Coin Combinations maths mission

Quick answer

You can make any amount of money using different combinations of coins, and learning how to do this helps you practice your number bonds and become better at adding up money.

Learning outcome

By the end of this page, you will be able to find different ways to make a given amount of money using UK coins, and you will understand how to add up different coin values to reach a total.

• You can use different coin combinations to make the same amount of money
• You can add up coin values to find the total
• You can spot patterns in how coins can be grouped to make money
• You can solve small money problems using your knowledge of coin values

Why this matters

Learning about coin combinations helps you understand how money works in real life. When you go shopping, you might need to give the right amount of money or work out how much change you should get. By practising coin combinations, you're getting better at adding numbers, using number bonds, and thinking about how to solve money problems.

Whether you're saving up for a toy, helping your parent with a shop, or playing a game where you earn coins, coin combinations are useful for many everyday situations. You'll also be building a strong base for understanding larger amounts of money, like pounds and pence, and even how to count money in your head.

How it works

Let’s start with the UK coins: 1p, 2p, 5p, 10p, 20p, 50p, £1, and £2. These are the coins you’ll be working with.

Step 1: Look at the amount of money you want to make.

Step 2: Start with the biggest coin and work your way down to the smallest coin.

Step 3: See how many of that coin you can use without going over the amount.

Step 4: Keep adding coins until you reach the exact amount.

Step 5: Try different combinations to see how many ways you can make that amount.

Examples you can see

Let’s imagine you want to make 25p. Here’s how you can do it:

• One 20p coin and one 5p coin
• Two 10p coins and one 5p coin
• Five 5p coins
• One 10p coin, one 5p coin, and ten 1p coins
• Two 10p coins and five 1p coins

Try to make 20p using different combinations. You might use:

• Two 10p coins
• One 10p coin, two 5p coins, and one 2p coin
• One 10p coin, one 5p coin, and five 1p coins

You can also try with £1. For example, you can make £1 with:

• Ten 10p coins
• Two 50p coins
• One 50p coin, two 20p coins, and one 10p coin
• One £1 coin (of course!)

Try it as a mini adventure

Adventure: The Coin Collector’s Challenge

You are a coin collector who wants to fill a special box with exactly 50p. You can only use coins from your piggy bank. You find these coins:

• One 20p coin
• Two 10p coins
• One 5p coin
• Three 2p coins
• Four 1p coins

Can you make exactly 50p using these coins? How many different ways can you do it?

Step 1: Start with the biggest coin. You have a 20p coin. So you can use it and then find the rest to make 30p.

Step 2: You have two 10p coins. You can use both and then make 10p with the rest.

Step 3: Try to use the 5p coin and see how much more you need.

Step 4: Use the 2p and 1p coins to make the final amount.

Now, try to find all the different combinations you can make to reach 50p using the coins you have.

Common mistakes

• Mistake: Thinking that 10p + 10p + 10p + 10p + 10p = 50p, but forgetting to check if you have that many 10p coins.
• Why it happens: It's easy to count coins quickly and forget to double-check if you have enough of each type.
• Fix: Always check how many coins you have before you start.
• Mistake: Adding 10p + 5p + 2p + 1p and getting 18p instead of 18p (this is actually correct, but the mistake is in the thinking).
• Why it happens: When adding many coins, it's easy to lose track of what you're counting.
• Fix: Use a table or write down the coins you are using as you go.
• Mistake: Trying to make 25p with only 1p and 2p coins, but forgetting that 2p coins are worth more than 1p coins.
• Why it happens: Children may not fully understand the value of coins and might get confused by smaller numbers.
• Fix: Use a visual chart or real coins to help compare values.

Parent and carer guide

Helping your child with coin combinations can be a fun way to practice maths. Here’s how:

1. Start with small amounts: Begin with 5p or 10p to build confidence.
2. Use real coins: Let your child handle real UK coins to understand their value.
3. Play a game: Challenge them to make a certain amount using the fewest coins.
4. Encourage exploration: Let them try different combinations and ask "How many ways can you make this?"
5. Be patient: It takes time to understand how different coins can be grouped. Don’t rush them.

Remember, your child is learning to add, think strategically, and solve problems. Celebrate their efforts, not just the correct answers!

Practice questions

1. How many ways can you make 15p using UK coins?
2. Can you make 30p using only 10p and 5p coins?
3. What is the smallest number of coins you can use to make 40p?
4. How many 2p coins are needed to make 10p?
5. Can you make 50p using exactly 5 coins?

Answers:

1. There are several ways, such as 10p + 5p, 5p + 5p + 5p, 10p + 2p + 2p + 1p, etc.
2. Yes, you can use 2 × 10p + 2 × 5p or 6 × 5p.
3. Two 20p coins make 40p with the fewest coins.
4. You need 5 × 2p coins to make 10p.
5. Yes, for example, 10p + 10p + 10p + 10p + 10p.

FAQ

How can I help my child practice coin combinations at home?

You can use real coins or play money to make different amounts together. Ask your child to find different ways to make the same amount. You can also set up a pretend shop and let them practice paying with coins.

What coins are used in the UK?

The UK coins are 1p, 2p, 5p, 10p, 20p, 50p, £1, and £2.

Why do we need to know coin combinations?

Understanding coin combinations helps you count money, give the right amount when shopping, and work out how much change you should get. It also helps you build your number bonds and mental maths skills.

Can I use coin combinations to learn about multiplication?

Yes! For example, if you have 3 coins of 10p, that’s 3 × 10p = 30p. This connects to multiplication and repeated addition.

How can I make coin combinations more fun for my child?

You can make a game where your child finds different combinations to make a target amount. You can also use coins to play board games or pretend to go shopping. You can even create a chart to track how many different ways they find to make a certain amount.