MA.3.A.1.1Archived Standard

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Model multiplication and division including problems presented in context: repeated addition, multiplicative comparison, array, how many combinations, measurement, and partitioning.

Remarks

Repeated addition: 4 bags of cookies with 8 in each bag. How many cookies are there?

 

Multiplicative comparison: Sam has 8 baseball cards. Elise has 8 times as many. How many does Elise have?

 

Array: A marching band has 8 rows with 7 students in each row. How many band members are marching?

 

Combination: Patrick is getting dressed for school. He has 4 different colored shirts; blue, red, yellow and green. He has blue, tan and black shorts. How many combinations of a shirt and a pair of shorts can he make?

 

Measurement: There are 35 bugs. You will put 5 bugs in each jar. How many jars will you need?

 

Partitive: You have 72 coins and 9 jars. If you want to place an equal number of coins in each jar, how many coins will you put in each jar?

General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 3
Body of Knowledge: Algebra
Idea: Level 2: Basic Application of Skills & Concepts
Big Idea: BIG IDEA 1 - Develop understandings of multiplication and division and strategies for basic multiplication facts and related division facts.
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
  • Item Type(s): This benchmark may be assessed using: MC item(s)

  • Clarification :

    Students will identify models of and/or solve problems involving multiplication and/or division situations.

    Examples might include, but are not limited to

    • Repeated addition: 4 bags of cookies with 8 in each bag. How many cookies are there? (8 + 8 + 8 + 8 = 32)
    • Multiplicative comparison (also known as scalar model): Sam has 8 baseball cards. Elise has 8 times as many. How many does Elise have?
    • Array: A marching band has 8 rows with 7 students in each row. How many band members? How many tiles would be in a floor that is 8 rows by 9 columns?
    • Combination: How many different combinations of one flavor of ice cream and one topping can be made from 4 different flavors and 5 different toppings?
    • Measurement: If there are 35 bugs all together and Robbie puts 5 bugs in each jar, how many jars does he need to hold all of the bugs?
    • Partitive: Robbie has 35 bugs and 7 jars. He will put all of the bugs in jars. If he puts the same number of bugs in each jar, how many bugs are in each jar?

    Other examples might include

    • Finding number of squares (area) of wrapping paper; using rate models, e.g., traveling 6 miles each day for 3 days; showing how 4 x 6 can be represented by 6 + 6 + 6 + 6 or 6 x 4 can be represented by 4 + 4 + 4 + 4 + 4 + 4.
  • Content Limits :
    Items may include whole-number multiplication facts from 0 X 0 through 9 X 9 and the related division facts. 

    Items may include division problems with remainders expressed only as whole numbers. Items will not require interpretation of the remainder.

  • Stimulus Attributes :
    Items may use graphics, symbols, expressions, or equations. 

    Items may be set in a real-world or mathematical context.

  • Response Attributes :
    Responses may include expressions, equations, graphic representations, or numerical values.
Sample Test Items (1)
  • Test Item #: Sample Item 1
  • Question: Nathan paid $2 for each of the 3 books he bought at a bookstore. He can use the expression 3 x 2 to find the total amount he paid for the 3 books. Which of the following is equal to 3 x 2 ?
  • Difficulty: N/A
  • Type: MC: Multiple Choice

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

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

Educational Game

Who Wants to be a Mathionaire?:

This online game replicates the popular "Who Wants to be a Millionaire?" format, using multiplication facts. It's a fun way for kids to practice multiplication!

Type: Educational Game

Lesson Plans

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.

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

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

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

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

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

Yogurt Shop Combinations:

In this lesson students will model multiplication using tree diagrams based in a real-world setting of a yogurt shop.

Type: Lesson Plan

Presentation/Slideshow

Multiplication with Arrays:

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

Type: Presentation/Slideshow

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

All About Multiplication: Bibliography:

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

Type: Text Resource

Unit/Lesson Sequences

All About Multiplication:

This four-lesson unit from NCTM's Illuminations has students explore several meaning and representations of multiplication (number line, equal sets, arrays, and balanced equations). Other multiplication topics covered include: the commutative (order) property, the results of multiplying by 1 and 0, and the inverse property. Students will write and solve multiplication story problems, and convert word problems into equations. A bibliography of children's literature with a focus on multiplication is provided, which can be integrated so that students can connect through literature.

Individual Lessons

    • Students are shown how to generate products on a number line, highlighting the measurement aspect of addition. After some practice, they are asked to predict and then verify sums, and are also introduced to the commutative property.
  • Lesson 2: Exploring Equal Sets
    • Students explore the set model for multiplication. They find products using equal sets and present their results in a table. Next students apply their knowledge about multiplication in the creation of pictographs.
  • Lesson 3: Modeling Multiplication With Streets and Avenues
    • The array model of multiplication lays the foundation for the later study of area, and in this lesson, students will create arrays of the factors of 4 and 6 using toothpicks as representations of streets and avenues. The teacher will ask how many stoplights would be needed to fill each intersection. Zero and one will also be used as factors. Finally they will write their results as multiplication problems.
  • Lesson 4: Balance Beam Discoveries
    • The balance beam model of multiplication is examined in this lesson, along with another important relationship, the inverse of multiplication. This will lead naturally into the representation of multiplication facts as equations. Students will also practice multiplication facts by playing the Product Game.

Type: 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 Manipulative

Bobbie Bear:

Using a virtual manipulative, children construct combinations of different colored shirts and pants to help Bobbie Bear, who is planning a vacation and wants to know how many different outfits he will be able to make from these combinations.

Type: Virtual Manipulative

STEM Lessons - Model Eliciting Activity

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.

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.

Student Resources

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

Parent Resources

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