Title Page

Jossey-Bass Teacher

Other Math Books by the Muschlas

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

# Jossey-Bass Teacher

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.

# Other Math Books by the Muschlas

• 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).

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).

# Acknowledgments

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.

# Operations and Algebraic Thinking: 3.OA.1

“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.”

## Background

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
1. Ask your students to think about the ways things are grouped so that each group has the same number of items. Present the example of the hamburger rolls that was provided in the Background section. You may suggest other examples, such as sports (the number of starting players per team), board games (4 cards per person), shopping (6 cupcakes per package), school (5 books per student), and so on. Encourage your students to brainstorm other possible groups.
2. Explain that students are to select an equal-sized group and then decide the number of groups they wish to represent. They are to draw a picture that illustrates their groups. For example, if they chose the packages of hamburger rolls, as noted in the Background section, they would draw 3 packages of hamburger rolls with 8 rolls per package.
3. Explain that after they complete their drawings, they are to write a description of their groups and a multiplication sentence.
Closure
Discuss and display students' drawings, descriptions, and multiplication sentences.

# Operations and Algebraic Thinking: 3.OA.2

“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.”

## Background

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
1. Present this situation to your class: Mr. Smith has a class of 30 students. How many different-sized groups can he form?
2. Explain that because Mr. Smith's class has 30 students, 1 counter represents 1 student.
3. Instruct your students to divide their counters into equal groups to represent the students of Mr. Smith's class. They must find how many groups are possible and then sketch the groups on graph paper. Finally, have students write division sentences that represent their sketches.
Closure
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

# Operations and Algebraic Thinking: 3.OA.3

“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.”

## Background

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
1. Explain that word problems involving multiplication and division can be solved by using equations or diagrams. In equations, symbols may be used to represent unknown numbers. For example, in the problem represents the product of which is 15.
2. Distribute copies of the reproducibles. Explain that together the reproducibles contain 24 boxes that have word problems (boxes 1–8), equations or diagrams (boxes 9–16), and answers (boxes 17–24).
3. Explain that students are to cut out each box.
4. Instruct students to start with problem 1. They should find the equation or diagram that matches the problem. Next they should find the answer that matches the problem. Students should continue in the same manner, matching equations, diagrams, and answers for problems 2, 3, and so on. They should place each set of correct “matchings” in separate piles.
Closure
Discuss students' results.
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

# Operations and Algebraic Thinking: 3.OA.4

“Represent and solve problems involving multiplication and division.”

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

## Background

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
1. Explain that students will play equation tic-tac-toe, but note that this is a little different from the standard game of tic-tac-toe. In this game, each student has his or her own board and everyone plays against everyone else at the same time.
2. Distribute the paper. (If you are considering playing more than one round, you might have your students fold their papers in half from top to bottom. Using the front and back of the paper results in four regions, each of which can easily accommodate one tic-tac-toe board. It is likely that you will need to create more equations to play more games.) Instruct your students to draw a tic-tac-toe board on (each region of) their papers as shown.
3. Explain to your students that they are to select any nine numbers from the numbers 1 through 50 and write one number in each space on the tic-tac-toe board. Note that they cannot use any number more than once.
4. Explain that you will present an equation. Students who have the answer on their boards should place an X over the number. There are two ways to win. The first student to get three Xs in a row or along a diagonal wins. If all of the equations have been presented, and no one has three Xs in a row, the student with the most Xs on his or her board is the winner.
5. Begin the game. Present the first equation from the Equation Bank, and continue until someone wins or all of the equations have been used.
Closure
Review the answers after each game to verify the winner. Create equations of your own to play additional games.

# Operations and Algebraic Thinking: 3.OA.5

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

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

## Background

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
1. Hand out copies of the reproducible. Explain to your students that the reproducible contains 20 fact cards. Each card is equivalent to 1 of 4 different values.
2. Explain that students are to cut out the cards. They are then to place each card with the other cards that have the same value. (Note: They should finish with four sets of cards, though not all sets will have the same number of cards.)
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.
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

# Operations and Algebraic Thinking: 3.OA.6

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

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

## Background

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
1. Hand out copies of the reproducibles. Note that “Multiplication, Division, and Factors, I” contains six rows (1 through 6) and that “Multiplication, Division, and Factors, II” contains four rows (7–10). Each row is divided into three parts. The first part contains a division problem. The second part contains a related multiplication sentence that students must complete. The third part contains the answer to the multiplication sentence, which students must provide. Following row 10 is a Number Bank.
2. Explain that students are to cut out the numbers in the Number Bank. They are to glue the correct numbers in the boxes to complete the multiplication sentences. They are also to glue the correct numbers in the boxes for the answers to the multiplication sentences. Note that each multiplication sentence is related to the division problem in its row.
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.
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

# Operations and Algebraic Thinking: 3.OA.7

“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.”

## Background

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
1. Hand out copies of the bingo boards. Explain that there is a Number Bank below the board.
2. Explain that students should randomly fill in each square on their board with a number from the Number Bank. They should not fill in the free space with a number. As they fill in a number, suggest that they cross out the number in the Number Bank so that they will not use the same number twice. Note that some numbers will not be used.
3. Explain the rules of the game. You will call out a multiplication or division problem from the “Problem Bank for Multiplication and Division Bingo.” (Note: The answers are written in parentheses after the problems.) Students who find the answer to the problem on their boards should place a counter on the number. (Note: Having students use counters to place on numbers allows you to use the same bingo board for additional games.) After presenting a problem, place a check beside the problems you use on the Problem Bank so that you do not use the problem again. Continue calling out problems until a student gets bingo.
4. Check the answers the student has covered on his bingo board to make sure he is correct.
Closure
Announce the correct answers and review any problems that students found confusing.

Multiplication and Division Bingo

Problem Bank for Multiplication and Division Bingo

# Operations and Algebraic Thinking: 3.OA.8

“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.”

## Background

Solving two-step word problems requires several steps:

2. Identify what you are to find.
3. Decide what information to use.
4. Write an equation using a letter to stand for the unknown quantity.
5. Solve the equation.

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
1. Review the steps for writing and solving two-step word problems that were presented in the Background of this activity.
2. Hand out copies of the reproducible. Explain that it contains five word problems, each of which is followed by two equations. Students are to select the equation that can be used to solve the problem. They must then solve the problem.
3. Depending on the abilities of your students, you might find it helpful to do the first problem together as a class.
4. Emphasize that after students have selected the correct equation and solved a problem, they must consider whether their answer makes sense by using estimation or mental math. For example, imagine an answer to a problem that the cost of a school lunch is \$175. This is unlikely. A probable mistake here is omission of a decimal point that would make a correct (and reasonable) answer of \$1.75.
Closure
The correct equations are listed, followed by their solution. (1) (2) (3) (4) (5)

Names ____________________________________ Date ____________
Two-Step Word Problems
Directions: Choose the equation, or equations, that describe each problem. Solve the problem. Decide if your answer is reasonable.
1. Mason has 27 new coins to add to his collection. He will put them in a coin album. Each page holds 9 coins. He already has 4 full pages of coins. After he puts the new coins in his album, how many full pages will he have? stands for the total number of pages.
2. Mrs. Sanchez plans to hand out markers to 5 groups of students. She wants each group to have 3 markers. She has 14 markers. How many more markers does she need? stands for the number of additional markers.
3. Audrey is paid \$6 a week for walking Ruffles, Mrs. Hanson's dog. Audrey needs \$54 to buy her brother a birthday present. She has already earned \$12. How many more weeks must she walk Ruffles so that she has enough money to buy the gift? stands for the number of weeks she must work.
4. Sal is decorating 8 cupcakes. He places 6 candies on one of the cupcakes. He places 4 candies on the other 7 cupcakes. How many candies will he need? stands for the number of candies he needs.
5. Carla is taking 4 packages of soda to a family picnic. Each package has 6 cans. 20 people are at the picnic. Each person drinks one can of soda. How many cans will be left over? stands for the number of soda cans left over.

# Operations and Algebraic Thinking: 3.OA.9

“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.”

## Background

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.