Cluster 1: Represent and solve problems involving multiplication and division. (Major Cluster)Archived

This website is a game that incorporates algebraic thinking with patterning. It can be used for third or fourth grade students.

Type: Educational Game

This interactive Flash applet offers three ways for students to practice basic fact skills related to multiplication and division. Users control the challenge level by choosing the size of the blank multiplication grid displayed by the applet. In Multiply mode users type in the product that completes a multiplication sentence. In Factor mode users click a grid cell that matches a given product. In Divide mode users type in a missing factor in the displayed multiplication sentence. A sound effect and timing feature are optional.

Type: Educational Game

Students are given multiplication and division equations within 100 and asked to find the missing numbers. The missing numbers are presented in all positions.

Type: Formative Assessment

Students are given multiplication equations with products within 50 and are asked to find missing numbers. The missing numbers are presented in all positions.

Type: Formative Assessment

Students are given division equations involving numbers within 50 and are asked to find missing numbers. The missing numbers are presented in all positions.

Type: Formative Assessment

Students are given multiplication and division equations within 50 and are asked to find missing numbers. The missing numbers are presented in all positions.

Type: Formative Assessment

Students are asked to solve a division equation and then interpret the quotient by writing a word problem that can be modeled by the equation.

Type: Formative Assessment

Students are asked to explain how to use a number line for dividing, in the context of a word problem.

Type: Formative Assessment

Students are asked to illustrate a division problem and write a corresponding equation.

Type: Formative Assessment

Students are given division word problem and asked to determine how it might have been solved and what the quotient means.

Type: Formative Assessment

Students are asked to model a multiplication and a division problem that involve measurement quantities with multiplication and division equations and then solve each problem.

Type: Formative Assessment

Students are asked to model an equal groups and an array problem in which the number of groups is unknown with multiplication or division equations and then solve each problem.

Type: Formative Assessment

Students are asked to model an equal groups and an array problem in which the product is unknown with multiplication or division equations and then solve each problem.

Type: Formative Assessment

Students are asked to model an equal groups and an array problem in which the group size is unknown with multiplication or division equations and then solve each problem.

Type: Formative Assessment

Students are asked to write multiplication word problems prompted by pictures and then to write both an addition and a multiplication expression that can be used to solve the problem.

Type: Formative Assessment

Students are given a context for a multiplication problem and asked to determine how to solve it and what the product means.

Type: Formative Assessment

Students are asked to explain how to use a number line for multiplying, in the context of a word problem.

Type: Formative Assessment

Students are asked to explain what 5 x 7 means and to provide a real-world context for 5 x 7.

Type: Formative Assessment

Through the use of a theatrical performance the students will use math counter manipulatives to make equal groups, demonstrating understanding of the concept of division.

Type: Lesson Plan

This lesson is a hands-on activity that includes multiplication using arrays. The lesson also serves as a great transition from repeated addition to multiplication.

Type: Lesson Plan

Students will learn how multiplication is related to repeated addition and use different strategies to find the product of equal groups situations.

Type: Lesson Plan

Students will learn how to represent and count equal groups through the use of literature and situational story problems. Using the book Each Orange Had 8 Slices, students will use manipulatives to find the total number of objects in a collection of equal groups. Students will learn to write corresponding multiplication equations.

Type: Lesson Plan

“How many Circles? How many Stars?” is an activity that will give students a visual representation of multiplication. It will also help students see multiplication as the combining of equal-size groups that can be represented with a multiplication equation.

Type: Lesson Plan

Students will develop their understanding of arrays by building arrays using hands on activities.  Students will have the opportunity to play a game to practice their skills with arrays. 

Type: Lesson Plan

The lesson is developed to introduce the bridging concept of repeated addition to multiplication. Students will be able to work with a partner and build flips books to demonstrate understating of grouping to multiply.

Type: Lesson Plan

This lesson builds upon student knowledge of arrays to using the Van de Walle 100-Dot Matrix model to solve multiplication problems involving rows and columns.

Type: Lesson Plan

This introductory lesson uses word problems to help students make connections between arrays and multiplication with single and/or two-digit quantities within 100.

Type: Lesson Plan

In this lesson, students will learn to use the structure of array frames to build familiarity and fluency with the array as a tool. Students will explore multiplication by solving several multiplication word problems involving rows and columns situations using the array as a representation.

Type: Lesson Plan

Students will begin with the use of manipualtives to solve for unknown factors by building arrays. They will progress to drawn models as mastery is shown with manipulatives. 

Type: Lesson Plan

In this MEA, third graders will be required to rank musical instrument lesson packages based on the length, frequency, and quality of the lessons. Part of the task involves students figuring out the elapsed time of the lessons based on their start and stop times. They will also need to figure out the total weekly cost of the lessons based on the number of lessons offered per week.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

This is an introductory lesson to prepare students to move from using repeated addition to using multiplication to represent equal groups situations.

Type: Lesson Plan

The 3rd grade chess club members will make two wish lists on how to spend $75 on chess related materials. Then they have to make two new wish lists on how to spend $750 on chess related materials.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

In this lesson, students will look at different carnival rides and will determine which ride will make the most profit by looking at factors such as number of tickets per ride, the cost per ticket, the length of the ride, the number of hours the ride is open and the cost to operate the ride. Students will need to use different operations in order to solve the tasks and will be required to do multi-steps.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

This 3rd grade MEA asks students to work as a team to figure out which candidate is the best possible choice for the 8th grade boys' basketball coach. They will have to analyze data, decide on a procedure, and create a ranking system to choose the best candidate. They are also given multiplication and division problems based on the data.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

This task involves having students look at three different fish tank sizes and determine, using a data list, which fish will fit in these fish tanks based on their size. They will also need to look at other characteristics to determine how to group the fish together. Students will have to either multiply, divide or add repeatedly in order to find different solutions on how to place the fish in each tank size.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Third grade students will decide which performing arts facility their parents should choose for them to take group singing lessons at. They will apply multiplication, division, and time skills for telling time to the nearest minute and time intervals. Students will work collaboratively as a group to analyze this Model Eliciting Activity (MEA), and engage in collaborative discussion that involves higher level critical thinking. They will write argumentation letters on which performing arts facility is the best choice.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

In this lesson, students will use pictures in arrays and groups to write multiplication story problems, write an equation, solve the problem, and identify the factors and products.

Type: Lesson Plan

Students will solve multiplication and division word problems by drawing arrays and writing the related equation.

Type: Lesson Plan

The lesson uses a movie making theme to teach the characteristics and purpose of arrays, as well as the vocabulary, factor and product.

Type: Lesson Plan

Students will be able to use counters to create equal groups and write multiplication equations to represent these representations.

Type: Lesson Plan

This lesson allows students to use everyday objects to understand equal groups by representing a total number of objects using rectangular arrays and repeated addition equations. The lesson uses "The Doorbell Rang" by Pat Hutchins to engage students during the lesson and to make a connection by using literacy in mathematics. This lesson will provide a foundation for the conceptual understanding of division by creating equal groups using arrays and repeated addition.

Type: Lesson Plan

In this MEA, students will rank pets from most family friendly to least family friendly by considering data such as purchase price, cost to feed, cleanliness, etc. as well as notes regarding the physical description of the pet. In the twist, students will be given information on additional pets as well as information on cleanliness and life expectancy. Students may need to make trade-offs in regards to cost to adopt, feed, and house along with life expectancy, ease of clean up, etc.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

This is an introductory lesson to explore the use of arrays to solve multiplication problems. Students build arrays and save the arrays in a class Multiplication Chart. They learn to use arrays to find products and factors, and by placing them in the Multiplication Chart, they learn how to read the chart. They learn how to write equations to represent situations that are modeled with arrays. An overall theme is the organization of the multiplication chart and how it includes arrays within.

Type: Lesson Plan

The definition of the Zero Property of Multiplication will be analyzed, modeled and practiced.   

Type: Lesson Plan

In this lesson, students will learn to solve division problems by relating them to multiplication facts. Practice materials focus on the 6's and 8's multiplication facts.

Type: Lesson Plan

In this lesson students will model partitive division through the real-world activity of a pet store owner.

Type: Lesson Plan

Students work together to create arrays to represent given numbers.

Type: Lesson Plan

In this lesson, students will understand the concept of arrays and will be able to create/draw an array for multiplication sentences. Engaging center game is used to help students with concrete visual representation of multiplication sentences.

Type: Lesson Plan

In this lesson students will use Cheerios to solve multiplication equations relating 3 whole numbers from word problems that include missing factors ranging from one through ten. Students will also argue the validity of multiplication equations that include missing factors and products with corresponding word problems.

Type: Lesson Plan

This is a hands-on lesson for introducing and practicing building arrays to create models that represent the distributive property of multiplication, and then using those arrays to draw models of the equations they represent.

Type: Lesson Plan

In this lesson, the students will work in independently or in small groups to write equations to represent situations as well as their own math riddles around the concepts of multiplication. The teacher will use the book, The Grapes of Math by Greg Tang, to support this lesson.

Type: Lesson Plan

This 3rd grade MEA asks students to work as a team to figure out which product would be the best choice for their fundraiser for their field trip. They will compare two vendor's products and make a decision about which product would be the best option for their school.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

In this hands-on math exploration, students will use knowledge of estimation and multiplication to develop strategies for estimating how many seeds are in a medium-sized pumpkin.

Type: Lesson Plan

This lesson plan can be used to introduce the concept of multiplication to students through the use of literature. The story Amanda Bean's Amazing Dream is used to demonstrate the different ways to count items and how multiplication can make that process much faster.

Type: Lesson Plan

In this lesson students will be creating, describing, and analyzing arrays as they relate to multiplication. In addition, they will be working on hands on activities that allow them to justify their answers and prove their reasoning.

Type: Lesson Plan

In this lesson, students will learn that in some word problems too much information is given. They will learn to identify what information is needed to solve a single digit multiplication problem and what is "additional information" or way too much! With this information, they will represent their answers using arrays and explain their thinking. This is a good lesson to use after students have become comfortable with multiplication and prior to introducing multi-step problems.

Type: Lesson Plan

Come play with Marty the monkey as he teaches you how to understand the concept of multiplication in this interactive tutorial. 

Type: Original Student Tutorial

Allie learns to be fair when she shares and she learns more about division in this interactive tutorial.

Type: Original Student Tutorial

PowerPoint presentation showing the relationship between arrays, multiplication, and repeated addition.

Type: Presentation/Slideshow

Both of the questions are solved by the division problem 12÷3 but what happens to the ribbon is different in each case. The problem can be solved with a drawing of a tape diagram or number line. For problem 1, the line must be divided into 3 equal parts. The second problem can be solved by successive subtraction of 3 feet to see how many times it fits in 12.

Type: Problem-Solving Task

The first of these is a multiplication problem involving equal-sized groups. The next two reflect the two related division problems, namely, "How many groups?" and "How many in each group?"

Type: Problem-Solving Task

In this task, the students are not asked to find an answer, but are asked to analyze the problems and explain their thinking. In the process, they are faced with varying ways of thinking about multiplication.

Type: Problem-Solving Task

The purpose of this task is for students to solve problems involving the four operations and draw a scaled bar graph to represent a data set with several categories.

Type: Problem-Solving Task

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

In this activity, the students demonstrate that numbers can be used to describe various quantities and relationships between quantities. Students gain experience adding, subtracting, multiplying, and dividing - building their understanding of how numbers are put together and taken apart. Students connect what they know to symbolic representation using number sentences.

Type: Teaching Idea

A measurement activity to give students experience with the grouping model of division and practice with rulers and tape measures.

Type: Teaching Idea

The lesson in narrative form gives students experience with the partitioning (sharing) model of division. "The context for the lesson is Sheila Bruce's book Everybody Wins! , Kane Press, 2001, in which Oscar, Emmy, Hugo, and Tony calculate how to share pizzas, baseball tickets, bubble gum, and more.

This narrative is from the introductory lesson in Maryann Wickett, Susan Ohanian, and Marilyn Burns's book, Teaching Arithmetic: Lessons for Introducing Division, Grades 3–4 (Math Solutions Publications,2002). This book is a revision of Math By All Means, Unit Division, Grades 3–4." (from Math Solutions Professional Development)

Type: Teaching Idea

List of five children's books with a multiplication focus (found on NCTM Illuminations site under "All About Multiplication").

Type: Text Resource

Use a picture and understanding of multiplication to solve a division word problem. Watch out for unnecessary information.

Type: Tutorial

In this Khan Academy video tutorial, learn to use arrays and repeated addition to multiply. This is not an introductory video to either concept, to either concept. An array of 8 items is used to show how one array can be represented in multiple ways, using different factors of the whole.

Type: Tutorial

In this Khan Acadmey tutorial video, learn to use arrays to show different groups of objects while relating this to multiplication.

Type: Tutorial

In this Khan Academy tutorial vidoe, learn to use arrays and repeated addition to visualize multiplication.

Type: Tutorial

This collection of 10 lessons uses children's literature to engage students in addition, subtraction, multiplication, and division. The lesson arrangement is flexible and adaptable for any scope and sequence.

Type: Unit/Lesson Sequence

This fun game lets the learners use their multiplication skills to beat the computer. Both the learner and the computer take turns moving one marker at a time. Whoever get 4 in a row first will win the game.

Type: Virtual Manipulative

The students will be given mutiplication and division problems which they must answer. They also have the option of being given a number then stating the factors of how that number was attained using either multiplication or division.

Type: Virtual Manipulative

This tool helps students better understand that equality is a relationship and not an operational command to "find the answer." The applet features a pan balance that allows the student to input each half of an equation in the pans, which responds to the numerical expression's value by raising, lowering or balancing.

Type: Virtual Manipulative