Associative property for children

Quick answer

The associative property means that when you multiply three or more numbers, you can group them in any order and still get the same answer. It's like saying (2 × 3) × 4 = 2 × (3 × 4), and both give the same result.

Learning outcome

By the end of this page, you will understand that you can change the grouping of numbers when multiplying and still get the same answer. You will be able to use this to make multiplication easier and faster.

Success signs:

• You can show that (2 × 3) × 4 = 2 × (3 × 4)
• You can solve multiplication problems by changing the order of grouping
• You can explain why the answer stays the same when you group numbers differently
• You can use this property to help you multiply bigger numbers more easily

Why this matters

Knowing the associative property helps you multiply numbers more quickly and easily. It's like having a secret trick that lets you solve problems faster!

In games, you might use this when counting how many points you get from groups of items. In real life, it helps you work out how many cookies you need if you're making batches, or how many seats are in a theatre with rows and columns.

This property also helps when you're learning more advanced maths later, like algebra and working with bigger numbers.

How it works

Let’s think of multiplication like a group of friends. If you have 2 groups of 3 friends, and each friend brings 4 toys, how many toys do you have?

You can work it out in two ways:

1. First, find how many toys one group has: 3 friends × 4 toys = 12 toys
2. Then, multiply by the number of groups: 2 groups × 12 toys = 24 toys

Or, you can do it the other way:

1. First, find how many toys all the friends have together: 2 friends × 3 friends = 6 friends
2. Then, multiply by the number of toys each friend brings: 6 friends × 4 toys = 24 toys

Both ways give you the same answer: 24 toys!

This is the associative property in action. No matter how you group the numbers, the result is the same.

Examples you can see

Let’s look at some examples to see how this works:

Here’s another one:

Try drawing it out! You can use blocks or draw groups to see how it works.

Try it as a mini adventure

Adventure: The Magic Multiplication Garden

You are a gardener with a magical garden. You plant 3 rows of 4 flowers, and each flower has 2 petals. You want to know how many petals there are in total.

You can do it in two ways:

1. First, count how many petals are on one flower: 2 petals
2. Then, count how many flowers are in one row: 4 flowers
3. Then, count how many rows: 3 rows
4. So: (2 × 4) × 3 = 8 × 3 = 24 petals

Or:

1. First, count how many flowers are in one row: 4 flowers
2. Then, count how many rows: 3 rows
3. Then, count how many petals are on each flower: 2 petals
4. So: 3 × (4 × 2) = 3 × 8 = 24 petals

Both ways give the same answer! The magic garden helps you see that it doesn’t matter how you group the numbers.

Common mistakes

• Mistake: Thinking that (2 × 3) × 4 is different from 2 × (3 × 4) because the numbers are in different orders.
• Why it happens: Children may think that changing the order of the brackets changes the answer, but that’s not true.
• Fix: Practice both ways and show that the answer is the same. Use drawings or blocks to prove it.

• Mistake: Forgetting to multiply all the numbers when solving a problem.
• Why it happens: When working with more than two numbers, it's easy to miss one step.
• Fix: Write out each step clearly. Check your work and make sure you’ve multiplied everything.

• Mistake: Believing that the associative property only works with two numbers.
• Why it happens: Children may only see examples with two numbers and not understand it works with three or more.
• Fix: Show examples with three or more numbers. For example: (2 × 3) × (4 × 5) = 2 × (3 × 4) × 5.

Parent and carer guide

Helping your child understand the associative property is simple and fun!

• What to say: “You can group numbers in any way when multiplying, and it won’t change the answer!”
• What to do: Use everyday objects like counters, blocks, or even food items to show the concept. For example, 3 boxes of 4 toys each, and each toy has 2 stickers.
• What not to worry about: Don’t stress if they don’t get it right away. Practice a few times and it will come naturally.
• How to check: Ask your child to solve a problem in two different ways and compare the answers.
• How to encourage: Praise effort and patience. Say things like “You’re doing great trying different ways to solve it!”

Practice questions

1. What is (2 × 3) × 4?
2. What is 2 × (3 × 4)?
3. Is (5 × 2) × 3 the same as 5 × (2 × 3)?
4. Calculate (4 × 2) × 5.
5. Calculate 4 × (2 × 5).

Answers:

1. (2 × 3) × 4 = 6 × 4 = 24
2. 2 × (3 × 4) = 2 × 12 = 24
3. Yes, both equal 30
4. (4 × 2) × 5 = 8 × 5 = 40
5. 4 × (2 × 5) = 4 × 10 = 40

FAQ

What is the associative property?

It's a rule that says when you multiply numbers, you can group them in any way and still get the same answer.

Does it work with addition too?

Yes! The associative property also works for addition. For example, (2 + 3) + 4 = 2 + (3 + 4).

Can I use it with more than three numbers?

Yes! You can use it with any number of numbers. For example, (2 × 3 × 4) × 5 = 2 × (3 × 4 × 5).

Why is it useful?

It helps you solve multiplication problems more quickly and easily by grouping numbers in a way that's easier for you to calculate.

Can I use it in real life?

Absolutely! You can use it when counting items in groups, like how many cookies are in a box, or how many seats are in a theatre.