Math Games: Skill-Based Practice for Third Grade [1 ed.] 9781425896119, 9781425812904

Citation preview

3 Grade

Ted H. Hull Ruth Harbin Miles Don S. Balka

Authors Ted H. Hull, Ed.D. Ruth Harbin Miles, Ed.S. Don S. Balka, Ph.D.

Consultant

Publishing Credits

Don W. Scheuer, Jr., M.S.Ed. Mathematics Specialist The Haverford School (ret.)

Robin Erickson, Production Director; Lee Aucoin, Creative Director; Tim J. Bradley, Illustration Manager; Sara Johnson, M.S.Ed., Editorial Director; Maribel Rendón M.A.Ed., Editor; Jennifer Viñas, Editor; Grace Alba, Designer; Corinne Burton, M.A.Ed., Publisher

Image Credits all images Shutterstock

Standards © 2007 Teachers of English to Speakers of Other Languages, Inc. (TESOL) © 2007 Board of Regents of the University of Wisconsin System.  World-Class Instructional Design and Assessment (WIDA).  For more information on using the WIDA ELP Standards, please visit the WIDA website at www.wida.us. © 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers (CCSS)

Shell Education

5301 Oceanus Drive Huntington Beach, CA 92649-1030 http://www.shelleducation.com

ISBN 978-1-4258-1290-4 © 2014 Shell Education Publishing, Inc.

The classroom teacher may reproduce copies of materials in this book for classroom use only. The reproduction of any part for an entire school or school system is strictly prohibited. No part of this publication may be transmitted, stored, or recorded in any form without written permission from the publisher.

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Table of Contents Introduction Importance of Games. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Mathematical Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Games vs. Worksheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

How to Use This Book. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Correlation to the Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 About the Authors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Math Games Domain: Operations and Algebraic Thinking Go Team Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Grand Champion Racer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Math Facts Matchup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Serve and Return with Unknown Factors. . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Fact Face-off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 World Series of Word Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Domain: Number and Operations in Base Ten Spinning ’Round. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Big Number Checkmate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Sum It Up. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Submarine Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

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Table of Contents (cont.) Domain: Number and Operations—Fractions Secret Identity Sleuth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Fraction Throwdown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Fraction Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Domain: Measurement and Data Time Flies! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Data Dash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Volume and Mass Madness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Area Arrays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Fence Me In. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Domain: Geometry Geo Tic-Tac-Toe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Divide My Shape. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Appendices Appendix A: References Cited and Accessing the Digital Resources . . . 128 Appendix B: Digital Resources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129. Appendix C: Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.

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Introduction

Importance of Games Students learn from play. Play begins when we are infants and continues through adulthood. Games are motivational and educational (Hull, Harbin Miles, and Balka 2013; Burns 2009). They can assist and encourage students to operate as learning communities by requiring students to work together by following rules and being respectful. Games also foster students’ thinking and reasoning since students formulate winning strategies. They provide much more sustained practices than do worksheets, and students are more motivated to be accurate. Worksheets may provide 20 to 30 opportunities for students to practice a skill, while games far exceed such prescribed practice opportunities. Lastly, games provide immediate feedback to students concerning their abilities. Games must be part of the overall instructional approach that teachers use because successful learning requires active student engagement (Hull, Harbin Miles, and Balka 2013; National Research Council 2004), and games provide students with the motivation and interest to become highly engaged. Instructional routines need balance between concept development and skill development. They must also balance teacher-led and teacher-facilitated lessons. Students need time to work independently and collaboratively in order to assimilate information, and games can help support this.

When games are used appropriately, students also learn mathematical concepts.

Mathematical Learning Students must learn mathematics with understanding (NCTM 2000). Understanding means that students know the relationship between mathematical concepts and mathematical skills—mathematical procedures and algorithms work because of the underlying mathematical concepts. In addition, skill proficiency allows students to explore more rigorous mathematical concepts. From this relationship, it is clear that a balance between skill development and conceptual development must exist. There cannot be an emphasis of one over the other. The National Council of Teachers of Mathematics (2000) and the National Research Council (2001) reinforce this idea. Both organizations state that learning mathematics requires both conceptual understanding and procedural fluency. This means that students need to practice procedures as well as develop their understanding of mathematical concepts in order to achieve success. The games presented in this book reinforce skill‑based practice and support students’ development of proficiency. These games can also be used as a springboard for discourse about mathematical concepts. The counterpart to this resource is Math Games: Getting to the Core of Conceptual Understanding, which builds students’ conceptual understanding of mathematics through games.

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Introduction

Importance of Games (cont.) The Common Core State Standards for Mathematics (2010) advocate a balanced mathematics curriculum by focusing standards both on mathematical concepts and skills. This is also stressed in the Standards for Mathematical Practice, which discuss the process of “doing” mathematics and the habits of mind students need to possess in order to be successful. The Standards for Mathematical Practice also focus on the activities that foster thinking and reasoning in which students need to be involved while learning mathematics. Games are an easy way to initiate students in the development of many of the practices. Each game clearly identifies a Common Core domain, a standard, and a skill, and allows students to practice them in a fun and meaningful way.

Games vs. Worksheets In all likelihood, many mathematics lessons are skill related and are taught and practiced through worksheets. Worksheets heavily dominate elementary mathematics instruction. They are not without value, but they often command too much time in instruction. While students need to practice skills and procedures, the way to practice these skills should be broadened. Worksheets generally don’t promote thinking and reasoning. They become so mechanical that students cease thinking. They are lulled into a feeling that completing is the goal. This sense of “just completing” is not what the Common Core Standards for Mathematical Practice mean when they encourage students to “persevere in solving problems.”

Students need to be actively engaged in learning.

Students need to be actively engaged in learning. While worksheets do serve a limited purpose in skill practice, they also contain many potential difficulties. Problems that can occur include the following: Ë Worksheets are often completed in isolation, meaning that students who are performing a skill incorrectly most likely practice the skill incorrectly for the entire worksheet. The misunderstanding may not be immediately discovered, and in fact, will most likely not be discovered for several days! Ë Worksheets are often boring to students. Learning a skill correctly is not the students’ goal. Their goal becomes to finish the worksheet. As a result, careless errors are often made, and again, these errors may not be immediately discovered or corrected.

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Introduction

Importance of Games (cont.) Ë Worksheets are often viewed as a form of subtle punishment. While perhaps not obvious, the perceived punishment is there. Students who have mastered the skill and can complete the worksheet correctly are frequently “rewarded” for their efforts with another worksheet while they wait for their classmates to finish. At the same time, students who have not mastered the skill and do not finish the worksheet on time are “rewarded” with the requirement to take the worksheet home to complete, or they finish during another portion of the day, often recess or lunch. Ë Worksheets provide little motivation to learn a skill correctly. There is no immediate correction for mistakes, and often, students do not really care if a mistake is made. When a game is involved, students want and need to get correct answers. The Common Core State Standards for Mathematics, including the Standards for Mathematical Practice, demand this approach change. These are the reasons teachers and teacher leaders must consciously support the idea of using games to support skill development in mathematics.

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How to Use This Book

How to Use This Book There are many ways to effectively utilize this book. Teachers, mathematics leaders, and parents may use this book to engage students in fun, meaningful, practical mathematics learning. These games can be used as a way to help students maintain skill proficiency or remind them of particular skills prior to a critical concept lesson. These games may also be useful during tutorial sessions, or during class when students have completed their work.

Games at Home Parents may use these games to work with their child to learn important skills. The games also provide easier ways for parents to interest their child in learning mathematics rather than simply memorizing facts. In many cases, their child is more interested in listening to explanations than correcting their errors. Parents want to help their children succeed in school, yet they may dread the frequently unpleasant encounters created by completing mathematics worksheets at home. Families can easily use the games in this book by assuming the role of one of the players. At other times, parents provide support and encouragement as their child engages in the game. In either situation, parents are able to work with their children in a way that is fun, educational, and informative.

Games in the Classroom During game play, teachers are provided excellent opportunities to assess students’ abilities and current skill development. Students are normally doing their best and drawing upon their current understanding and ability to play the games, so teachers see an accurate picture of student learning. Some monitoring ideas for teacher assessment include: Ë Move about the room listening and observing Ë Ask student pairs to explain what they are doing Ë Ask the entire class about the game procedures after play Ë Play the game against the class Ë Draw a small group of students together for closer supervision Ë Gather game sheets to analyze students’ proficiencies Ongoing formative assessment and timely intervention are cornerstones of effective classroom instruction. Teachers need to use every available opportunity to make student thinking visible and to respond wisely to what students’ visible thinking reveals. Games are an invaluable instructional tool that teachers need to effectively use.

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How to Use This Book

How to Use This Book (cont.) Students are able to work collaboratively during game play, thus promoting student discourse and deeper learning. The games can also be used to reduce the amount of time students spend completing worksheets. Each game in this book is based upon a common format. This format is designed to assist teachers in understanding how the game activities are played and which standards and mathematical skills students will be practicing. Domain The domain that students will practice is noted at the beginning of each lesson. Each of the five domains addressed in this series has its own icon.

Opera tions and Algebraic Thinki ng

Grand Cham pion Racer Domain Operations and Algebraic Think ing

Standards One or more Common Core State Standards will state the specific skills that students will practice during game play.

• Copy and cut out one set of Grand Champion Word Problem Cards for each player.

Standard Use multiplica tion and divis ion within 100 to solve word prob lems in situations involving equa l groups, arrays, and meas urement quan tities.

• Make 2 cop ies of the Gran d Champion Reco rding Sheet for each player. • Group a s et of three card s for each playe r to play during each round. For example, make four copies of prob lem cards 1–3 for the first round. Place 4 sets of cards in a ziptop bag. E ach group receives ziptop bags labeled Roun ds 1–8.

Number of Pla yers

4 Players

Materials • Grand Cham pion Word Prob lem Cards (page s 30–31) • Grand Cham pion Recording Sheet (page 32) • Grand Cham pion Racer Answ er Key (page 131)

Game Directio ns

1 Distribute materials to playe rs. 2 Each player receives a copy of the first three cards, keeping them facedown.

• ziptop bag s • pencils

Number of Players The number of players varies for each game. Some may include whole-group game play, while others may call for different-size groups.

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Play begins when the teacher says, “Racers, start your engines. Go!”

Get Prepared! Everything a teacher needs to be prepared for game play is noted in the Get Prepared! section. This includes how many copies are needed as well as other tasks that need to be completed with the materials.

Game Directions The directions allow for step-by-step guidance on how to easily implement each game.

Practi ce © Shell Educa tion

All game resources can be found in the Digital Resources. For a complete list of files, see page 129–130.

Materials A materials list is provided for each game to notify the teacher what to have available in order to play the games.

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How to Use This Book

How to Use This Book (cont.) Many games include materials such as game boards, activity cards, score cards, and spinners. You may wish to laminate materials for durability. Game Boards Some game boards spread across multiple book pages in order to make them larger for game play. When this is the case, cut out each part of the game board and tape them together. Once you cut them apart and tape them together, you may wish to glue them to a large sheet of construction paper and laminate them for durability.

Go Team

Activity Cards Some games include activity cards. Once you cut them apart, you may wish to laminate them for durability.

Division

Spinners Some games include spinners. To use a spinner, cut it out from the page. Place the tip of a pencil in the center with a paperclip around it. Use your other hand to flick the other side of the paperclip.

Go Team Di Practice Car

Opera tions and Algebraic Thinki ng

vision

ds

Directions: Cop y and cut out of players. one set of card s

63 ÷ 7 =

48 ÷ 6 =

56 ÷ 7 =

36 ÷ 6 =

49 ÷ 7 =

27 ÷ 9 =

below for each

group

25 ÷ 5 =

72 ÷ 9 =

28 ÷ 7 =

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Correlation to the Standards

Correlation to the Standards Shell Education is committed to producing educational materials that are research and standards based. In this effort, we have correlated all of our products to the academic standards of all 50 United States, the District of Columbia, the Department of Defense Dependent Schools, and all Canadian provinces.

How to Find Standards Correlations To print a customized correlation report of this product for your state, visit our website at http://www.shelleducation.com and follow the on-screen directions. If you require assistance in printing correlation reports, please contact Customer Service at 1-877-777-3450.

Purpose and Intent of Standards Legislation mandates that all states adopt academic standards that identify the skills students will learn in kindergarten through grade twelve. Many states also have standards for Pre–K. This same legislation sets requirements to ensure the standards are detailed and comprehensive. Standards are designed to focus instruction and guide adoption of curricula. Standards are statements that describe the criteria necessary for students to meet specific academic goals. They define the knowledge, skills, and content students should acquire at each level. Standards are also used to develop standardized tests to evaluate students’ academic progress. Teachers are required to demonstrate how their lessons meet state standards. State standards are used in the development of all of our products, so educators can be assured they meet the academic requirements of each state.

Common Core State Standards Many games in this book are aligned to the Common Core State Standards. The standards support the objectives presented throughout the lessons and are provided in the Digital Resources (standards.pdf).

TESOL and WIDA Standards The lessons in this book promote English language development for English language learners. The standards listed on the Digital Resources (standards.pdf) support the language objectives presented throughout the lessons.

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Correlation to the Standards

Standards Correlation Chart Standard

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Game(s)

3.OA.A.2—Interpret whole-number quotients of whole numbers.

Go Team Division (p. 16)

3.OA.A.3—Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.

Grand Champion Racer (p. 28)

3.OA.A.4—Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 x ? = 48, 5 = ÷ 3, 6 x 6 = ?

Math Facts Matchup (p. 33)

3.OA.B.6—Understand division as an unknown‑factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

Serve and Return with Unknown Factors (p. 37)

3.OA.C.7—Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Fact Face-off (p. 45)

3.OA.D.8—Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies, including rounding.

World Series of Word Problems (p. 49)

3.NBT.A.1—Use place value understanding to round whole numbers to the nearest 10 or 100.

Spinning ’Round (p. 58)

3.NBT.A.2—Fluently add and subtract within 1,000, using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Big Number Checkmate (page 64); Sum It Up (p. 71); Submarine Subtraction (p. 75)

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Correlation to the Standards

Standards Correlation Chart (cont.) Standard

Game(s)

3.NBT.A.3—Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

Big Number Checkmate (p. 64)

3.NBT.A.1—Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by parts of size 1/b.

Fraction Action (p. 94)

3.NF.A.3—Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Secret Identity Sleuth (p. 79); Fraction Throwdown (p. 87)

3.NF.A.3a—Understand 2 fractions as equivalent (equal) if they are the same size, or at the same point on a number line.

Secret Identity Sleuth (p. 79)

3.NF.A.3d—Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or , =, or , =, or