Age 11 guide to ratio beginnings
Age-appropriate activities, explanations and practice ideas for ratio beginnings.
Quick answer
By the end of this page, you will understand what ratios are and how to use them to compare amounts of things, like 3 red apples to 2 green apples, or 4 cookies to 1 cup of milk.
Learning outcome
By the end of this page, you will be able to:
- Understand what a ratio is and how it compares two amounts
- Write ratios in the form "a to b" or "a:b"
- Use ratios to describe real-life situations like sharing food or mixing drinks
- Find equivalent ratios by multiplying both parts of the ratio by the same number
Why this matters
Ratios help you understand how things relate to each other. You use ratios every day without realising it! For example, when you share a pizza with a friend, you might split it 2 slices for you and 1 slice for them – that’s a ratio of 2 to 1. When you make a smoothie, you might use 3 bananas to 2 cups of milk – that’s also a ratio. Understanding ratios helps you share fairly, cook properly, and solve problems in games, sports, and everyday life.
How it works
Ratios are a way to compare two amounts. They show how much of one thing there is compared to another. For example, if you have 3 red marbles and 2 blue marbles, the ratio of red to blue is 3 to 2 or 3:2.
- First, count how many of each thing you have.
- Then, write the numbers in the order you're comparing them.
- Use either "to" or a colon (:) to separate the numbers.
- You can simplify a ratio by dividing both numbers by the same amount.
Examples you can see
Let’s imagine you’re making a fruit salad with 4 strawberries and 6 blueberries.
| Fruit | Count | Ratio |
|---|---|---|
| Strawberries | 4 | 4 to 6 |
| Blueberries | 6 | 4:6 |
You can simplify this ratio by dividing both numbers by 2:
| Original | Simplified |
|---|---|
| 4 to 6 | 2 to 3 |
| 4:6 | 2:3 |
So, the ratio of strawberries to blueberries is 2 to 3.
Another example: In a class, there are 10 boys and 15 girls.
- Boys to girls = 10 to 15
- Boys to girls = 10:15
- Simplified = 2 to 3
Try it as a mini adventure
Adventure: The Magic Kitchen
You are a chef in a magical kitchen where recipes come to life! You have to make a potion using 2 drops of blue magic and 3 drops of red magic.
Step 1: You have 2 blue drops and 3 red drops. What is the ratio of blue to red? Answer: 2 to 3
Step 2: You need to make 10 times more potion. How many drops of each colour do you need? Answer: 20 blue drops and 30 red drops
Step 3: What is the ratio now? Answer: 20 to 30, which simplifies to 2 to 3
Step 4: You have 12 blue drops. How many red drops do you need? Answer: 18 red drops
Common mistakes
- Mistake: Writing the ratio in the wrong order (e.g., 3 to 2 instead of 2 to 3)
Why it happens: Confusing which item comes first when counting.
Fix: Always check the question and make sure you're comparing the right things. - Mistake: Forgetting to simplify the ratio
Why it happens: Thinking that 4:6 is already simple.
Fix: Divide both numbers by the same number to find the simplest form. - Mistake: Thinking that 1:2 and 2:4 are different ratios
Why it happens: Not knowing that they show the same relationship.
Fix: Simplify both ratios to see if they are the same.
Parent and carer guide
Helping your child with ratios is easy and fun! Here are 5 ways to support them:
- Use everyday situations like cooking or sharing snacks to talk about ratios.
- Ask questions like, “If you have 3 red toys and 5 blue toys, what is the ratio of red to blue?”
- Use visual aids like counters or drawings to show the comparison.
- Play games where they have to make ratios with objects (e.g., 2 red blocks to 3 blue blocks).
- Don’t worry if they get it wrong at first – ratios take practice!
Remember: ratios are about comparing, not adding or multiplying. Keep it simple and use real-life examples to make it stick.
Practice questions
- There are 6 cats and 4 dogs. What is the ratio of cats to dogs? Answer: 6 to 4 or 3 to 2
- There are 8 blue marbles and 12 green marbles. What is the ratio of blue to green? Answer: 8 to 12 or 2 to 3
- If the ratio of boys to girls is 3 to 5, and there are 15 girls, how many boys are there? Answer: 9 boys
- Write the ratio of 10 to 15 in its simplest form. Answer: 2 to 3
- What is the ratio of 12 to 18 in simplest form? Answer: 2 to 3
FAQ
What is a ratio?
A ratio is a way to compare two amounts. It shows how much of one thing there is compared to another. For example, if you have 3 red apples and 2 green apples, the ratio of red to green apples is 3 to 2.
How do I write a ratio?
You can write a ratio using "to" or a colon (:). For example, 3 to 2 or 3:2. The first number is the first thing you are comparing, and the second number is the second thing.
Can ratios be simplified?
Yes! If both numbers in a ratio can be divided by the same number, you can simplify it. For example, 6 to 8 can be simplified to 3 to 4.
Why do we need to know about ratios?
Ratios help us share things fairly, follow recipes, understand sports scores, and solve many problems in everyday life. They are useful for cooking, shopping, games, and more!
What if I have more than two things to compare?
Ratios can compare more than two things. For example, if you have 2 red, 3 blue, and 5 green marbles, the ratio is 2:3:5. You just keep adding numbers separated by colons.