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Maths Adventures

Fairground maths quest: ratio

A story-led junior maths adventure using rides, tickets and chance games to mix recipes, scale drawings and compare quantities.

Quick answer

Ratio is a way to compare how much of one thing there is compared to another. You can use ratio when sharing sweets, mixing paint, or planning a fairground ride.

Learning outcome

By the end of this page, you will be able to compare amounts using ratio in simple real-life situations, like sharing rides, mixing drinks, or planning fairground stalls. Success signs:
  • You can say "For every 2 red balls, there is 1 blue ball" or "The ratio of adults to children is 1:3"
  • You can match ratios to pictures or objects
  • You can solve simple ratio problems with real-world examples
  • You can explain why ratio helps us share things fairly

Why this matters

Ratios help us understand how things relate to each other. When you're at a fairground, ratios help you know how many tickets to buy, how much to share with friends, or how much paint to mix for a big banner. Understanding ratio is important for cooking, shopping, and even planning your own dream fairground.

How it works

Ratios compare two or more amounts. We write them using a colon (:) like this: 2:3. This means "2 of one thing, and 3 of another thing". Let's start with simple examples:
  1. Imagine you have 2 red balls and 3 blue balls. The ratio is 2:3
  2. If you have 4 apples and 2 oranges, the ratio is 4:2 (or simplified to 2:1)
  3. Ratios can compare more than two things. If you have 3 red, 2 blue, and 1 green ball, the ratio is 3:2:1

Examples you can see

Here are some fun fairground examples to help you understand ratios: Example 1: Balloons You have 6 yellow balloons and 3 purple balloons. The ratio of yellow to purple is 6:3. This can be simplified to 2:1 (because 6 ÷ 3 = 2 and 3 ÷ 3 = 1). So for every 2 yellow balloons, there is 1 purple balloon. Example 2: Ticket Machines At the fairground, there are 8 ticket machines and 4 staff members. The ratio of machines to staff is 8:4. This simplifies to 2:1. So for every 2 ticket machines, there is 1 staff member. Example 3: Candy Mix You want to make a candy mix with 10 red candies and 15 green candies. The ratio is 10:15. This simplifies to 2:3. So for every 2 red candies, there are 3 green candies. Example 4: Ride Capacity A rollercoaster holds 12 people, and there are 4 cars. The ratio of people to cars is 12:4. This simplifies to 3:1. So for every 3 people, there is 1 car.

Try it as a mini adventure

Adventure: The Fairground Ratio Quest You are the head of a new fairground and need to plan how to set up your rides and stalls. Step 1: You have 12 ticket machines and 6 staff members. What is the ratio of machines to staff? Answer: 12:6 = 2:1 Step 2: You want to mix 15 red candies and 10 blue candies for a sweet stall. What is the ratio of red to blue? Answer: 15:10 = 3:2 Step 3: You have 8 Ferris wheels and 16 seats. What is the ratio of wheels to seats? Answer: 8:16 = 1:2 Step 4: You are planning a game where you give out 20 prizes and 50 tickets. What is the ratio of prizes to tickets? Answer: 20:50 = 2:5 Step 5: You have 9 cotton candy stalls and 3 ice cream stalls. What is the ratio of cotton candy to ice cream? Answer: 9:3 = 3:1

Common mistakes

  • Mistake: Thinking 6:4 and 4:6 are the same ratio Why it happens: Children mix up the order of numbers Fix: Remember the first number always refers to the first thing you're comparing
  • Mistake: Not simplifying ratios Why it happens: Not knowing that 6:4 can be simplified to 3:2 Fix: Divide both numbers by the same amount to find the simplest form
  • Mistake: Adding instead of comparing Why it happens: Confusing ratio with addition Fix: Ratio compares parts, not total amounts
  • Mistake: Using the wrong units Why it happens: Mixing up what you're comparing Fix: Make sure both sides of the ratio measure the same type of thing

Parent and carer guide

How to help your child at home:
  1. Use everyday examples like sharing snacks or mixing drinks
  2. Ask your child to find ratios in their room (e.g., 3 books to 1 toy)
  3. Play ratio games: "For every 2 red blocks, use 1 blue block"
  4. Use visual aids like drawings or objects to show ratios
  5. Keep practice fun and short - 5-10 minutes at a time
What to watch for:
  • Children may mix up the order of numbers in a ratio
  • They might not understand that ratios can be simplified
  • They may confuse ratio with addition or subtraction
  • They might struggle with three-part ratios
What not to worry about:
  • It's normal for children to need practice with ratios
  • Mistakes are learning opportunities
  • Don't rush - understanding takes time
  • Keep it playful and connected to real-life situations

Practice questions

  1. There are 4 red cars and 6 blue cars. What is the ratio of red to blue cars?
  2. You have 12 blue balloons and 8 green balloons. What is the ratio of blue to green?
  3. There are 5 strawberry cakes and 10 chocolate cakes. What is the ratio of strawberry to chocolate?
  4. You have 15 yellow marbles and 5 red marbles. What is the ratio of yellow to red?
  5. There are 8 swings and 12 slides. What is the ratio of swings to slides?
Answers:
  1. 4:6 = 2:3
  2. 12:8 = 3:2
  3. 5:10 = 1:2
  4. 15:5 = 3:1
  5. 8:12 = 2:3

FAQ

What is a ratio?

A ratio is a way to compare how much of one thing there is compared to another. It tells us the relationship between two or more amounts.

How do you write a ratio?

We write ratios using a colon (:). For example, 3:5 means 3 of one thing and 5 of another.

Can ratios be simplified?

Yes! Just like fractions, ratios can be simplified by dividing both numbers by the same amount. For example, 6:4 simplifies to 3:2.

Where can I find ratios in real life?

Ratios appear everywhere: in recipes (2 cups of flour to 1 cup of sugar), in games (1 player to 2 teams), in maps (1 cm to 1 km), and at the fairground (2 rides to 1 staff member).

How can I practice ratios at home?

Try these activities: share snacks with a ratio (like 2 cookies for every 1 biscuit), look for ratios in your room, or use toys to make different ratios (3 cars to 1 train).