Session 4, Part B:
Area Models for Multiplication and Division (45 minutes)

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

Models and manipulative materials can help make multiplication and division with integers more tangible. They provide a visual representation of the algorithms we use to perform these operations and help us see how the algorithms relate to what is actually happening with the manipulatives.

In this and the following area model examples, we will use three sizes of manipulatives: large 10 • 10 squares (we'll call them flats); 1 • 10 rectangles (we'll call them longs); and small 1 • 1 squares (we'll call them units):

Let's try some multi-digit multiplication problems; for example, 13 • 12. Note 7

This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. For a non-interactive version of this activity, use manipulatives, or print and cut several copies of the shapes from a PDF file.

Problem B1

 a. What is the fewest number of pieces you would need to make a rectangle of 13 units by 12 units? How would you arrange them? b. How can you represent this model using mathematical computations?

 Session 4: Index | Notes | Solutions | Video