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.
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.
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)