher

Base Ten Area/Linear Pieces, Overhead1 set of each per teacher

Segment Strips, Overhead1 set per teacher

Pattern Blocks, OverheadStandard set of 120 blocks

Colored Tiles, Overhead40 1-inch tile in 4 colors

MATERIALS AVAILABILITY AS OF NOVEMBER 2016