Time-travel maths quest: ratio

Quick answer

Ratios help us compare how much of one thing there is compared to another thing, like 2 cups of flour to 1 cup of sugar in a recipe. In our Time-travel maths quest, you'll use ratios to mix ancient potions, scale drawings of pyramids, and compare the number of stars in different constellations.

Learning outcome

By the end of this page, you will be able to use ratios to compare quantities and solve simple problems, like mixing ingredients for a time-travel potion or scaling up a drawing of a dinosaur.

• You can describe ratios using words like "for every 2 apples, there is 1 orange"
• You can write ratios using numbers like 2:1
• You can find equivalent ratios by multiplying or dividing both parts by the same number
• You can solve simple ratio problems using pictures, objects, or simple calculations

Why this matters

Ratios are used everywhere! In cooking, you need ratios to make sure your cake tastes right. In maps, ratios help us see how far places are. In time travel, ratios help us mix the right ingredients for our potions. Understanding ratios helps you solve problems and make better decisions in real life.

How it works

Ratios compare two or more quantities. They show the relationship between things. You can write ratios in three ways:

1. Using words: "For every 3 red marbles, there are 2 blue marbles"
2. Using a colon: "3:2"
3. Using fractions: "3/2"

Let's start with simple ratios and then build up to more complex ones. Think of ratios like a recipe for relationships between things.

Examples you can see

Imagine you're a time-traveler visiting ancient Egypt. You want to mix a special potion for the pharaoh. The recipe says:

• For every 2 drops of magic water, you need 1 drop of sunflower oil
• This is written as 2:1

Let's try another example:

• For every 4 stars in the Big Dipper, there are 3 stars in the Little Dipper
• This is written as 4:3

Here's how to make a simple ratio with objects:

Notice how 4:2 and 6:3 are the same as 2:1? These are equivalent ratios!

Try it as a mini adventure

Join our Time-travel maths quest! You are a time-traveler who has landed in ancient Rome. You need to help the Romans build a new amphitheatre. You have a scale drawing of the amphitheatre that shows 1 cm represents 10 cm of the real building.

Let's go on a quest to find the right ratios:

1. First time: You see a small arch that is 3 cm on your drawing. How tall is the real arch? Answer: 30 cm
2. Second time: The real entrance is 40 cm wide. How wide is it on your drawing? Answer: 4 cm
3. Third time: You measure a column that is 12 cm on your drawing. What is the real height? Answer: 120 cm
4. Fourth time: The real stage is 50 cm wide. How wide is it on your drawing? Answer: 5 cm
5. Fifth time: You see a window that is 25 cm wide on the drawing. What is the real width? Answer: 250 cm

Great job! You've used ratios to scale up and down the drawing. This is how ancient builders and modern architects use ratios to make buildings.

Common mistakes

• Mistake: Writing 2:3 as 3:2
  Why it happens: Mixing up the order of the numbers
  Fix: Always read the ratio from left to right as "first thing to second thing"
• Mistake: Thinking 4:2 and 2:1 are different ratios
  Why it happens: Not understanding equivalent ratios
  Fix: Divide both sides by the same number to see if they're the same
• Mistake: Adding instead of multiplying to find equivalent ratios
  Why it happens: Confusing operations
  Fix: Multiply or divide both sides by the same number
• Mistake: Using the wrong units in ratios
  Why it happens: Not paying attention to what's being compared
  Fix: Make sure both quantities are in the same unit before comparing

Parent and carer guide

Help your child understand ratios by:

1. Using everyday examples like mixing paint, cooking, or sharing snacks
2. Letting them create their own ratios with objects like blocks, toys, or food
3. Practicing with simple drawings or maps where 1 cm = 10 cm
4. Encouraging them to explain their thinking out loud
5. Not worrying if they make mistakes - they're learning!

Watch for:

• Confusion about the order of numbers in ratios
• Difficulty with equivalent ratios
• Using ratios in real-life situations

Remember: Ratios are about relationships, not just numbers. Make it fun!

Practice questions

1. There are 6 red cars and 3 blue cars. What is the ratio of red cars to blue cars? Answer: 6:3 or 2:1
2. If 5 children eat 10 apples, what is the ratio of children to apples? Answer: 5:10 or 1:2
3. Write the ratio 8:4 in its simplest form. Answer: 2:1
4. What is the ratio of 15 boys to 10 girls? Answer: 15:10 or 3:2
5. There are 12 red blocks and 8 blue blocks. What is the ratio of red to blue? Answer: 12:8 or 3:2
6. If 3 cups of flour are mixed with 1 cup of sugar, what is the ratio? Answer: 3:1
7. Write 18:12 in simplest form. Answer: 3:2
8. There are 4 green leaves and 2 yellow leaves. What is the ratio? Answer: 4:2 or 2:1
9. What is the ratio of 7 to 14? Answer: 7:14 or 1:2
10. If 10 eggs are used with 5 cups of flour, what is the ratio? Answer: 10:5 or 2:1

FAQ

What is a ratio?

A ratio compares how much of one thing there is compared to another thing. It shows the relationship between two quantities.

How do I write a ratio?

You can write a ratio using words like "for every 3 red blocks, there are 2 blue blocks", using a colon like "3:2", or as a fraction like "3/2".

What are equivalent ratios?

Equivalent ratios are ratios that have the same relationship but use different numbers. For example, 2:1 and 4:2 are equivalent ratios.

How do I find equivalent ratios?

Find equivalent ratios by multiplying or dividing both parts of the ratio by the same number.

Why do we need ratios?

Ratios help us compare things, make recipes work, understand maps, and solve problems in everyday life. They're used in cooking, building, science, and many other areas.