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  • Middle SchoolMathematics Assessments

    The Charles A. Dana Centerat The University of Texas at Austin

    With funding fromthe Texas Education Agency andthe National Science Foundation

    Proportional Reasoning

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    About the Charles A. Dana Centers Work in Mathematics and Science

    The Charles A. Dana Center at The University of Texas at Austin works to support education leaders and policymakers in strengthening Texas education. As a research unit of UT Austins College of Natural Sciences, the Dana Center maintains a special emphasis on mathematics and science education. We offer professional development institutes and produce research-based mathematics and science resources for educators to use in helping all students achieve academic success. For more information, visit the Dana Center website at www.utdanacenter.org.

    The development of this work was supported in part by the Texas Education Agency, the National Science Foundation under cooperative agreement #ESR-9712001, and the Charles A. Dana Center at The University of Texas at Austin. Any opinions, ndings, conclusions, or recommendations expressed in this material are those of the author(s) and do not necessarily re ect the views of the Texas Education Agency, the National Science Foundation, or The University of Texas at Austin.

    Permission is given to any person, group, or organization to copy and distribute this publication, Middle School Mathematics Assessments: Proportional Reasoning, for noncommercial educational purposes only, so long as the appropriate credit is given. This permission is granted by the Charles A. Dana Center, a unit of the College of Natural Sciences at The University of Texas at Austin.

    First printing February 2004

    2004, The University of Texas at Austin. All rights reserved.

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    Authors

    Brenda DeBorde, Independent Mathematics ConsultantMary Alice Hatchett, Independent Mathematics ConsultantGena Silvas Lopez, Corpus Christi Independent School DistrictVicki Veigel Massey, Austin Independent School DistrictMaggie Myers, Charles A. Dana CenterPatricia A. Rossman, Austin Independent School DistrictTeresa Salas, Corpus Christi Independent School DistrictCarmen Whitman, Charles A. Dana Center

    Charles A. Dana Center Production Team

    Carmen Whitman, EditorDiane McGowan, Co-EditorBonnie McNemar, Co-EditorSusan Hudson Hull, Co-EditorAmy Dolejs, Production EditorPhil Swann, DesignerGeoff Potter, Graphics Assistant

    Content EditorEva Gates, Independent Mathematics Consultant

    Advisory TeamAmy L. Anding, Bryan Independent School DistrictCatherine Banks, Texas Womans UniversityLisa C. Brown, Austin Independent School DistrictShirl Chapman, Region 7 Education Service CenterSusan B. Empson, University of Texas at AustinYvonne Grant, Michigan State UniversityLynn Granzin, Region 15 Education Service CenterJulia Hankin, Austin Independent School DistrictSusan Hudson Hull, Charles A. Dana Center Ted H. Hull, Charles A. Dana CenterCarl Juenke, Charles A. Dana CenterGarland Linkenhoger, McAllen Independent School DistrictLaurie Mathis, Charles A. Dana CenterDiane McGowan, Charles A. Dana CenterTerri McLaughlin, Spring Branch Independent School DistrictBonnie McNemar, Charles A. Dana CenterBarbara J. Montalto, Texas Education AgencyLois G. Moseley, Mathematics EducatorMaggie Myers, Charles A. Dana Center

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    Rebecca Ontiveros, Region 19 Education Service CenterErika Pierce, Charles A. Dana CenterJoyce Schaeffer, North Lamar Independent School DistrictCathy L. Seeley, University of Texas at AustinCaren Sorrells, Birdville Independent School DistrictVanessa Spiegel, Port Neches-Grove Independent School DistrictPam Summers, Lubbock Independent School DistrictFrances M. Thompson, Texas Womans UniversityEmma Trevio, Charles A. Dana CenterLuAnn Weynand, North East Independent School District

    With Special Thanks To:Brian Sargent, Charles A. Dana CenterHee-Joon Kim, Charles A. Dana CenterMountain Creek Neighborhood Kids, P ugerville, TexasMartin Middle School Students, Corpus Christi, TexasBaker Middle School Students, Corpus Christi, TexasBedichek Middle School Students, Austin, Texas

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    TEKS and TAKS Resources

    The mathematics Texas Essential Knowledge and Skills (TEKS) were developed by the state of Texas to clarify what all students should know and be able to do in mathematics in kindergarten through grade 12. Districts are required to provide instruction that is aligned with the mathematics TEKS, which were adopted by the State Board of Education in 1997 and implemented statewide in 1998. The mathematics TEKS also form the objectives and student expectations for the mathematics portion of the Texas Assessment of Knowledge and Skills (TAKS) for grades 3 through 10 and for the Grade 11 Exit Level assessment.

    The mathematics TEKS can be downloaded in printable format, free of charge, from the Texas Education Agency website (www.tea.state.tx.us/teks). Bound versions of the mathematics and science TEKS are available for a fee from the Charles A. Dana Center at The University of Texas at Austin (www.utdanacenter.org).

    Resources for implementing the mathematics TEKS, including professional development opportunities, are available through the Texas Education Agency and the Charles A. Dana Center, formerly the state-designated Mathematics Center for Educator Development. Online resources can be found in the Mathematics TEKS Toolkit at www.mathtekstoolkit.org.

    Additional products and services that may be of interest are available from the Dana Center at www.utdanacenter.org. These include the following:

    TEKS, TAAS, and TAKS: Whats Tested at Grades 38? charts

    Mathematics Abridged TEKS charts

    Mathematics TEKS Big Picture posters

    Mathematics Standards in the Classroom; Resources for Grades 35

    Mathematics Standards in the Classroom; Resources for Grades 68

    Algebra I Assessments and the corresponding professional development

    Geometry Assessments and the corresponding professional development

    Algebra II Assessments and the corresponding professional development

    TEXTEAMS professional development mathematics institutes

    TEKS for Leaders professional development modules for principals and other administrators

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    CONTENTS

    Introduction xi

    Middle School Mathematics Assessment Solution Guide xiv

    Mathematics TEKS Alignment xv

    Mathematics Grade 6 TAKS Alignment xxi

    Mathematics Grade 7 TAKS Alignment xxii

    Mathematics Grade 8 TAKS Alignment xxiii

    Chapter 1: Number, Operation andQuantitative Reasoning 1Overarching Fun Park Party Grade 6 3 Fun Park Party Grade 7 13 Fun Park Saturday Grade 8 17

    Grade 6 Homecooking Chili 23 Spring Sensations 27

    Grade 7 Bargain Shopping 31 Rose Garden Plan 37

    Grade 8 Talk, Talk, Talk 43 Half-Life Happening 48

    Chapter 2: Patterns, Relationships, andAlgebraic Thinking 55Overarching At Home in Space Grade 6 57 Solar Cells for Science Grade 7 61 City in Space Grade 8 67

    Grade 6 Community Clean-Up 75 Towering Pizzas 85

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    Grade 7 South Texas Natives 95 Working Smarter 99

    Grade 8 Fast Food Workout 103 Global Warming: Texas-Size 109

    Chapter 3: Geometry and Spatial Reasoning 115Overarching By the Sea Grade 6 117 By the Sea Grade 7 123 By the Sea Grade 8 135

    Grade 6 Sweet Trip to the Candy Shop 147 The Round Table 155

    Grade 7 Sorting Rectangles 159 Mighty Mascot! 163

    Grade 8 Javier Builds a Model 169 Student Council President 175

    Chapter 4: Measurement 185Overarching Lights at the Marleys and Farleys Grade 6 187 Gardens at the Marleys and Farleys Grade 7 193 Storage Boxes at the Marleys and Farleys Grade 8 201

    Grade 6 Extravaganza 211 Matchmaker 221

    Grade 7 Bug Juice 235 Photographic Memories 241

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    Grade 8 Liberty Enlightening the World 251 In the Rafters 257

    Chapter 5: Probability and Statistics 263Overarching Perplexing Polygons Grade 6 265 Perplexing Polygons Grade 7 270 Perplexing Polygons Grade 8 279

    Grade 6 Science Quiz 287

    Grade 7 Big Money Prizes 293

    Grade 8 Five Friends 297

    Chapter 6: Underlying Processes andMathematical Tools 305Overarching Whats in Your Wallet? Grade 6 307 Whats in Your Wallet? Grade 7 315 Whats in Your Wallet? Grade 8 323

    Grade 6 Gone Fishin 331 Secret Recipe 343

    Grade 7 Rx 353 Its a Weighty Matter 361

    Grade 8 Java Joes 369 How Green is Green? 379

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    1 National Council of Teachers of Mathematics. 2000. Principles and Standards for School Mathematics.

    Reston, VA: National Council of Teachers of Mathematics.

    Introduction

    The Dana Center developed Middle School Mathematics Assessments: Proportional Reasoning as a resource for teachers to use to provide ongoing assessment integrated with middle school mathematics instruction.

    Principles and Standards for School Mathematics (National Council of Teachers of Mathematics, 2000) states: Assessment should support the learning of important mathematics and furnish useful information to both teachers and students. 1 Further, NCTM (1995) identi ed the following six standards to guide classroom assessment: 2

    Standard 1: Assessment should re ect the mathematics that all students needto know and be able to do.

    Standard 2: Assessment should enhance mathematics learning.

    Standard 3: Assessmen

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