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Practicing with fact families is a good way to deepen your child’s understanding of the interconnection between multiplication and division.

Activities properties

These involve lots of practice with multiplication and divisibility playing with Turning the Tables. Practice multiples by using them when you play Beep.

Families

In Stage 3 we explored the fact families that connect addition and subtraction, and we saw how useful they are in understanding the interconnections between those two operations. Similar to what was done for addition and subtraction, group multiplication and division facts by families to gain a deeper understanding of them. For example, 3 x 4 = 12, 4 x 3 = 12, 12 / 3 = 4, and 12 / 4 = 3 form a fact family.

Multiplying and dividing are related

For the 3 x 4 = 12 fact family, visualize this interconnection using a rectangle that is 3 by 4. The area of this rectangle is 12, which is 3 times 4 or 4 times 3 – its width times its length. To get an area of 12 for a rectangle of width 3, the length must be 4. To get an area of 12 for a rectangle of length 4, its width must be 3. All these facts are tied together.

Multiplying and dividing undo each other

Let’s continue to use the example of 3 times 4. If we start with 3 and multiply it by 4 we arrive at 12. If we then take 12 and divide it by 4, the result is back to 3. Multiplying by 4 and then dividing by 4 gets back to where we started.

Similarly, if we take 12 and divide by 4 the answer is 3. If we then multiply 3 by 4 the answer is 12, which is where we started. Dividing by 4 and then multiplying by 4 returns things to the beginning.