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Pocket Money Maths

Maths hiding in pocket money: coin combinations

Make the same amount in different coin combinations.

Quick answer

You can make the same amount of money using different combinations of coins. For example, 50p can be made with 2 x 20p + 10p, or 5 x 10p, or 10 x 5p.

Learning outcome

By the end of this page, you will be able to find different ways to make the same amount of money using different coin combinations. Success signs:
  • You can make 20p using different coin combinations
  • You can explain how to find new ways to make the same amount
  • You can work out how many different ways there are to make 50p
  • You can help a friend find different coin combinations

Why this matters

When you have pocket money, you often need to pay for things. Sometimes you might not have the exact coins you need. Learning how to make the same amount using different combinations helps you:
  • Understand how money works
  • Be more confident when shopping
  • Count and add coins quickly
  • Think of different solutions to the same problem
In games, you might need to collect coins and then spend them. In real life, you'll use this skill when shopping or saving up for something special.

How it works

To find different coin combinations that make the same amount:
  1. Start with the amount you want to make
  2. Think of the biggest coin you have that fits into that amount
  3. Use that coin as many times as possible
  4. Then use smaller coins to make up the rest
  5. Try different starting coins to find new combinations
Let's say you want to make 30p:
  • You could use 1 x 20p + 1 x 10p
  • You could use 3 x 10p
  • You could use 6 x 5p
  • You could use 1 x 20p + 2 x 5p

Examples you can see

Let's look at making 20p in different ways:
Combination Coins used Total
1 1 x 20p 20p
2 2 x 10p 20p
3 1 x 10p + 2 x 5p 20p
4 4 x 5p 20p
5 1 x 10p + 1 x 5p + 1 x 5p 20p
6 1 x 5p + 3 x 5p 20p
Here's how you might count these:
  • Try to make 20p with 1 coin: 1 x 20p = 20p
  • Try to make 20p with 2 coins: 2 x 10p = 20p
  • Try to make 20p with 4 coins: 4 x 5p = 20p
  • Try to make 20p with 5 coins: 1 x 10p + 2 x 5p = 20p

Try it as a mini adventure

Adventure: The Coin Collector's Challenge You are a coin collector who wants to make exactly 50p. You have a bag full of different coins: 20p, 10p, 5p, and 2p. You want to find all the different ways you can make 50p. Step 1: Start with the biggest coin you have – 20p.
  • How many 20p coins can you use? 2 x 20p = 40p
  • How much more do you need? 50p - 40p = 10p
  • How can you make 10p? 1 x 10p = 10p
  • So one way is: 2 x 20p + 1 x 10p = 50p
Step 2: Try using 1 x 20p.
  • 1 x 20p = 20p
  • You need 30p more
  • How can you make 30p with 10p, 5p, and 2p coins?
  • 3 x 10p = 30p
  • So another way: 1 x 20p + 3 x 10p = 50p
Step 3: Try using 0 x 20p.
  • You need 50p using only 10p, 5p, and 2p coins
  • How many 10p coins can you use? 5 x 10p = 50p
  • So: 5 x 10p = 50p
Step 4: Try using 4 x 10p.
  • 4 x 10p = 40p
  • Need 10p more
  • How can you make 10p with 5p and 2p coins?
  • 2 x 5p = 10p
  • So: 4 x 10p + 2 x 5p = 50p
Step 5: Try using 3 x 10p.
  • 3 x 10p = 30p
  • Need 20p more
  • How can you make 20p with 5p and 2p coins?
  • 10 x 2p = 20p
  • So: 3 x 10p + 10 x 2p = 50p
Step 6: Try using 2 x 10p.
  • 2 x 10p = 20p
  • Need 30p more
  • How can you make 30p with 5p and 2p coins?
  • 15 x 2p = 30p
  • So: 2 x 10p + 15 x 2p = 50p
Step 7: Try using 1 x 10p.
  • 1 x 10p = 10p
  • Need 40p more
  • How can you make 40p with 5p and 2p coins?
  • 20 x 2p = 40p
  • So: 1 x 10p + 20 x 2p = 50p
Step 8: Try using 0 x 10p.
  • Need 50p with only 5p and 2p coins
  • How can you make 50p with 5p coins? 10 x 5p = 50p
  • So: 10 x 5p = 50p
Step 9: Try using 0 x 5p.
  • Need 50p with only 2p coins
  • How many 2p coins make 50p? 25 x 2p = 50p
  • So: 25 x 2p = 50p
You found 9 different ways to make 50p using your coins!

Common mistakes

  • Mistake: Using too many coins of the same type.
    Why it happens: You might think more coins always mean more money.
    Fix: Remember that 10 x 5p = 50p, but 2 x 20p + 1 x 10p = 50p too. Smaller numbers of bigger coins can work just as well.
  • Mistake: Forgetting to check that all combinations add up to the same amount.
    Why it happens: You might get excited and not double-check.
    Fix: Always add up your coins to check the total matches the target amount.
  • Mistake: Only using the biggest coins first.
    Why it happens: It's easier to start with big numbers.
    Fix: Try different starting points to find more combinations.
  • Mistake: Counting coins in the wrong order.
    Why it happens: You might skip a coin or count it twice.
    Fix: Count each coin once and write down the combination as you go.

Parent and carer guide

How to help your child:
  • Set up a pretend shop with different items and prices
  • Give your child 50p and ask them to find different ways to make that amount
  • Ask questions like: "Can you make 30p with only 5p coins?" or "What if you had to use exactly 6 coins?"
  • Encourage them to write down their combinations to see patterns
  • Use real coins or play money to make it hands-on
  • Notice when they're using different strategies – this shows understanding
  • Don't worry if they get confused at first – it's normal to try different ways
  • Give praise for effort, not just correct answers
  • Ask them to explain their thinking to you – this helps solidify learning
  • Make it fun – turn it into a game or challenge

Practice questions

  1. How many ways can you make 10p using 10p, 5p, and 2p coins?
  2. Find 3 ways to make 25p using 10p, 5p, and 2p coins.
  3. Can you make 40p using only 10p and 5p coins?
  4. How many 5p coins do you need to make 30p?
  5. Find a way to make 35p using exactly 7 coins.
Answers:
  1. 4 ways: 1 x 10p, 2 x 5p, 1 x 5p + 5 x 2p, 5 x 2p + 1 x 5p
  2. Answers may vary. Example: 2 x 10p + 1 x 5p, 1 x 10p + 3 x 5p, 5 x 5p
  3. Yes: 4 x 10p or 8 x 5p
  4. 6 coins
  5. Example: 5 x 5p + 2 x 10p = 35p

FAQ

How many ways can you make 20p?

There are 9 different ways to make 20p using 20p, 10p, 5p, and 2p coins.

Can you make the same amount with different coins?

Yes! For example, 20p can be made with 1 x 20p, or 2 x 10p, or 4 x 5p, or 10 x 2p, or other combinations.

Why do we need to know how to make the same amount in different ways?

It helps us understand how money works, count coins quickly, and solve problems when we don't have the exact coins we need.

What coins do you usually use in the UK?

UK coins are 1p, 2p, 5p, 10p, 20p, and 50p. We also have £1 and £2 coins.

How can I practice this at home?

Use real coins or play money to make different amounts. Try to find as many ways as you can to make the same amount. You can also use online coin games or apps to practice.