Multiplication with base-ten blocks

Quick answer

You can use base-ten blocks to build multiplication problems by making groups of tens and ones, then counting all the blocks to find the answer.

Learning outcome

By the end of this page, you will be able to multiply numbers by making groups with base-ten blocks and counting the total blocks you have.

• You can make equal groups of tens and ones blocks to show multiplication.
• You can count the total number of blocks in your groups to find the answer.
• You can use base-ten blocks to solve simple multiplication problems.
• You can explain how multiplication is about making equal groups.

Why this matters

Multiplication is like making equal groups, and base-ten blocks help you see that. When you're shopping, sharing snacks, or playing games, you often need to know how many things you have when you have the same amount many times. Base-ten blocks help you understand this idea by letting you build and count with physical objects. This makes multiplication easier to understand than just using numbers on paper.

How it works

Base-ten blocks help you understand multiplication by building equal groups:

1. First, you decide how many groups you need.
2. Then, you decide how many blocks go in each group.
3. Next, you make that many groups with the same number of blocks.
4. Finally, you count all the blocks you used to get your answer.

Examples you can see

Let's look at how to multiply using base-ten blocks with a simple example:

Example 1: 3 × 4

Here, you need 3 groups with 4 blocks in each group.

• First group: 4 ones blocks
• Second group: 4 ones blocks
• Third group: 4 ones blocks

Now count all the ones blocks: 4 + 4 + 4 = 12 blocks total.

Example 2: 2 × 10

Here, you make 2 groups with 10 blocks in each group.

• First group: 1 tens block and 0 ones blocks
• Second group: 1 tens block and 0 ones blocks

Count all the blocks: 2 tens blocks = 20 blocks total.

Try it as a mini adventure

The Block Builder's Challenge

You are a builder who needs to make a tower. Each layer of the tower has 5 blocks. You need to make 4 layers. How many blocks do you need in total?

Step 1: Decide how many groups you need: 4 layers.

Step 2: Decide how many blocks are in each group: 5 blocks per layer.

Step 3: Build 4 groups of 5 blocks each.

Step 4: Count all the blocks you used.

Step 5: Write your answer: 4 × 5 = 20 blocks.

Common mistakes

• Mistake: Counting only one group instead of all groups.
• Why it happens: Forgetting that multiplication is about equal groups.
• Fix: Make sure you build the correct number of groups, and count all of them.
• Mistake: Mixing up tens and ones blocks.
• Why it happens: Not paying attention to what each block represents.
• Fix: Remember that a long block is 10, and a small block is 1.
• Mistake: Adding the number of groups and blocks instead of multiplying.
• Why it happens: Thinking that 3 groups of 4 means 3 + 4.
• Fix: Remember that multiplication means "groups of" and you need to count the total blocks in all groups.

Parent and carer guide

Helping your child with multiplication using base-ten blocks is a fun way to learn. Here’s how to support them in 5-10 minutes:

• Give your child a set of base-ten blocks and ask them to make 3 groups of 6 blocks.
• Ask them to count the total blocks and explain how they did it.
• Encourage them to use words like "groups of" and "equal groups" to describe what they built.
• Ask them to try a new problem, like 5 × 3, and see if they can build it themselves.
• Don’t worry if they make a mistake — it’s part of learning!

Practice questions

1. What is 4 × 5?
2. What is 2 × 8?
3. What is 6 × 3?
4. What is 10 × 2?
5. What is 7 × 4?

Answers:

1. 20
2. 16
3. 18
4. 20
5. 28

FAQ

What are base-ten blocks?

Base-ten blocks are physical tools that help you understand numbers. They include small cubes for ones, long rods for tens, and flat squares for hundreds.

How do I use base-ten blocks for multiplication?

You make equal groups of blocks and count all the blocks to find the answer to your multiplication problem.

Can I use base-ten blocks for bigger numbers?

Yes! You can use base-ten blocks for any multiplication problem, even with bigger numbers, by making more groups or using hundreds blocks.

Why are base-ten blocks helpful?

They help you see multiplication as groups, which makes it easier to understand than just memorising facts.

Can I use base-ten blocks to learn times tables?

Yes! You can use base-ten blocks to build and count groups for each times table, which helps you learn and remember the facts.