Table of Contents

Title Page

Copyright

Jossey-Bass Teacher

Other Math Books by the Muschlas

About this Book

About the Authors

Acknowledgments

Section 1: Standards and Activities for Grade 3

Operations and Algebraic Thinking: 3.OA.1

Operations and Algebraic Thinking: 3.OA.2

Operations and Algebraic Thinking: 3.OA.3

Operations and Algebraic Thinking: 3.OA.4

Operations and Algebraic Thinking: 3.OA.5

Operations and Algebraic Thinking: 3.OA.6

Operations and Algebraic Thinking: 3.OA.7

Operations and Algebraic Thinking: 3.OA.8

Operations and Algebraic Thinking: 3.OA.9

Number and Operations in Base Ten: 3.NBT.1

Number and Operations in Base Ten: 3.NBT.2

Number and Operations in Base Ten: 3.NBT.3

Number and Operations—Fractions: 3.NF.1

Number and Operations—Fractions: 3.NF.2

Number and Operations—Fractions: 3.NF.3

Measurement and Data: 3.MD.1

Measurement and Data: 3.MD.2

Measurement and Data: 3.MD.7

Measurement and Data: 3.MD.8

Geometry: 3.G.1

Geometry: 3.G.2

Section 2: Standards and Activities for Grade 4

Operations and Algebraic Thinking: 4.OA.1

Number and Operations in Base Ten: 4.NBT.3

Number and Operations in Base Ten: 4.NBT.4

Number and Operations in Base Ten: 4.NBT.5

Number and Operations in Base Ten: 4.NBT.6

Number and Operations—Fractions: 4.NF.1

Number and Operations—Fractions: 4.NF.2

Number and Operations—Fractions: 4.NF.3

Number and Operations—Fractions: 4.NF.4

Number and Operations—Fractions: 4.NF.5

Number and Operations—Fractions: 4.NF.6

Number and Operations—Fractions: 4.NF.7

Measurement and Data: 4.MD.1

Measurement and Data: 4.MD.2

Measurement and Data: 4.MD.3

Measurement and Data: 4.MD.4

Measurement and Data: 4.MD.5

Measurement and Data: 4.MD.6

Measurement and Data: 4.MD.7

Geometry: 4.G.1

Geometry: 4.G.2

Geometry: 4.G.3

Section 3: Standards and Activities for Grade 5

Operations and Algebraic Thinking: 5.OA.1

Operations and Algebraic Thinking: 5.OA.2

Operations and Algebraic Thinking: 5.OA.3

Number and Operations in Base Ten: 5.NBT.1

Number and Operations in Base Ten: 5.NBT.2

Number and Operations in Base Ten: 5.NBT.3

Number and Operations in Base Ten: 5.NBT.4

Number and Operations in Base Ten: 5.NBT.5

Number and Operations in Base Ten: 5.NBT.6

Number and Operations in Base Ten: 5.NBT.7

Number and Operations—Fractions: 5.NF.1

Number and Operations—Fractions: 5.NF.2

Number and Operations—Fractions: 5.NF.3

Number and Operations—Fractions: 5.NF.4

Number and Operations—Fractions: 5.NF.5

Number and Operations—Fractions: 5.NF.6

Number and Operations—Fractions: 5.NF.7

Measurement and Data: 5.MD.1

Measurement and Data: 5.MD.2

Measurement and Data: 5.MD.3

Measurement and Data: 5.MD.4

Measurement and Data: 5.MD.5

Geometry: 5.G.1

Geometry: 5.G.2

Geometry: 5.G.3

Geometry: 5.G.4

Index

Cover design by Wiley

Cover art by Thinkstock

Cover image by © iStockphoto.com/jenifoto

Copyright © 2014 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla-Berry. All rights reserved.

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**Library of Congress Cataloging-in-Publication Data**

Library of Congress Cataloging-in-Publication Data has been applied for and is on file with the Library of Congress.

ISBN 978-1-118-71033-3 (pbk); ISBN 978-1-118-83552-4 (ebk); ISBN 978-1-118-71044-9 (ebk)

Jossey-Bass Teacher provides educators with practical knowledge and tools to create a positive and lifelong impact on student learning. We offer classroom-tested and research-based teaching resources for a variety of grade levels and subject areas. Whether you are an aspiring, new, or veteran teacher, we want to help you make every teaching day your best.

From ready-to-use classroom activities to the latest teaching framework, our value-packed books provide insightful, practical, and comprehensive materials on the topics that matter most to K–12 teachers. We hope to become your trusted source for the best ideas from the most experienced and respected experts in the field.

*Geometry Teacher's Activities Kit: Ready-to-Use Lessons and Worksheets for Grades 6–12**Math Smart!: Over 220 Ready-to-Use Activities to Motivate and Challenge Students, Grades 6–12**Algebra Teacher's Activities Kit: 150 Ready-to-Use Activities with Real-World Applications**Math Games: 180 Reproducible Activities to Motivate, Excite, and Challenge Students, Grades 6–12**The Math Teacher's Book of Lists, 2nd Edition**The Math Teacher's Problem-a-Day, Grades 4–8: Over 180 Reproducible Pages of Quick Skill Builders**Hands-On Math Projects with Real-Life Applications, Grades 3–5**Hands-On Math Projects with Real-Life Applications: Grades 6–12, 2nd Edition**Math Teacher's Survival Guide: Practical Strategies, Management Techniques, and Reproducibles for New and Experienced Teachers, Grades 5–12**The Algebra Teacher's Guide to Reteaching Essential Concepts and Skills: 150 Mini-Lessons for Correcting Common Mistakes**Teaching the Common Core Math Standards with Hands-On Activities, Grades 6–8**Math Starters: 5- to 10-Minute Activities Aligned with the Common Core Math Standards, Grades 6–12, 2nd Edition*

The Common Core State Standards Initiative for Mathematics identifies the concepts, skills, and practices that students should understand and apply at their grade level. Mastery of these Standards at the elementary level will enable students to successfully move on to middle school mathematics.

*Teaching the Common Core Math Standards with Hands-On Activities, Grades 3–5* offers a variety of activities that support instruction of the Standards. The Table of Contents provides a list of the Standards and supporting activities, enabling you to easily find material for developing your lessons. The book is divided into three sections:

- Section 1: Standards and Activities for Grade 3
- Section 2: Standards and Activities for Grade 4
- Section 3: Standards and Activities for Grade 5

The book is designed for easy implementation. The activities build on concepts and skills that you have already taught and expand the scope of your instruction through reinforcement and enrichment. Each activity is preceded by the Domain, which is a group of related Standards, followed by the specific Standard that the activity addresses. For example, “Operations and Algebraic Thinking: 4.OA.3” refers to the Domain, which is Operations and Algebraic Thinking, Grade 4, and Standard 3. Next, you will find background information on the topic, the title and a brief summary of the activity, special materials needed for the activity, and any special preparation that is necessary. Where applicable, the activities are identified with icons that indicate a major component of the activity will be cooperative learning , technology , or real-world focus . All of the activities include specific steps for implementation, and many include reproducibles.

Each standard for grades 3–5 is supported by at least one activity. The typical activity can be completed in a single class period and focuses on application of concepts or skills, demonstration of understanding, or communication about math. Students may be required to solve problems; create mathematical models, charts, and graphs; conduct investigations with both physical and virtual manipulatives; play mathematical games; and write problems and explanations. Many of the activities are open-ended; however, an answer key is provided for those problems requiring specific answers.

Because many activities offer multiple avenues for development and learning, we encourage you to modify them in ways that best meet the needs of your students. For example, in some activities where we suggest that students work in pairs or groups of three, you may feel that your students will gain the most from the activity by working individually. Conversely, for some activities, rather than having students work individually, you may find it more practical to have them work with a partner. For activities that require the use of computers and the Internet, instead of having students work at a Web site on their own, you may prefer to use a computer and digital projector to lead your students through the Web site in a whole-class activity. You should present each activity in a manner that satisfies your objectives and is appropriate for the capabilities of your students.

To enhance your instruction of the activities, consider the following:

- Use a variety of instructional tools, such as traditional boards, whiteboards, overhead projectors, computers, scanners, digital projectors, and document cameras to present material in an effective and interesting manner.
- Preview every Web site and work through any exercises so that you are better able to offer guidance during the activity.
- Demonstrate the use of Web sites to your students before they begin working at the site.
- Paste the URLs of Web sites in your browser to make the Web site easy to access.
- For activities that require students to cut out number cards, copy the cards on card stock and laminate them to preserve them for future use.
- For activities that include games, provide a homework pass or other prize to the winners.

We hope that the activities in this resource prove to be both interesting and enjoyable for you and your students, and that the activities help your students master the math concepts and skills of the Standards at your grade level. We extend to you our best wishes for a successful and rewarding year.

Judith A. Muschla

Gary Robert Muschla

Erin Muschla-Berry

**Judith A. Muschla** received her BA in mathematics from Douglass College at Rutgers University and is certified to teach K–12. She taught mathematics in South River, New Jersey, for over twenty-five years at various levels at both South River High School and South River Middle School. As a team leader at the middle school, she wrote several math curriculums, coordinated interdisciplinary units, and conducted mathematics workshops for teachers and parents. She also served as a member of the state Review Panel for New Jersey's Mathematics Core Curriculum Content Standards.

Together, Judith and Gary Muschla have coauthored a number of math books published by Jossey-Bass: *Hands-On Math Projects with Real-Life Applications, Grades 3–5* (2009); *The Math Teacher's Problem-a-Day, Grades 4–8* (2008); *Hands-On Math Projects with Real-Life Applications, Grades 6–12* (1996; second edition, 2006); *The Math Teacher's Book of Lists* (1995; second edition, 2005); *Math Games: 180 Reproducible Activities to Motivate, Excite, and Challenge Students, Grades 6–12* (2004); *Algebra Teacher's Activities Kit* (2003); *Math Smart! Over 220 Ready-to-Use Activities to Motivate and Challenge Students, Grades 6–12* (2002); *Geometry Teacher's Activities Kit* (2000); and *Math Starters! 5- to 10-Minute Activities to Make Kids Think, Grades 6–12* (1999).

**Gary Robert Muschla** received his BA and MAT from Trenton State College and taught in Spotswood, New Jersey, for more than twenty-five years at the elementary school level. He is a successful author and a member of the Authors Guild and the National Writers Association. In addition to math resources, he has written several resources for English and writing teachers; among them are *Writing Workshop Survival Kit* (1993; second edition, 2005); *The Writing Teacher's Book of Lists* (1991; second edition, 2004); *Ready-to Use Reading Proficiency Lessons and Activities, 10th Grade Level* (2003); *Ready-to-Use Reading Proficiency Lessons and Activities, 8th Grade Level* (2002); *Ready-to-Use Reading Proficiency Lessons and Activities, 4th Grade Level* (2002); *Reading Workshop Survival Kit* (1997); and *English Teacher's Great Books Activities Kit* (1994), all published by Jossey-Bass.

**Erin Muschla-Berry** received her BS and MEd from The College of New Jersey. She is certified to teach grades K–8 with Mathematics Specialization in grades 5–8. She currently teaches math at Monroe Township Middle School in Monroe, New Jersey, and has presented workshops for math teachers for the Association of Mathematics Teachers of New Jersey. She has coauthored four books with Judith and Gary Muschla for Jossey-Bass: *Math Starters, 2nd Edition: 5- to-10 Minute Activities Aligned with the Common Core Standards, Grades 6–12* (2013); *Teaching the Common Core Math Standards with Hands-On Activities, Grades 6–8* (2012); *The Algebra Teacher's Guide to Reteaching Essential Concepts and Skills* (2011); *The Elementary Teacher's Book of Lists* (2010); and *Math Teacher's Survival Guide, Grades 5–12* (2010).

We thank Jeff Corey Gorman, EdD, assistant superintendent of Monroe Township Public Schools, Chari Chanley, EdS, principal of Monroe Township Middle School, James Higgins, vice principal of Monroe Township Middle School, and Scott Sidler, vice principal of Monroe Township Middle School, for their support.

We also thank Kate Bradford, our editor at Jossey-Bass, for her guidance and suggestions on yet another book.

We want to thank Diane Turso for proofreading this book and putting it into its final form, as she has done with so many others in the past.

We appreciate the support of our many colleagues who, over the years, have encouraged us in our work.

And, of course, we wish to acknowledge the many students we have had the satisfaction of teaching.

“Represent and solve problems involving multiplication and division.”

1. “Interpret products of whole numbers, e.g., interpret as the total number of objects in 5 groups of 7 objects each.”

When items in equal-sized groups are combined, multiplication can be used to find the total number of items. For example, hamburger rolls are sold in packages of 8 rolls. If 3 bags are purchased, you can multiply to find the total number of rolls. Three packages (groups) of 8 rolls can be expressed as The product is 24 rolls. Note also that but in this case there are 8 groups of 3 items per group.

Activity: Combining Groups

Working in pairs or groups of three, students will generate ways that groups of items can be represented in real-world situations. They will then draw an illustration of the groups and write a description and a related multiplication sentence.

Materials

Drawing paper; crayons; colored pencils for each pair or group of students.

Procedure

Closure

Discuss and display students' drawings, descriptions, and multiplication sentences.

“Represent and solve problems involving multiplication and division.”

2. “Interpret whole-number quotients of whole numbers, e.g., interpret as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.”

Division is the process of separating a quantity into equal groups. It is the inverse (opposite) of multiplication, which is the process of combining equal groups.

Activity: Breaking into Groups

Working in pairs or groups of three, students will find the number of groups that can be formed from a class of 30 students. They will represent their groups on graph paper.

Materials

Two to three sheets of graph paper; 30 counters for each pair or group of students.

Procedure

Closure

Discuss your students' answers.

Answers

1 group of 30; 2 groups of 15; 3 groups of 10; 5 groups of 6; 6 groups of 5; 10 groups of 3; 15 groups of 2; 30 “groups” of 1

“Represent and solve problems involving multiplication and division.”

3. “Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.”

Diagrams and equations may be used with the operations of multiplication and division to solve word problems. Letters are commonly used to represent unknown numbers in equations.

Activity: It's a Match

Working in groups, students will match word problems with equations, diagrams, and answers.

Materials

Scissors; one copy of reproducibles, “Matchings, I” and “Matchings, II,” for each group of students.

Procedure

Closure

Discuss students' results.

Answers

The card number of the problem, equation or diagram, and answer are listed in order: 1, 12, 23; 2, 13, 18; 3, 15, 19; 4, 14, 17; 5, 10, 20; 6, 11, 24; 7, 16, 22; 8, 9, 21

Matchings, I

Matchings, II

“Represent and solve problems involving multiplication and division.”

4. “Determine the unknown whole number in a multiplication or division equation relating three whole numbers.”

To find the missing number in a multiplication or division equation, students should know their basic facts. For example, knowing that is necessary to find the missing number in equations such as and

Activity: Equation Tic-Tac-Toe

In a twist on the traditional game of tic-tac-toe, students will complete tic-tac-toe boards by randomly choosing and writing nine numbers from 1 to 50 on their boards. After the boards are completed, the teacher presents an equation to the class. If the answer to the equation is on a student's board, the student writes an X over it. The first person who gets three Xs in a row or along a diagonal wins. If no student gets three Xs in a row or along a diagonal, the student who has the most Xs after completing all of the equations is the winner.

Materials

One sheet of unlined paper for each student.

Procedure

Closure

Review the answers after each game to verify the winner. Create equations of your own to play additional games.

“Understand properties of multiplication and the relationship between multiplication and division.”

5. “Apply properties of operations as strategies to multiply and divide.”

Applying mathematical properties can help students compute by changing the order of factors, grouping factors, and expressing a factor as the sum of two numbers.

- The commutative property of multiplication, states that the order of multiplying two factors does not affect their product.
- The associative property of multiplication, states that the order of grouping factors does not affect their product.
- The distributive property, states that the product of a factor and a sum is equal to multiplying each addend in the sum by the factor and then adding the products.

Although students need not know the names of these properties to complete this activity, an intuitive grasp of the properties will be helpful.

Activity: Applying Properties

Working in pairs or groups of three, students will apply properties of operations to complete math equations.

Materials

Scissors; one copy of reproducible, “Fact Cards,” for each pair or group of students.

Procedure

Closure

Check students' results. Ask your students to share strategies they used to arrange their cards correctly. Emphasize that problems can often be solved in different ways.

Answers

Cards that equal 60: 1, 6, 14, 17, 18, and 20. Cards that equal 40: 2, 7, 9, 15, and 19. Cards that equal 27: 3, 12, and 16. Cards that equal 24: 4, 5, 8, 10, 11, and 13.

Fact Cards

“Understand properties of multiplication and the relationship between multiplication and division.”

6. “Understand division as an unknown-factor problem.”

Since division and multiplication are inverse operations, every division problem has a related multiplication problem.

For example, can be posed as “3 times what number is 18?” Students can solve this problem by finding the missing factor of 18. The missing factor is 6.

Activity: Number Scramble

Working in pairs or groups of three, students will be given a division problem. They will find the number that completes a multiplication sentence and then find the missing factor.

Materials

Scissors; glue sticks; one copy of reproducibles, “Multiplication, Division, and Factors, I” and “Multiplication, Division, and Factors, II,” for each pair or group of students.

Procedure

Closure

Discuss students' results. While still working in pairs or groups, for more practice, ask your students to write a division problem for their partners. Their partner should then write a related multiplication sentence.

Answers

The missing numbers in each row follow: **(1)** 5, 5, 25; **(2)** 6, 4, 24; **(3)** 3, 2, 6; **(4)** 3, 3, 9; **(5)** 2, 4, 8; **(6)** 8, 5, 40; **(7)** 3, 9, 27; **(8)** 5, 6, 30; **(9)** 8, 3, 24; **(10)** 6, 9, 54

Multiplication, Division, and Factors, I

Multiplication, Division, and Factors, II

“Multiply and divide within 100.”

7. “Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that one knows that ) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.”

The first step to mastering multiplication and division is to understand how these operations are related. The next step is to be able to multiply and divide quickly and accurately all products of two one-digit numbers. This is achieved through practice and memorization.

Activity: Multiplication and Division Bingo

Students will create a math bingo board by placing numbers from a Number Bank in each square on the board. The teacher will call out multiplication and division problems. If the answer is on the student's board, the student will cover the square with a counter. The first student to cover the squares in a row, column, or diagonal is the winner.

Materials

24 1-inch diameter (or smaller) counters; reproducible, “Multiplication and Division Bingo,” for each student. Optional: One copy of reproducible, “Problem Bank for Multiplication and Division Bingo,” for the teacher.

Procedure

Closure

Announce the correct answers and review any problems that students found confusing.

Multiplication and Division Bingo

Problem Bank for Multiplication and Division Bingo

“Solve problems involving the four operations, and identify and explain patterns in arithmetic.”

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.”

Solving two-step word problems requires several steps:

Activity: Which Equation?

Working in pairs or groups of three, students will choose an equation that can be used to solve word problems. They will then solve the problem.

Materials

Reproducible, “Two-Step Word Problems,” for each pair or group of students.

Procedure

Closure

Discuss the answers to the problems, including students' assessments of the reasonableness of their answers. Ask how they determined if an answer made sense.

Answers

The correct equations are listed, followed by their solution. **(1)** **(2)** **(3)** **(4)** **(5)**

Two-Step Word Problems

Directions: Choose the equation, or equations, that describe each problem. Solve the problem. Decide if your answer is reasonable.

“Solve problems involving the four operations, and identify and explain patterns in arithmetic.”

9. “Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.”

Patterns abound in mathematics. Multiples present students with a variety of patterns. Some are noted below:

- All multiples of 2, 4, 6, 8, and 10 are even.
- Every multiple of 4, 6, 8, and 10 is a multiple of 2.
- Every multiple of 6 and 9 is a multiple of 3.
- Every multiple of 10 is a multiple of 5.