Whole Number and Decimal Multiplication

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In this lesson, we focus on the dimensions of rectangles to develop strategies for computing decimal products that can later used in fraction and algebraic multiplication. For example, the following edge piece dimensions could represent two products:

If the small piece is one linear unit, then the dimensions are 30 x 13. If the larger piece is the linear unit, then the dimensions are 3.0 x 1.3. Let's use the longer one.

There are several ways we can think about the area of this rectangle:

-or-

-or-

• What do you suppose the product would be if the shorter piece were the linear unit?

Students may have other strategies, or combinations of strategies - the purpose is to become familiar with a variety of approaches since some work better in certain situations than others.

We do lots of exploring and discussing in class, and look for patterns in the different examples that might help us make conjectures or generalizations about decimal multiplication. Here are some problems to model with your child:

• 45 X 27
• 15.2 X 3
• 1.4 X 2.5
• 10 X 5.4
• 3.2 X 2
• 2.2 X 5.3
• 15 X 30

As usual, we're more interested that students develop the ability to think flexibly about computing products, and develop mental computation strategies that can help them in problem solving. There are many examples you'd come across in your daily life - share them and talk about them with your child.