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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:
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