# Inside Track: Multiplication & Division Fact Families

### Key Idea:

Every basic multiplication number fact can be turned around to show other related facts: for most examples*, there are four separate facts that include the same three numbers.

By pointing this fact out to students, we will help them make sense of the facts they are learning, and help them to learn the facts faster.

When I was at school in the 1960s, we were taught the times tables by chanting them until they stuck.

In fact, the teacher had no idea when they stuck, so we pretty well chanted the facts every day, just in case.

Haven’t we come a long way since then? Well…

Only if you teach students to memorize facts. Sadly, I keep seeing young children who haven’t a clue about number facts unless they happen to be holding a calculator.

To help students learn number facts (because they will NEED them in the future), we can show them cool and clever ways that the facts relate to each other. One of these ways is…

Show students the facts that (as Sesame Street used to say), “Belong together”. For every single multiplication fact, just about, there are 3 other related facts, that use the same numbers. For example:

• 4 x 8 = 32
• 8 x 4 = 32
• 32 / 8 = 4
• 32 / 4 = 8

### Extending These Activities:

Try this: teach your student a new fact that is beyond the basic facts. Ask the student for another three facts that relate. For example:

• 5 x 1600 = 8000
• 90 x 1400 = 126,000
• 0.02 x 0.0045 = 0.000 09

In case you were wondering, the multiplication facts that don’t have four related facts are the square numbers:

• 7 x 7 = 49
• 49 / 7 = 7