MA.3.NSO.2.2

Explore multiplication of two whole numbers with products from 0 to 144, and related division facts.

Clarifications

Clarification 1: Instruction includes equal groups, arrays, area models and equations.

Clarification 2: Within the benchmark, it is the expectation that one problem can be represented in multiple ways and understanding how the different representations are related to each other.

Clarification 3: Factors and divisors are limited to up to 12.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 3
Strand: Number Sense and Operations
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

Terms from the K-12 Glossary

  • Area Model 
  • Commutative Property of Multiplication 
  • Dividend 
  • Divisor 
  • Equation 
  • Expression 
  • Factors 
  • Rectangular Array

Vertical Alignment

Previous Benchmarks

Next Benchmarks

Purpose and Instructional Strategies

The purpose of this benchmark is for students to build a conceptual understanding of what multiplication is and how it relates to division. Because the expectation of this benchmark is at the explore level, instruction should focus on building an understanding of multiplication and division facts from 0 to 144 using manipulatives (e.g., counters), visual models (e.g., rectangular arrays, equal groups), discussions, estimation and drawings (e.g., rectangular arrays, equal groups) (MTR.2.1). 
  • Instruction should relate multiplication to repeated addition work that began in Grade 2. In Grade 2, students used repeated addition to find the total number of objects using rectangular arrays and equations (MA.2.AR.3.2). 
  • Students should explore multiplication and division through word problems, writing expressions and drawing models that match the problems’ contexts (MTR.2.1, MTR.3.1). 
  • In division, students should see examples of sharing, or partitive division (where the number of groups are given and students determine the number in each group), as well as measurement, or quotative division (where the number in each group is given and students determine the number of groups). 
  • Instruction should relate division facts to known multiplication facts (e.g., fact families). Fact families can be explored through arrays and equal groups (MTR.5.1).

Common Misconceptions or Errors

  • Students may have difficulty relating word problems and real-world scenarios to models, expressions, and equations. For example, students may not differentiate the number of groups versus the number in each group in multiplication, which then impacts their models, expressions, and equations. 
  • Students may be confused by measurement (or quotative) division when the amount in each group is given and the number of equal-sized groups is found.

Strategies to Support Tiered Instruction

  • Instruction includes demonstrating the use of counters, arrays, and skip counting to model groups of objects, including the use of real-world scenarios to support students’ understanding of the number of groups versus the size of each group. Students represent their models with equations to reinforce the concept of multiplication. 
    • For example, a farmer is planting rows of sunflowers. He plants 6 rows with 5 sunflowers in each row. How many sunflowers does he plant? 

counters

    • For example, there are 3 tables in the library. There are 4 students sitting at each table. How many students are sitting at tables in the library? 

3 tables of students

  • Instruction includes demonstrating the use of counters and arrays to model division problems where the amount in each group is given and the number of equal-sized groups is found. The teacher provides real-world scenarios to represent the number of objects in each group and the number of groups Students form a group based on the context of the problem continuing to form groups of that size until the total is reached. Students can skip counting to keep track of how many counters they have used, representing their models with equations to reinforce the concept of division. 
    • For example, Renee is setting up chairs in the library. She is placing 24 chairs into rows. If she places 6 chairs in each row, how many rows of chairs will she have? 

24 chairs in rows

    • For example, there are 15 students working on an art project. The art teacher divides them into groups of 3 students to work on the project. How many groups are there?

5 groups of 3

Instructional Tasks

Instructional Task 1 

  • Tina has 4 shelves on her bookshelf. Each row has 6 books. How many books are on Tina’s bookshelf in all? Draw a model and write an equation to represent your answer.

Instructional Items

Instructional Item 1 

  • A total of 56 chairs are in the cafeteria for an assembly. The principal arranges the chairs into 8 rows with the same number of chairs in each. Which equation shows the quotient as the number of chairs that will be in each row? 
    • a. 56÷8=7 
    • b. 56÷8=48 
    • c. 56÷8=64 
    • d. 56÷8=6 
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

Related Courses

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

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.3.NSO.2.AP.2: Explore the concept of multiplication of two single-digit whole numbers using objects.

Related Resources

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

Formative Assessments

Kate and Her Doll:

Students are given a context for a multiplicative comparison and asked to explain the comparison.

Type: Formative Assessment

Pet Snakes:

Students discuss the relationship between the lengths of two snakes in a multiplicative comparison problem that includes an equation.

Type: Formative Assessment

Writing an Equation to Match a Word Problem:

Students write an equation to match a given word problem.

Type: Formative Assessment

Animal Photographs:

Students read a multiplicative comparison word problem and are asked to write an equation that matches the problem.

Type: Formative Assessment

Using A Number Line to Solve a Division Problem:

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

Type: Formative Assessment

Interpreting Division:

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

Type: Formative Assessment

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

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”:

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

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 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?:

“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

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 problems involving rows and columns.

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 explore multiplication by solving several multiplication word problems involving rows and columns situations using the array as a representation.

Type: Lesson Plan

Circles and Stars:

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

Zero on a Hero (Exploring the Zero Property of Multiplication):

Students will explore the Zero Property of Multiplication using array and equal-group models for multiplication. Students will model story problems, translate problems into multiplication facts, and identify patterns in a set of multiplication facts to develop understanding of the Zero Property of Multiplication.

Type: Lesson Plan

One with a Bun (Exploring the Multiplicative Identity Property of 1):

In this lesson students will explore the Multiplicative Identity Property of 1, using array and equal-group models for multiplication. Students will model story problems, translate problems into multiplication equations, and identify patterns in a set of multiplication facts to develop understanding of the Multiplicative Identity Property of 1.

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

Multiply by Multiples of 10 with Number Cubes:

In this lesson students will use various strategies to multiply one-digit numbers by multiples of 10 within the range of 10-90. The strategies will encompass the Distributive, Commutative, and Associative properties, place value, number lines, base-ten blocks, diagrams, hundreds chart. Students will play a game with number cubes to practice this multiplication.

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

Giddy Up, Round Up: Relating Division to Multiplication:

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

Great Estimations!:

In this lesson, students will deepen their knowledge of using equal groups in multiplication and their ability to visualize the quantity of an item in a given object. They will use problem-solving skills and see the value in using benchmarks.

Type: Lesson Plan

Efficient Multiplication:

Students will engage with questions to evaluate the students' abilities to select and apply multiplication strategies with fluency and efficiency. The focus of the lesson is decomposing numbers to multiply using the Distributive property and understanding and applying the Commutative property. Then, students will reinforce decomposing of factors while playing Decomposition of Factors. The lesson concludes with a real world application problem on an Exit Slip.

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

Area Isn't Just for Squares:

This lesson helps students make the connections between area and multiplication using square tiles.

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

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

Original Student Tutorials

Birthday at Home: Multiplication & Division Fluency Part 2:

Help Jaliah continue to plan her birthday party and be fluent in her math facts using helpful facts she already knows, and the relationship between multiplication and division in Part 2 of this interactive tutorial.  

This is part 2 of 2-part series, click HERE to view part 1.

Type: Original Student Tutorial

Birthday at Home: Multiplication & Division Fluency Part 1:

Jaliah is ready to celebrate her birthday and use strategies of doubling and halving and relating multiplication and division for building fluency with multiplication and division facts in this interactive tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Type: 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

Be Fair When You Share:

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

Type: Original Student Tutorial

Perspectives Video: Expert

B.E.S.T. Journey:

What roles do exploration, procedural reliability, automaticity, and procedural fluency play in a student's journey through the B.E.S.T. benchmarks? Dr. Lawrence Gray explains the path through the B.E.S.T. maththematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

Perspectives Video: Teaching Ideas

Making Connections with the Area Model:

Unlock an effective teaching strategy for making connections in area models in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

The Van de Walle Dot Matrix: A tool to support concepts from counting to multiplying polynomials:

Unlock an effective teaching tool that can help students all the way from basic counting principles to multiplying polynomials.

Type: Perspectives Video: Teaching Idea

Multiplying Multi-digit Numbers:

Unlock an effective teaching strategy for teaching multiplying multi-digit numbers using ten frames in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

MFAS Formative Assessments

Animal Photographs:

Students read a multiplicative comparison word problem and are asked to write an equation that matches the problem.

Interpreting Division:

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

Interpreting Multiplication:

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

Kate and Her Doll:

Students are given a context for a multiplicative comparison and asked to explain the comparison.

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.

Pet Snakes:

Students discuss the relationship between the lengths of two snakes in a multiplicative comparison problem that includes an equation.

Using A Number Line to Solve a Division Problem:

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

Writing an Equation to Match a Word Problem:

Students write an equation to match a given word problem.

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

Be Fair When You Share:

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

Birthday at Home: Multiplication & Division Fluency Part 1:

Jaliah is ready to celebrate her birthday and use strategies of doubling and halving and relating multiplication and division for building fluency with multiplication and division facts in this interactive tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Birthday at Home: Multiplication & Division Fluency Part 2:

Help Jaliah continue to plan her birthday party and be fluent in her math facts using helpful facts she already knows, and the relationship between multiplication and division in Part 2 of this interactive tutorial.  

This is part 2 of 2-part series, click HERE to view part 1.

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 Tutorials

Birthday at Home: Multiplication & Division Fluency Part 2:

Help Jaliah continue to plan her birthday party and be fluent in her math facts using helpful facts she already knows, and the relationship between multiplication and division in Part 2 of this interactive tutorial.  

This is part 2 of 2-part series, click HERE to view part 1.

Type: Original Student Tutorial

Birthday at Home: Multiplication & Division Fluency Part 1:

Jaliah is ready to celebrate her birthday and use strategies of doubling and halving and relating multiplication and division for building fluency with multiplication and division facts in this interactive tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Type: 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

Be Fair When You Share:

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

Type: Original Student Tutorial

Parent Resources

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