Multiplication as repeated addition

Quick answer

Multiplication is like adding the same number over and over again. If you have 3 groups of 4 apples, that's 4 + 4 + 4 = 12 apples. That's the same as 3 × 4 = 12.

Learning outcome

By the end of this page, you will understand that multiplication is repeated addition and be able to use this idea to solve simple multiplication problems.

• You can show multiplication as adding the same number many times.
• You can match repeated addition sentences to multiplication sentences.
• You can solve simple multiplication problems using repeated addition.
• You can explain how groups of objects help you understand multiplication.

Why this matters

Multiplication as repeated addition helps you understand what multiplication really means. It's a way to think about multiplication that makes it easier to solve problems, especially when you're just starting to learn times tables. This idea is helpful when you're learning how to multiply numbers, and it helps you build a strong foundation for more advanced maths later on. You'll use this idea when you're sharing cookies, counting your toys, or even playing games!

How it works

Let's imagine you have some objects and you want to count them quickly. Instead of counting one by one, you can group them and then add the same number again and again. Here's how it works:

1. Look at the number of groups you have.
2. Look at how many items are in each group.
3. Add the number of items in each group together.
4. That total is the same as multiplying the number of groups by the number in each group.

For example, if you have 4 groups of 3 sweets, you can add 3 + 3 + 3 + 3 = 12. That's the same as 4 × 3 = 12.

Examples you can see

Let's look at some real examples that show how multiplication is repeated addition:

Try this with your hands or toys:

• Put 3 groups of 4 pencils on your table.
• Count all the pencils by adding: 4 + 4 + 4 = 12.
• That's the same as 3 × 4 = 12.

Try it as a mini adventure

Imagine you're a treasure hunter and you found a chest with 6 treasure maps. Each map shows 3 gold coins. How many gold coins are there in total?

Let's solve this like a detective:

1. You have 6 treasure maps.
2. Each map shows 3 gold coins.
3. So you add: 3 + 3 + 3 + 3 + 3 + 3 = 18.
4. That means 6 × 3 = 18.

Great detective work! You found 18 gold coins in total.

Common mistakes

• Mistake: Thinking 5 × 3 means 5 + 3 = 8.
• Why it happens: Confusing multiplication with addition.
• Fix: Remember that 5 × 3 means 5 groups of 3, so add 3 five times: 3 + 3 + 3 + 3 + 3 = 15.

• Mistake: Counting the number of groups instead of the number in each group.
• Why it happens: Not paying attention to what the numbers mean.
• Fix: Always ask, "How many groups?" and "How many in each group?"

• Mistake: Forgetting to count all the groups.
• Why it happens: Getting distracted or rushing.
• Fix: Count your groups carefully, or use a visual aid like fingers or counters.

Parent and carer guide

Helping your child understand multiplication as repeated addition is simple and fun:

• Use everyday objects like toys, fruit, or crayons to show groups.
• Ask your child to count the groups and items in each group.
• Encourage them to write the repeated addition sentence and the multiplication sentence.
• Play games like "How many legs do 3 cats have?" or "How many wheels do 4 cars have?"
• Don't worry if they make mistakes – it's part of learning!

Try this activity: Give your child 12 counters and ask them to make 3 groups with 4 in each group. Then ask them to add 4 + 4 + 4 = 12 and write 3 × 4 = 12. This helps them see the connection clearly.

Practice questions

1. What is 4 × 3? Show your repeated addition.
2. What is 5 × 2? Show your repeated addition.
3. What is 3 × 6? Show your repeated addition.
4. What is 2 × 7? Show your repeated addition.
5. What is 6 × 4? Show your repeated addition.

Answers:

1. 4 × 3 = 12; 3 + 3 + 3 + 3 = 12
2. 5 × 2 = 10; 2 + 2 + 2 + 2 + 2 = 10
3. 3 × 6 = 18; 6 + 6 + 6 = 18
4. 2 × 7 = 14; 7 + 7 = 14
5. 6 × 4 = 24; 4 + 4 + 4 + 4 + 4 + 4 = 24

FAQ

What is multiplication as repeated addition?

Multiplication is when you add the same number over and over again. For example, 3 × 4 means 4 + 4 + 4 = 12.

Why is repeated addition helpful?

It helps you understand what multiplication really means, especially when you're just learning. It makes the idea of groups and equal amounts easier to see.

Can all multiplication be shown as repeated addition?

Yes, all multiplication can be shown as repeated addition. Even 0 × 5 = 0 is 5 + 5 + 5 + 5 + 5 = 0 if you have 0 groups of 5.

How can I practice this at home?

Use everyday items like toys, fruits, or crayons. Make groups and add them up. For example, 4 groups of 3 apples is 3 + 3 + 3 + 3 = 12.

What comes next after learning repeated addition?

After repeated addition, children learn to memorize times tables and use them quickly. But understanding repeated addition helps them remember and use times tables better.