This mat is used to explain the inverse relationship between multiplication and division. By using numbers in the same fact family, the students will realize how the two operations are related.

I have found it easiest to use it with stackable counting blocks.

First, have the students write "multiplication" on the arrow pointing up. Then, have them write "division" on the arrow going down. Explain that multiplication makes smaller groups of objects into one larger group, while division takes a large group of objects and breaks them down into smaller groups of objects.

How to Use the Mat:

Multiplication Example:

2 x 3 =

Have the students place 2 blocks or counters in 3 of the circles. After they have done that, they gather all of the blocks, from all of the circles and place them in the rectangle at the top of the mat. They figure out their answer by counting the blocks in the rectangle.

Division Example:

6 / 3

Have the students place 6 counters in the large rectangle at the top of the mat. Have them place one counter in three circles. Then have them repeat the process until all the counters are gone.

Their answer to the division problem will be how many counters are in each circle.

While using this mat, I have found that it is important, (at least in the beginning) to make sure the students do not skip steps. To really understand the relationship, they need to make sure their counters go in and out of the large rectangle on the top.

I usually give each table of students a stack of cards with multiplication and division problems on them. The students then have to write down the problem they are working on and the answers on a piece of paper as they figure them out. This way, I know the students are staying on task, and it is an easy visual assess understanding.

Heather Diedtrich