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  1. Make a table like the one Nick and his friends made. Sort the problems.
  2. Does everyone have to agree on the same method for each problem? Explain.

Rectangle Model and Expanded Form

Mr. Moreno decided to use some of the multiplication problems his students sorted to review paper-and-pencil multiplication. Mr. Moreno selected 6 47. He drew a rectangle and filled it in as shown below.

Mr. Moreno broke apart 47 into 40 + 7. He multiplied the 6 40 and got 240. Then he multiplied the 6 7 and got 42. Finally, he added 240 + 42 to get 282.

Here is another way to show the same idea using expanded form:

  1. Explain how using rectangles is similar to using expanded form. Identify where each number in each method comes from.

Solve these problems in two ways. First use the rectangle model. Then use the expanded-form method.

  1. 27 7
  2. 38 8
  3. 76 3
Mr. Moreno asked his class, “Can you multiply a three-digit number times a one-digit number using rectangles and the expanded-form method? Try it using 4 237.”

The class thought for awhile before Maya raised her hand. She said, “I think we can use them. Let me explain with rectangles.”