MAFS.3.OA.1.3

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.

Clarifications

Examples of Opportunities for In-Depth Focus

Word problems involving equal groups, arrays, and measurement quantities can be used to build students’ understanding of and skill with multiplication and division, as well as to allow students to demonstrate their understanding of and skill with these operations.

General Information
Subject Area: Mathematics
Domain-Subdomain: Operations and Algebraic Thinking
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Represent and solve problems involving multiplication and division. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications

• Assessment Limits :
All values in items may not exceed whole number multiplication facts of 10 x 10 or the related division facts. Items may not contain more than one unknown per equation. Items may not contain the words “times as much/many.”
• Calculator :

No

• Context :

Required

Sample Test Items (2)
• Test Item #: Sample Item 1
• Question: Craig has 72 grapes. He separates the grapes into 9 equal groups. How many grapes are in each group?
• Difficulty: N/A
• Type: EE: Equation Editor

• Test Item #: Sample Item 2
• Question: Mr. Soto gave a total of 54 fire-safety posters to 9 schools. He gave the same number of posters to each school.

What is the total number of posters that Mr. Soto gave to each school?

• Difficulty: N/A
• Type: EE: Equation Editor

Related Courses

This benchmark is part of these courses.
5012050: Grade Three Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7712040: Access Mathematics Grade 3 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022 (current), 2022 and beyond)
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.3.OA.1.AP.3a: Solve and check one- or two-step word problems requiring multiplication or division with the product or quotient up to 50.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Assessments

Sample 4 - Third Grade Math State Interim Assessment:

This is a State Interim Assessment for third grade.

Type: Assessment

Sample 3 - Third Grade Math State Interim Assessment:

This is a State Interim Assessment for third grade.

Type: Assessment

Formative Assessments

Measurement Problems:

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

Finding the Number of Groups:

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

Finding an Unknown Product:

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

Finding the Group Size:

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

Lesson Plans

The Doorbell Rang - A Lesson in Division and Theater:

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

Cheezy Arrays:

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

From Array to Van De Walle 100-Dot Matrix:

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

Type: Lesson Plan

Bridging Addition and Multiplication with Word Problems:

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

The Array Frame, your best friend:

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 solve several multiplication word problems using the array as a representation.

Type: Lesson Plan

How Long is Your Music Lesson?:

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.

Type: Lesson Plan

Chess Wish List:

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.

Type: Lesson Plan

Cupid's Carnival Rides:

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.

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.

Type: Lesson Plan

Florida Fish Aquarium Challenge:

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.

Type: Lesson Plan

Let's Multiply using Groups and Arrays:

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

This lesson allows students to use everyday objects in order to understand equal shares. 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.

Type: Lesson Plan

Pick a Pet:

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.

Type: Lesson Plan

Arrays Show the Way to the Multiplication Chart:

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

Hungry Zero:

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

Type: Lesson Plan

Pet Store Partitive Division:

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

Type: Lesson Plan

Chip Chip Array!:

Students work together to create arrays to represent given numbers.

Type: Lesson Plan

Array to Multiply:

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

Tasty Algebra: Using toasted O cereal to find the missing factor in a multiplication equation.:

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

Apples, Oranges, and Bananas of Math?:

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

How Many Seeds in a Pumpkin?:

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

Introduction to Multiplication using Literature :

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

Magnificent, Amazing Multiplication Arrays!:

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

Way Too Much!:

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

Lesson Study Resource Kit

Operations and Algebraic Thinking Lesson Study Resource Kit – Third Grade:

This lesson study resource kit can be used to guide and support teams of third grade teachers as they engage in lesson study focused on the academic standards in the Operations and Algebraic Thinking domain.

Type: Lesson Study Resource Kit

Two interpretations of division:

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.

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?"

Analyzing Word Problems Involving Multiplication:

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.

Classroom Supplies:

The purpose of this task is for students to "Solve problems involving the four operations" (3.OA.A) and "Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories" (3.MD.3).

Student Center Activity

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

Teaching Ideas

Shamu Math-SeaWorld Classroom 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

Hand Spans, A Lesson for Third and Fourth Graders (Division and Measurement):

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

Type: Teaching Idea

Everybody Wins! A Lesson for Third Graders (Division):

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

Text Resource

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

Type: Text Resource

Tutorial

Average Height of a Building's Floor:

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

Type: Tutorial

Unit/Lesson Sequence

Computation Through Literature :

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

Virtual Manipulatives

Animal Legs (multiply using repeated addition):

Students use repeated addition as a strategy to solve multiplication story problems.

Type: Virtual Manipulative

Groups of Dogs (multiplication):

Students use arrays to understand the meaning of multiplication.

Type: Virtual Manipulative

STEM Lessons - Model Eliciting Activity

Chess Wish List:

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.

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.

Cupid's Carnival Rides:

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.

Florida Fish Aquarium Challenge:

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.

How Long is Your Music Lesson?:

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.

Pick a Pet:

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.

MFAS Formative Assessments

Finding an Unknown Product:

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.

Finding the Group Size:

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.

Finding the Number of Groups:

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.

Measurement Problems:

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.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Two interpretations of division:

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.

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?"

Analyzing Word Problems Involving Multiplication:

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.

Classroom Supplies:

The purpose of this task is for students to "Solve problems involving the four operations" (3.OA.A) and "Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories" (3.MD.3).

Student Center Activity

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

Tutorial

Average Height of a Building's Floor:

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

Type: Tutorial

Virtual Manipulatives

Animal Legs (multiply using repeated addition):

Students use repeated addition as a strategy to solve multiplication story problems.

Type: Virtual Manipulative

Groups of Dogs (multiplication):

Students use arrays to understand the meaning of multiplication.

Type: Virtual Manipulative

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Two interpretations of division:

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.

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?"