Standard #: MA.3.A.1.2 (Archived Standard)


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Solve multiplication and division fact problems by using strategies that result from applying number properties.


Remarks


Remarks:  The use of multiple strategies might incorporate number properties for both multiplication and division including the commutative property, associative property, distributive property, and the identity property.   The zero property of multiplication may also be used to solve problems.

A problem such as 8 x 6 can be solved by finding 4 x 6 then doubling the product. This strategy uses the associative property in that 8 x 6 = 2 x (4 x 6).

The distributive property is applied to 7 x 8 when we find 5 x 8 and add it to 2 x 8.  Hence, 7 x 8 = (5 + 2) x 8 = (5 x 8) + (2 x 8).

Consider the following solution using the distributive property as a mental math strategy. Given 14 x 5 we may conclude (10+4) x 5= (10 x 5) + (4 x 5) = 50 + 20 = 70. 

Another application of a mental math strategy using the distributive property may lead one to conclude 19 x 5 = (20 -1) x 5 = (20 x 5) - (5 x 1) = 100 - 5 = 95.

 

Example:  Sally and Thomas each have a $5 bill and three $1 bills to spend at the book fair.  Together the total amount of money they have can be shown using the expression below. 

 

2 x (3 + 5)

 

Write a different expression that represents the total amount that Sally and Thomas have together.  How much money do they have altogether?


 

 



General Information

Subject Area: X-Mathematics (former standards - 2008)
Grade: 3
Body of Knowledge: Algebra
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 3: Strategic Thinking & Complex Reasoning - 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)
    N/A

    Clarification :
    Students will recognize equivalent representations of equations or expressions by using number properties, including the commutative, associative, distributive, and identity properties for multiplication and division and the zero property of multiplication.
    Content Limits :
    Items will not include identifying the properties by name. 

    Items will not require the use of more than two properties to convert one expression or equation to its equivalent. 

    Items may include only factors or divisors of 0 through 9.

    Stimulus Attributes :
    Items may be set in either a real-world or mathematical context.


Sample Test Items (1)

Test Item # Question Difficulty Type
Sample Item 1

Raymond has 5 pictures of each of 3 types of ocean dolphins. He also has 4 pictures of river dolphins. The expression below represents the total number of dolphin pictures Raymond has.

(3 x 5) + 4

Which expression below also represents the total number of dolphin pictures Raymond has?

 N/A MC: Multiple Choice


Related Resources

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 Plan

Name Description
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.

Teaching Idea

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.

Unit/Lesson Sequence

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.
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