Arctic maths quest: ratio

Quick answer

Ratios help us compare how much of one thing there is compared to another, like mixing ingredients for a survival recipe or sharing supplies between team members. You can use ratios to solve problems in the Arctic or anywhere else!

Learning outcome

By the end of this page, you will understand how to use ratios to compare amounts and solve problems, just like explorers do when planning survival supplies or mixing ice recipes in the Arctic.

• You can show how two amounts relate to each other using a ratio.
• You can simplify ratios to their smallest form.
• You can use ratios to share or divide things fairly.
• You can solve simple ratio problems using real-life examples.

Why this matters

Ratios are super useful for explorers, cooks, scientists, and anyone who needs to share or mix things properly. When you're planning a survival trip to the Arctic, you need to know how much food, water, and warm clothes to take. You might need to mix a special ice recipe or share your supplies fairly with your team. Ratios help you do this without making mistakes.

Learning ratios helps you understand how things relate to each other in everyday life, like sharing snacks with friends, making the perfect smoothie, or even building with LEGO blocks. Once you get the hang of ratios, you’ll see them everywhere!

How it works

Ratios are a way to compare two or more amounts. You write them using a colon (:) like this: 3:2. This means for every 3 parts of one thing, there are 2 parts of another.

Here’s how to think about it:

1. First, identify what you're comparing.
2. Then, write the amounts in the order you're comparing them.
3. You can simplify the ratio by dividing both numbers by the same amount.
4. Use the ratio to solve problems like sharing or mixing.

For example, if you have 6 apples and 4 oranges, the ratio of apples to oranges is 6:4. You can simplify this to 3:2 by dividing both numbers by 2.

Examples you can see

Let’s imagine you are an explorer in the Arctic. You need to make a survival recipe using ice and salt to create a cold mixture for keeping food fresh. The recipe says: for every 3 parts of ice, you need 2 parts of salt. This is a ratio of 3:2.

Let’s say you have 12 parts of ice. How much salt do you need?

1. You know the ratio is 3:2 (ice:salt).
2. You have 12 parts of ice.
3. Find how many times 3 goes into 12: 12 ÷ 3 = 4.
4. Multiply 2 by 4 to find the salt needed: 2 × 4 = 8.
5. You need 8 parts of salt.

Another example: You and your team have 15 survival blankets to share. The ratio of blankets to team members is 3:1. This means for every 3 blankets, there is 1 person. If there are 5 people in your team, you need to work out how many blankets each person gets.

1. Ratio is 3:1 (blankets:people).
2. There are 5 people.
3. Find how many groups of 3 are in 5: 5 ÷ 3 = 1 remainder 2.
4. Each person gets 3 blankets, but you have 2 left over.
5. So, you can give 1 extra blanket to 2 people.

Try it as a mini adventure

Arctic Exploration Challenge

You are part of a team exploring the Arctic. You need to make a special ice mixture for your survival kit. Your guide gives you a recipe:

• For every 4 parts of ice, you need 1 part of salt.
• You have 20 parts of ice.

How much salt do you need?

1. Ratio is 4:1 (ice:salt).
2. You have 20 parts of ice.
3. How many times does 4 go into 20? 20 ÷ 4 = 5.
4. Multiply 1 by 5: 1 × 5 = 5.
5. You need 5 parts of salt.

Now, you need to divide 15 survival food packets between 3 team members. What is the ratio of packets to people?

1. There are 15 packets and 3 people.
2. Ratio is 15:3.
3. Simplify by dividing both by 3: 15 ÷ 3 = 5, 3 ÷ 3 = 1.
4. Ratio is 5:1 (packets:people).

Each person gets 5 packets.

Common mistakes

• Mistake: Writing the ratio backwards, like 2:3 instead of 3:2.
  Why it happens: Confusing the order of items.
  Fix: Always check which item comes first in the problem.
• Mistake: Not simplifying the ratio.
  Why it happens: Thinking that 6:4 is already the simplest.
  Fix: Divide both numbers by the same number to make it smaller.
• Mistake: Mixing up ratios with fractions.
  Why it happens: Not knowing the difference between 3:2 and 3/2.
  Fix: Remember ratios compare parts, not a whole.

Parent and carer guide

Helping your child with ratios doesn’t have to be hard. Here are 5 simple ways you can support them:

1. Use everyday situations to talk about ratios. For example, when cooking, ask how many cups of flour are needed for every cup of sugar.
2. Draw pictures or use actual objects like counters or blocks to show the ratios.
3. Encourage your child to explain their thinking. Ask, “How did you work that out?”
4. Keep practice fun by making up silly Arctic-themed problems, like “If 3 penguins eat 6 fish, how many fish does each penguin eat?”
5. Don’t worry if they make a mistake. Ratios are tricky at first, but with practice, they’ll get better.

Remember, ratios are all around us. From sharing snacks to planning a party, they help us make fair and smart decisions.

Practice questions

1. What is the ratio of 8 apples to 4 oranges? Simplify it.
2. A recipe uses 5 parts flour and 2 parts sugar. How much sugar is needed for 15 parts flour?
3. There are 12 survival kits to share between 4 people. What is the ratio of kits to people?
4. If the ratio of blue to red paint is 3:5 and you have 15 blue parts, how many red parts do you need?
5. What is the simplified ratio of 10:15?

Answers:

1. 8:4 = 2:1
2. 6 parts sugar
3. 12:4 = 3:1
4. 25 parts red
5. 2:3

FAQ

What is a ratio?

A ratio compares two or more amounts. It shows how much of one thing there is compared to another, like 3:2 (three parts of one thing to two parts of another).

How do I simplify a ratio?

Find a number that divides both parts of the ratio evenly, then divide both parts by that number. For example, 6:4 becomes 3:2.

Can ratios be more than 2 numbers?

Yes! Ratios can compare more than two things. For example, 2:3:5 compares 2 parts of one thing, 3 parts of another, and 5 parts of a third.

Where do we use ratios in real life?

Ratios help us in cooking, sharing, maps, science, and even sports. For example, when you mix paint or split a pizza, you're using ratios.

How can I practice ratios at home?

Try making a recipe with your child and ask them to adjust the amounts. Or, use a collection of toys or food to create ratios and solve problems.