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Learning Math Home
Number and Operations Session 4, Part B: Area Models for Multiplication and Division
 
Session 4 Part A Part B Part C Homework
 
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Session 4, Part B:
Area Models for Multiplication and Division

In This Part: Multiplication with Manipulatives | Multiplication Model
Division with Manipulatives | Division Model

When thinking of Problem B1 as an area problem, you could represent 13 • 12 as a rectangle with length 13 and height 12.

As you filled the rectangle with manipulatives, you built a related intermediate algorithm for the multiplication process:

Notice how the area model for multiplication is an application of the distributive property. For example:

12 • 13 = (10 + 2) • (10 + 3) = [(10 + 2) • 10] + [(10 + 2) • 3] = (10 • 10) + (2 • 10) + (10 • 3) + (2 • 3)

You can review the distributive property in Session 1 of this course and in Session 9 of Learning Math: Patterns, Functions, and Algebra.

The area model for multiplication is closely related to the actual computation you perform using the standard algorithm for two-digit multiplication. The standard algorithm, however, combines the four steps shown above into two steps:


 

Problem B2

Solution  

Construct an area model and show the related intermediate algorithm for 24 • 13.


 

Problem B3

Solution  

Show how an area model could be used to compute (x + 3) • (x + 2) .


Next > Part B (Continued): Division with Manipulatives

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