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Place Value

Dienes blocks activities

Hands-on tasks with base-ten blocks for place value and regrouping.

Quick answer

Dienes blocks are base-ten blocks that help children understand place value by showing how numbers are made up of tens and ones. You can use them to build numbers, regroup, and solve addition and subtraction problems.

Learning outcome

By the end of this page, you will be able to use Dienes blocks to show how numbers are made up of tens and ones, and to solve simple addition and subtraction problems using these blocks. Success signs:
  • You can build any number from 1 to 100 using the blocks
  • You can regroup 10 ones into 1 ten block
  • You can add two numbers using the blocks
  • You can subtract by taking away blocks

Why this matters

Understanding place value is the foundation for all arithmetic. It helps you:
  • Read and write numbers correctly
  • Add and subtract larger numbers
  • Learn multiplication and division
  • Understand money, time, and measurement
Dienes blocks make these ideas concrete so you can see and touch the maths.

How it works

Dienes blocks are special blocks that help you understand how numbers work:
  1. One block = 1 unit
  2. Long block = 10 ten
  3. Flat block = 10 tens = 100 hundred
  4. Cube block = 10 hundreds = 1,000 thousand
You can use these blocks to build numbers and show how they are made up of tens and ones.

Examples you can see

Let's build the number 23 using Dienes blocks:
  • 2 long blocks (2 tens = 20)
  • 3 one blocks (3>
So 23 = 2 tens + 3 ones. Let's try another number: 57
  • 5 long blocks (5 tens = 50)
  • 7 one blocks (7>
So 57 = 5 tens + 7 ones. Let's see how to make 100:
  • 1 flat block (1 hundred = 100)
Or:
  • 10 long blocks (10 tens = 100)
Or:
  • 100 one blocks (100>

Try it as a mini adventure

The Block Treasure Hunt You are a treasure hunter looking for a hidden chest. The map says the chest is buried where the number 34 is hidden. To find it, you must:
  1. Use 3 long blocks to show 3 tens
  2. Use 4 one blocks to show 4 ones
  3. Put them together to make 34
  4. Count all the blocks you used
Now, let's solve a problem:
  1. You start with 27 blocks
  2. You find 15 more blocks
  3. How many blocks do you have now?
Build 27 blocks first:
  • 2 long blocks
  • 7 one blocks
Then add 15 more:
  • 1 long block
  • 5 one blocks
Now count all the blocks:
  • 2 + 1 = 3 long blocks
  • 7 + 5 = 12 one blocks
Since 12 ones make 1 ten and 2 ones, you can regroup:
  • 3 + 1 = 4 long blocks
  • 2 one blocks
So you have 42 blocks in total.

Common mistakes

  • Mistake: Thinking that 10 ones make 10 blocks instead of 1 long block. Why it happens: Confusing the number of blocks with the value. Fix: Remember that 10 long block = 10 units.
  • Mistake: Mixing up tens and ones when building numbers. Why it happens: Not paying attention to which block is which. Fix: Always check that you have the right number of long blocks for tens and one blocks for ones.
  • Mistake: Forgetting to regroup when you have 10 ones. Why it happens: Not understanding that 10 ten. Fix: Count your one blocks and if you have 10 or more, make 1 long block and keep the rest.
  • Mistake: Not knowing how to show numbers like 100 or 1,000. Why it happens: Not knowing about the flat and cube blocks. Fix: Remember that 10 tens = 1 flat = 100, and 10 flats = 1 cube = 1,000.

Parent and carer guide

You can help your child learn with Dienes blocks in just 5-10 minutes:
  • Ask your child to build a number like 36
  • Count the long blocks and one blocks together
  • Try adding 23 + 14 using blocks
  • Let them make up their own problems
  • Don't worry if they make mistakes – that's how they learn!
Encourage your child to talk through what they're doing. Ask questions like:
  • How many tens do you have?
  • How many ones do you have?
  • Can you make 10 ones into a long block?
Remember, the goal is understanding, not speed.

Practice questions

  1. Build the number 45 using Dienes blocks. How many long blocks and one blocks do you need?
  2. How many long blocks and one blocks make 72?
  3. What number is shown by 3 long blocks and 8 one blocks?
  4. Build 100 using only long blocks. How many long blocks do you need?
  5. How many one blocks make 100?
Answers:
  1. 4 long blocks and 5 one blocks
  2. 7 long blocks and 2 one blocks
  3. 38
  4. 10 long blocks
  5. 100 one blocks

FAQ

What are Dienes blocks?

Dienes blocks are base-ten blocks that help children understand place value. They come in four sizes: one block (1 unit), long block (10 units), flat block (100 units), and cube block (1,000 units).

Why are they called Dienes blocks?

They are named after Zoltán Dienes, a Hungarian mathematician who developed these blocks to help children learn mathematics in a concrete way.

Can I use Dienes blocks for numbers bigger than 100?

Yes! You can use flat blocks for hundreds, and cube blocks for thousands. For example, 1,234 would be 1 cube, 2 flats, 3 long blocks, and 4 one blocks.

How do I know when to regroup?

You regroup when you have 10 or more one blocks. Make 1 long block and keep the rest. You also regroup when you have 10 or more long blocks – make 1 flat block and keep the rest.

Are Dienes blocks only for young children?

No! Dienes blocks are helpful for all ages. They can be used to teach addition, subtraction, multiplication, division, and even algebra concepts.