Further Reading for Teachers

Distributive Law

Recall...

The Distributive Law says that, for any three numbers (called a, b and c, for example)

a×(b + c) = a×b + a×c

2×(b + 3) = 2×b + 6

Introducing the Distributive Law to Children

This is a little story that's been used in the past to break the ice. It is based on the motto "You can count the same amount of objects in two different ways — you are still going to get the same number!"

John and Mary are buying supplies for their 5-day-long camping trip. Presently, they are trying to figure out how many apples to get. John anticipates eating 4 apples a day, and Mary wants 2 apples per day. Let's compute in two different ways how many apples they need to buy.

First Way: compute how many apples per day John and Mary need: 4 + 2. Then multiply the number of days by 5: 5×(4 + 2)= 30.

Second Way: compute how many apples John needs for the whole trip: 5×4 and how many Mary needs for the whole trip: 5×2. Now add: 5×4 + 5×2 = 20 + 10 = 30.

In other words:

5×(4 + 2) = 5×4 + 5×2

Next, move on to more abstract ground. Call D the number of days, J the number of apples per day for John, and M the number of apples per day for Mary. Count how many apples are needed for the whole trip in the two different manners shown above, and obtain the following:

D×(J + M) = D×J + D×M

This is the Distributive Law for the variables D, J, and M.