# MAFS.3.OA.1.1

Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

### 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 1: Recall
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 :
Whole number factors may not exceed 10 x 10. Students may not be required to write an equation to represent a product of whole numbers.
• Calculator :
No
• Context :

Allowable

Sample Test Items (2)
• Test Item #: Sample Item 1
• Question: Tom told Mary he planted 48 flowers in the rectangular-shaped garden. Which sentence could Mary use to describe how the flowers were planted?

• Difficulty: N/A
• Type: MC: Multiple Choice

• Test Item #: Sample Item 2
• Question: At the beach in Key Largo, Diana saw 10 dolphins each day for 7 days. Which of the following could be used to find the total number of dolphins Diana saw?

• Difficulty: N/A
• Type: MC: Multiple Choice

## 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.1a: Find the total number inside an array with neither number in the columns or rows greater than five.
MAFS.3.OA.1.AP.1b: Solve multiplication problems with neither number greater than five.
MAFS.3.OA.1.AP.1c: Use objects to model multiplication involving up to five groups with up to five objects in each.

## 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 2 - Third Grade Math State Interim Assessment:

This is a State Interim Assessment for third grade.

Type: Assessment

## Educational Game

Arithmetic Workout:

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

## Formative Assessments

Writing Multiplication Word Problems:

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

What does the 21 mean?:

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

Multiplication on the Number Line:

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

Type: Formative Assessment

Interpreting Multiplication:

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

Type: Formative Assessment

## Lesson Plans

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

“Shoot for the Stars to Introduce Multiplication”:

"Shoot for the Stars to Introduce Multiplication": Students will learn how multiplication is related to repeated addition and using different strategies to find the product.

Type: Lesson Plan

Each Orange Had 8 Slices: Multiplying Equal Groups:

Students will learn how to represent and count equal groups through the use of literature and situational story problems. Using the story Each Orange Had 8 Slices, students will use manipulatives to create arrays to assist calculation of equal groups. Students will learn to write corresponding addition and multiplication sentences for the arrays.

Type: Lesson Plan

How many Circles? How many Stars?:

How many Circles? How many Stars? is an activity that will give students a visual representation of multiplication and repeated addition. 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

Hip, Hip, Array!:

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 Poo on my Shoe! Multiplying with five,ten, and two:

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

Circles and Stars:

This is an introduction lesson to prepare students to move from using repeated addition to using grouping of numbers when modeling arrays when solving multiplication problems. After completing this lesson you would then begin a lesson using arrays for equal groups.

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

Group Singing Lessons:

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.

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

Product Productions:

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

Just Group It:

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

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

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

Amazing Arrays:

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

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

## 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

## Original Student Tutorial

Monkeying Around with Multiplication :

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

## Presentation/Slideshow

Multiplication with Arrays:

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

Type: Presentation/Slideshow

## 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 Idea

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

## Text Resource

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

Type: Text Resource

## Tutorials

Using arrays to multiply:

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

Multiplication as groups of objects:

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

Type: Tutorial

Intro to multiplication:

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

Type: Tutorial

## Virtual Manipulatives

Pan Balance - Numbers:

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

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

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.

Group Singing Lessons:

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.

## MFAS Formative Assessments

Interpreting Multiplication:

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

Multiplication on the Number Line:

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

What does the 21 mean?:

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

Writing Multiplication Word Problems:

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.

## Original Student Tutorials Mathematics - Grades K-5

Monkeying Around with Multiplication :

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

## Student Resources

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

## Original Student Tutorial

Monkeying Around with Multiplication :

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

## 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

## Tutorials

Using arrays to multiply:

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

Multiplication as groups of objects:

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

Type: Tutorial

Intro to multiplication:

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

Type: Tutorial

## Virtual Manipulatives

Pan Balance - Numbers:

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

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.

## Tutorials

Using arrays to multiply:

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

Multiplication as groups of objects:

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

Type: Tutorial

Intro to multiplication:

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

Type: Tutorial