# Worksheet #1 – The Area Model for Whole Numbers

Example 1.

Draw a picture that shows why 3 copies of the rectangle with sides 1 and b make the rectangle with sides 3 and b.

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Exercise 1.

Draw a picture that shows why 5 copies of the rectangle with sides 1 and b make the rectangle with sides 5 and b.

Let n be a whole number. Note that n copies of the rectangle with sides 1 and b make the rectangle with sides n and b. It follows the rectangle with sides n and b has n times as much area as the rectangle with sides 1 and b. Hence, we must assign nb to the measure of the area of the rectangle with sides n and b (why?).

Example 2.

Let’s use the area model definition of multiplication to show that 3(4) = 12. First we construct a rectangle with sides 3 and 4 as shown below.
Next partition the rectangle into unit squares.
And finally place the top two rows alongside the bottom one.

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We note that the squares on the bottom row extend to a length of 12 units.

Exercise 2.

Go through the same process for the cases of 2(3) and 3(2)