Maths Adventures
Train maths quest: ratio
A story-led junior maths adventure using timetables, distances and platform clues to mix recipes, scale drawings and compare quantities.
Quick answer
You can use ratios to compare amounts and solve problems, like figuring out how much of each ingredient you need to make a recipe, or how many stops a train makes between two places.Learning outcome
By the end of this page, you will understand how to use ratios to compare quantities and solve problems in everyday life, like planning a train journey or mixing ingredients for a recipe. Success signs:- You can explain what a ratio is using examples like 2 red cars to 3 blue cars
- You can find the missing number in a simple ratio like 2 : 3 = 4 : ?
- You can use ratios to solve problems about train stops, ingredients, or sharing
- You can create your own ratio problem and solve it
Why this matters
Ratios help you understand how things relate to each other. When you're planning a train journey, you might need to know how many stops are between cities. When you're cooking, you might need to double a recipe. When you're building with blocks, you might need to make sure you have the right number of each type of block. Ratios are used everywhere – in sports, in science, in art, and in your daily life.How it works
A ratio compares two or more amounts. It can be written in different ways:- Using a colon: 2 : 3
- Using words: 2 to 3
- As a fraction: 2/3
Examples you can see
Let's imagine you're on a train journey. You're going from London to Manchester. On your way, you pass through 3 stations. The timetable shows:- London to Birmingham: 2 stops
- Birmingham to Leeds: 3 stops
- Leeds to Manchester: 1 stop
- Step 1: Write the ratio 2 : 3
- Step 2: If you use 4 cups of flour, that's double the amount in the ratio
- Step 3: So you need double the amount of sugar: 3 × 2 = 6 cups
- Answer: You need 6 cups of sugar
- Step 1: Count the red flowers: 4
- Step 2: Count the yellow flowers: 6
- Step 3: Write the ratio: 4 : 6
- Step 4: Simplify the ratio by dividing both numbers by 2: 4 ÷ 2 = 2, 6 ÷ 2 = 3
- Answer: The ratio is 2 : 3
Try it as a mini adventure
Train Maths Quest: The Journey of the Mixed Ingredients You are on a train journey from London to Edinburgh. Your train makes 3 stops: Birmingham, Leeds, and Newcastle. You are helping the train conductor by mixing ingredients for snacks. Here's your mission: Step 1: The train makes 2 stops in the first part of the journey. Step 2: The train makes 3 stops in the second part of the journey. Step 3: The train makes 1 stop in the final part of the journey. You need to make a snack mix using the ratio of 2 : 3 : 1 for nuts, fruits, and seeds. Step 4: If you use 10 cups of nuts, how many cups of fruits and seeds do you need? Step 5: If you have 15 cups of fruits, how many cups of nuts and seeds do you need? Step 6: If you use 12 cups of seeds, how many cups of nuts and fruits do you need? Step 7: Create your own ratio problem using the train journey stops and solve it.Common mistakes
- Mistake: Writing the ratio in the wrong order, like 3 : 2 instead of 2 : 3. Why it happens: Confusion about which amount comes first. Fix: Always read the ratio carefully and make sure you're comparing the correct amounts.
- Mistake: Forgetting to simplify the ratio. Why it happens: Not checking if both numbers can be divided by the same number. Fix: Divide both numbers by their greatest common factor to simplify the ratio.
- Mistake: Not using the same units when comparing. Why it happens: Mixing up cups, plates, and pieces. Fix: Always make sure you're comparing the same type of units.
- Mistake: Thinking that 2 : 3 means 2 + 3 = 5. Why it happens: Confusing ratio with addition. Fix: Remember that ratios show how amounts relate to each other, not how to add them.
Parent and carer guide
How to help your child:- Encourage your child to think of ratios in everyday situations, like sharing food or planning a trip.
- Ask your child to explain what a ratio means in their own words.
- Use real-life examples like mixing paint or making a recipe to show how ratios work.
- Play games where your child needs to find ratios, such as counting animals or objects and writing the ratios.
- Don't worry if your child makes mistakes – ratios are a new concept and practice helps.
- Your child might confuse ratios with fractions or addition.
- Your child might forget to simplify ratios.
- Your child might write ratios in the wrong order.
Practice questions
- Write the ratio of 4 red balls to 6 blue balls in its simplest form.
- If the ratio of boys to girls in a class is 3 : 5 and there are 15 boys, how many girls are there?
- A train journey has 2 stops in the first part, 4 stops in the second part, and 3 stops in the third part. What is the ratio of stops?
- If you need 3 cups of flour for every 2 cups of sugar, how much sugar do you need if you use 9 cups of flour?
- The ratio of cats to dogs in a pet shop is 5 : 7. If there are 35 cats, how many dogs are there?
- 2 : 3
- 25 girls
- 2 : 4 : 3
- 6 cups of sugar
- 49 dogs
FAQ
What is a ratio?
A ratio compares two or more amounts. It shows how much of one thing there is compared to another.
How do you simplify a ratio?
To simplify a ratio, divide both numbers by their greatest common factor. For example, 6 : 9 simplifies to 2 : 3.
Can you use ratios with different units?
No, ratios should compare the same type of units. For example, you can compare apples to oranges, but not apples to metres.
How are ratios used in real life?
Ratios are used in cooking, shopping, science, and many other areas of life. They help you compare and solve problems.
How can I help my child learn ratios?
You can help by using everyday examples, playing games, and encouraging your child to explain ratios in their own words.