How to Explain Multiplication to a Child

Here are 4 great ways to explain multiplication to a child. This can be made simple and fun by using examples the child can relate to such as visuals and hands-on activities.

• Before you start
• Repeated addition
• Arrays
• Equal groups
• Skip counting
• Try it together
• Learning the facts
• Tips for parents
• Summary
• Quiz

Before You Start: What Your Child Needs

Multiplication builds on things your child already knows. Before you start, check that your child can:

• count objects one by one and say how many there are in all;
• add small numbers, such as 5 + 5 or 4 + 4 + 4;
• count by 2s, 5s and 10s (2, 4, 6, 8, …), even if only with help.

In many US schools, children start with equal groups and arrays in grade 2, using addition to find the total. In grade 3 they learn that 5 × 7 means 5 groups of 7, and by the end of grade 3 they are expected to know all the products of two one-digit numbers from memory.

1. Relate Multiplication to Addition

If the child already knows addition, explain that 4 × 5 is like adding 5 four times:

5 + 5 + 5 + 5 = 20

Then, say that multiplication is a quicker way to do repeated addition.

2. Use Arrays to Explain Multiplication

Say to the child that multiplication is like arranging objects in rows and columns.

Draw a rectangle made of dots with 2 rows and 3 columns.

Count the total number of dots to show that 2 rows of 3 dots equal 6 dots.

Then, tell the child that this represents 2 × 3 = 6.

Turning an array on its side does not change the number of dots.

3. Make Groups of Objects to Explain Multiplication

If you have 3 groups of 4 pencils each, you can add 4 three times: 4 + 4 + 4 = 12.

Use 12 pencils to make 3 groups with 4 pencils in each group, and then show how you can count all the pencils together to get 12.

You could also say to the child that 3 groups of 4 means the same thing as 3 × 4.

4. Use Skip Counting to Explain Multiplication

Skip count by 2s: 2, 4, 6, 8. Explain that this is the same as multiplying 2 by the number of times you skip (2 × 4 = 8).

Skip count by 3s: 3, 6, 9. Explain that this is the same as multiplying 3 by the number of times you skip (3 × 3 = 9).

Skip count by 5s: 5, 10, 15, 20, 25, 30. Explain that this is the same as multiplying 5 by the number of times you skip (5 × 6 = 30).

Skip counting on a number line: each jump adds one more group.

Try It Together: See One Multiplication Three Ways

Choose the number of groups and the number in each group. Then switch between an array, equal groups and skip counting. Ask your child: "What stays the same?"

Next Step: Learning the Multiplication Facts

Once your child understands what multiplication means, the next goal is to know the facts (the times tables) quickly. Research on fact fluency suggests learning them in stages, using facts your child already knows to work out new ones, instead of memorizing all 100 facts at once.

Adding a group: 6 × 8 is 5 × 8 plus one more row of 8.

Tips for Parents

• Look for groups everywhere. Egg cartons (2 rows of 6), wheels on 4 cars (4 groups of 4), socks in pairs and fingers on hands are all multiplication.
• Ask before you tell. Ask "How did you figure that out?" Different ways of thinking are fine, as long as the child can explain them.
• Practice a little, often. About 10 minutes a day with a card game, dice or a board game works better than one long session.
• Use objects again when it gets hard. Going back to blocks or drawings is not a step backward. It is how understanding grows.
• Watch what you say about math. Instead of "I was never good at math," try "Let's figure this out together." Mistakes are part of learning.

Test Yourself: 10-Question Quiz

Check what you learned, or take the quiz together with your child. Every answer is explained, and each time you play you get new questions.