Age 12 guide to proportion

Quick answer

By the end of this page, you'll understand how to compare amounts using proportion – like sharing 12 biscuits equally between 4 friends or working out how much 3 cakes cost if 1 cake costs £2.

Learning outcome

By the end of this page, you will be able to:

• Compare quantities using equal parts (proportion)
• Use multiplication and division to solve proportion problems
• Recognise when two amounts are in proportion
• Apply proportion to real-life situations like sharing, shopping, and cooking

Why this matters

Understanding proportion helps you share things fairly, work out prices, and solve problems in everyday life. You use it when you're splitting a pizza between friends, buying 3 apples for the same price as 1 apple, or even when you're playing a board game and need to know how many spaces to move.

Proportion is also a key part of more advanced maths like ratios, percentages, and fractions – so it's a strong foundation for your future learning!

How it works

Proportion is about comparing two amounts by seeing how many times one fits into the other. You can think of it as sharing things equally or finding how much one part is worth compared to the whole.

Here’s how to work with proportion:

1. Find equal parts – Decide how many equal groups you need.
2. Share or multiply – Either divide the total amount into equal parts, or multiply to find a bigger amount.
3. Check your answer – Make sure the amounts are fair and match the problem.

Examples you can see

Let’s look at some simple examples:

Example 1: Sharing equally

You have 12 sweets and want to share them equally between 3 friends. How many sweets does each friend get?

• Step 1: You have 12 sweets and 3 friends.
• Step 2: Divide 12 by 3 to find how many each friend gets.
• Step 3: 12 ÷ 3 = 4 sweets per friend.

This shows that 12 sweets in 3 equal parts means 4 sweets per part.

Example 2: Buying more

If 1 cake costs £2, how much do 5 cakes cost?

• Step 1: Find the cost of 1 cake = £2
• Step 2: Multiply by 5 to find the cost of 5 cakes.
• Step 3: £2 × 5 = £10

This shows that 5 times the amount of one cake gives you the total cost.

Example 3: Mixing ingredients

A recipe uses 2 cups of flour for every 1 cup of sugar. If you use 6 cups of flour, how much sugar do you need?

• Step 1: The ratio is 2 cups flour : 1 cup sugar
• Step 2: You have 6 cups of flour, which is 3 times more than 2 cups.
• Step 3: So you need 3 times more sugar = 3 × 1 = 3 cups of sugar.

This shows how proportion helps you keep recipes balanced!

Try it as a mini adventure

Adventure: The Supermarket Shopping Trip

You’re going to the supermarket with £10 to buy some snacks. You see 3 packets of crisps for £1.50 each. You also see 2 bags of sweets for £2.00 each. You want to buy as many items as possible without going over £10.

Your challenge:

1. How many packets of crisps can you buy with £10?
2. How many bags of sweets can you buy with £10?
3. If you buy 4 packets of crisps and 1 bag of sweets, how much will it cost?
4. Can you buy 3 packets of crisps and 2 bags of sweets with £10? Why or why not?

Hint: Use multiplication and division to work out the total costs and check if you stay under £10.

Common mistakes

• Mistake: Thinking that if you double one amount, you must double the other too.
• Why it happens: Children often forget that proportion means the relationship between amounts, not that they always increase together.
• Fix: Always check the relationship – does one amount increase or decrease with the other?

• Mistake: Confusing "how many times more" with "how many more".
• Why it happens: These phrases sound similar, but they mean different things.
• Fix: Use examples like "5 is 2 times more than 2.5" vs "5 is 2.5 more than 2.5".

• Mistake: Not checking if the answer makes sense in the real world.
• Why it happens: Sometimes children do the maths but forget to think if it’s realistic.
• Fix: Ask yourself, “Does this answer make sense?” For example, can you buy 1.5 bags of sweets?

Parent and carer guide

Helping your child understand proportion can be fun and practical:

1. Use everyday situations – Ask your child to share snacks or count items in equal groups.
2. Encourage drawing or using objects – Use counters, blocks, or drawings to show how things can be split.
3. Ask questions – “If you had 12 cookies and shared them with 4 friends, how many would each friend get?”
4. Keep it light – Don’t worry if they get it wrong – it’s part of learning!
5. Be patient – Some children need time to understand the idea of sharing and comparing.

Remember: proportion is about seeing the relationship between amounts, not just doing calculations.

Practice questions

1. There are 24 pencils shared equally between 6 students. How many pencils does each student get?
2. If 1 toy car costs £3, how much do 7 toy cars cost?
3. A recipe uses 3 cups of rice for every 1 cup of lentils. If you use 9 cups of rice, how many cups of lentils do you need?
4. You have £15 and want to buy ice creams that cost £2.50 each. How many ice creams can you buy?
5. If 10 apples cost £4, how much do 5 apples cost?

Answers:

1. 24 ÷ 6 = 4 pencils each
2. £3 × 7 = £21
3. 9 ÷ 3 = 3 cups of lentils
4. £15 ÷ £2.50 = 6 ice creams
5. £4 ÷ 10 = £0.40 per apple, so £0.40 × 5 = £2

FAQ

What is proportion?

Proportion is about comparing two amounts to see how they relate to each other, especially when you need to share or multiply them fairly.

How is proportion used in real life?

Proportion is used when sharing food, buying items, cooking recipes, and even playing games where you need to know how many points or spaces to move.

How can I help my child learn proportion?

You can help by using everyday situations like sharing snacks, cooking, or shopping, and asking questions about how amounts relate to each other.

Is proportion the same as ratio?

Not exactly! A ratio compares two amounts (like 2:1), while proportion shows how they relate in a fair way (like 2 parts to 1 part).

What if my child finds proportion hard?

Start with simple sharing problems using physical objects. Practice with drawings or counters to help them see the equal parts.