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

 Problem B3 Show how an area model could be used to compute (x + 3) • (x + 2) .

 Session 4: Index | Notes | Solutions | Video