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Linda Cooper Foreman and Alber t B Bennett, Jr 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 Contents vii INTRODUCTION LESSON 1 Introduction to Visual Mathematics 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 (Continues on next page) Contents (continued) 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 Materials NECESSARY MANIPULATIVES AND MATERIALS INSTRUCTIONAL MATERIALS Visual Mathematics, Course I (Lessons 1-45) Starting Points for Implementing Visual Mathematics Visual Mathematics, Course I Blackline Masters Blackline Masters include Student Activities Grids Segment Strips Print Masters MANIPULATIVES—MAKE FROM BLACKLINE MASTERS OR PURCHASE FROM MLC Base Five Area Pieces Base Ten Area Pieces sheet per student sheet per student Base Five Linear Pieces Base Ten Linear Pieces set per 36 students set per 36 students OVERHEAD ITEMS—MAKE FROM BLACKLINE MASTERS OR PURCHASE FROM MLC Base Five Area/Linear Pieces, Overhead Pattern Blocks, Overhead set of each per teacher Standard set of 120 blocks Base Ten Area/Linear Pieces, Overhead Colored Tiles, Overhead set of each per teacher 40 1-inch tile in colors Segment Strips, Overhead set per teacher MANIPULATIVES AVAILABLE FROM MLC Cubes, Wood (3⁄4" or 2-cm) Colored Tile 120 cubes About 1,200 1-inch tiles in colors Dice, 6-sided Geoboards, Clear dice per student and teacher Linear Pieces (1-inch red) Coffee Stirrers About 120 pieces About 60 stirrers Large Linear Unit Pieces (2-cm black) Overhead Pens set per teacher set per teacher Game Markers Rulers bag per 15 students per student Pattern Blocks Standard set of 250 blocks Visit catalog.mathlearningcenter.org to order these and other materials MATERIALS NOT AVAILABLE FROM MLC Blank Transparencies Scissors Yarn or String Poster Paper Tape, Glue, Glue Sticks Colored Markers Pom-Poms About 48 small pom-poms OPTIONAL MATERIALS ADDITIONAL VISUAL MATHEMATICS TEXTS Visual Mathematics, Course I Student Activities Packet 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 I / Appendix–1 ... LESSON 12 Probability 13 5 LESSON 13 Base Five Grouping & Numeration 14 5 LESSON 14 Place Value & Numeration 15 5 LESSON 15 Geoboard Figures 16 5 LESSON 16 Congruence & Symmetry 17 5 LESSON 17 Pattern... Primes 71 LESSON 8 Fraction Concepts with Egg Cartons 87 LESSON 9 Building Intuitions About Fraction Operations 10 1 LESSON 10 Averaging Two Numbers 11 3 LESSON 11 Averaging Several Numbers 12 3.. .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,
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