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Develop understandings of multiplication and division and strategies for basic multiplication facts and related division facts.

General Information

Number: MA.3.A.1

Title: BIG IDEA 1

Type: Big Idea

Subject: X-Mathematics (former standards - 2008) - Archived

Grade: 3

Body of Knowledge: Algebra

Related Benchmarks

This cluster includes the following benchmarks

Code	Description
MA.3.A.1.1:	Model multiplication and division including problems presented in context: repeated addition, multiplicative comparison, array, how many combinations, measurement, and partitioning.
MA.3.A.1.2:	Solve multiplication and division fact problems by using strategies that result from applying number properties.
MA.3.A.1.3:	Identify, describe, and apply division and multiplication as inverse operations.

Related Access Points

This cluster includes the following access points.

Independent

Access Point Number	Access Point Title
MA.3.A.1.In.a:	Solve problems that involve combining (multiplying) equal sets with quantities to 18 using objects and pictures with numerals.
MA.3.A.1.In.b:	Solve addition facts with sums to 18 and related subtraction one-digit fact families using the formal algorithm with numerals and signs (+, -, =).
MA.3.A.1.In.c:	Use one-to-one correspondence, grouping, and counting as strategies to solve real-world problems involving addition facts with sums to 18 and related subtraction facts.
MA.3.A.1.In.d:	Use objects and pictures to represent the inverse relationship between addition and subtraction facts.

Supported

Access Point Number	Access Point Title
MA.3.A.1.Su.a:	Solve problems that involve combining (multiplying) equal sets with sums to 9 using objects and pictures.
MA.3.A.1.Su.b:	Solve addition facts with sums to 9 and related subtraction facts using numerals with objects and pictures.
MA.3.A.1.Su.c:	Use one-to-one correspondence and counting as strategies to solve real-world problems with addition facts with sums to 9 and related subtraction facts.

Participatory

Access Point Number	Access Point Title
MA.3.A.1.Pa.a:	Solve simple problems involving joining or separating sets of objects to 3.
MA.3.A.1.Pa.b:	Recognize when 1 or 2 items have been added to or removed from sets of objects to 3.

Related Resources

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

Educational Game

Name	Description
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!

Lesson Plans

Name	Description
Cupid's Carnival Rides:	In this Model Eliciting Activity, MEA students will analyze different carnival rides to determine which ride would 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.
Just Group It:	Students will be able to use counters to create equal groups and write multiplication equations to represent these representations.
Pet Store Partitive Division:	In this lesson students will model partitive division through the real-world activity of a pet store owner.
Chip Chip Array!:	Students work together to create arrays to represent given numbers.
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.
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.
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.
Yogurt Shop Combinations:	In this lesson students will model multiplication using tree diagrams based in a real-world setting of a yogurt shop.

Presentation/Slideshow

Name	Description
Multiplication with Arrays:	PowerPoint presentation showing the relationship between arrays, multiplication, and repeated addition.

Teaching Ideas

Name	Description
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.
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.
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)

Text Resource

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

Unit/Lesson Sequences

Name

Description

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.

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.

Virtual Manipulative

Name	Description
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.

Big Idea 1 : BIG IDEA 1 (Archived)