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Maths skills for age 12

A clear guide to the main maths ideas children often meet around age 12, including algebra readiness, negative numbers, proportion, probability.

Quick answer

By the end of this page, you’ll understand the key maths skills that children typically learn around age 12, including working with negative numbers, solving simple algebra problems, understanding proportion and probability, and using these ideas in everyday life.

Learning outcome

By the end of this page, you will be able to:
  • Use negative numbers in real-life situations
  • Solve simple algebra problems using letters to represent unknown numbers
  • Understand and calculate proportions and ratios
  • Work out simple probability and chance
These skills will help you solve puzzles, understand money, plan trips, and even play games better.

Why this matters

At age 12, you're building on what you've learned before, and these new maths skills help you think more deeply about numbers. You’ll start to use letters like x and y to represent numbers you don’t know yet, which is the beginning of algebra. You’ll also learn to compare things using ratios and find out how likely something is to happen, which helps in games, science, and even cooking. Understanding these skills helps you make sense of the world around you, from working out how long a journey will take to figuring out if you’ll win a game. These skills are not just for school – they’re useful every day!

How it works

Let’s break down what you’ll learn step by step:
  1. Negative numbers are numbers less than zero. You might have seen them on a thermometer or in bank accounts.
  2. Algebra is using letters to represent unknown numbers. For example, if you know that x + 5 = 10, then x must be 5.
  3. Proportions are comparisons between two things, like how many apples you get for every orange.
  4. Probability is how likely something is to happen, like rolling a six on a dice.
Each of these ideas builds on what you already know and helps you solve bigger problems.

Examples you can see

Let’s look at some real-life examples of these ideas: Negative numbers: Imagine you’re in a lift going down. If you go down 3 floors, you can say you’re at floor -3. Or if the temperature drops to -5°C, it’s colder than zero. Algebra: Let’s say you have a bag of sweets. You eat 4 and now you have 7 left. How many sweets were there at the start? We can write this as: x – 4 = 7 To find x, we add 4 to both sides: x = 7 + 4 = 11 So there were 11 sweets at the start. Proportions: If you have 2 red sweets and 3 blue sweets, the ratio of red to blue sweets is 2:3. This means for every 2 red sweets, there are 3 blue ones. Probability: If you roll a dice, there are 6 possible outcomes. The chance of rolling a 3 is 1 in 6, or 1/6.

Try it as a mini adventure

Adventure: The Treasure Hunt You are on a treasure hunt. You need to solve clues to find the treasure. Each clue gives you a number or a puzzle. Clue 1: You start at a point that is 5 steps east. Then you go 8 steps west. Where are you now? Answer: You move 5 steps east, then 8 steps west. So you end up 3 steps west of the start. That’s -3 steps. Clue 2: You have a bag of coins. You take out 6 coins and now you have 9 left. How many coins did you start with? Answer: Let x = the number of coins at the start. x – 6 = 9 x = 15 So you started with 15 coins. Clue 3: You need to mix paint. For every 3 parts of red paint, you need 2 parts of blue. If you use 6 parts of red, how many parts of blue do you need? Answer: The ratio is 3:2. If 3 parts = 6, then 1 part = 2. So 2 parts of blue = 4. Clue 4: You flip a coin. What is the chance it lands on heads? Answer: There are 2 possible outcomes – heads or tails. So the chance is 1 in 2, or 1/2.

Common mistakes

  • Mistake: Thinking that a negative number is always smaller than a positive number. Why it happens: Some children think that because a number is negative, it must be less than zero. Fix: Remember, -5 is less than 3, but -5 is still greater than -10. Negative numbers get smaller as they go further from zero.
  • Mistake: Confusing x + 5 = 10 with x = 10 – 5. Why it happens: Children might not understand that to find x, you need to do the opposite of what is done to it. Fix: Always do the same thing to both sides of the equation to keep it balanced.
  • Mistake: Thinking that a ratio of 2:3 means 2 + 3 = 5 parts. Why it happens: Children might add the numbers in a ratio instead of understanding that the ratio compares parts. Fix: A ratio 2:3 means 2 parts of one thing and 3 parts of another – not 5 parts total.
  • Mistake: Thinking that probability is always 1/2 for any event. Why it happens: Children may think all events are equally likely. Fix: Probability depends on how many ways something can happen compared to how many total outcomes there are.

Parent and carer guide

Parents and carers can help by:
  • Using real-life examples like money, cooking, or games to show how these ideas are useful.
  • Encouraging your child to explain their thinking when solving problems.
  • Practising with simple algebra problems, like: x + 3 = 7.
  • Playing games that involve chance or ratios, like board games or card games.
  • Not worrying if your child makes mistakes – they’re part of learning!
You can also ask questions like:
  • “How did you work out that answer?”
  • “Can you show me how you solved that?”
  • “What would happen if you changed the numbers?”
These questions help your child think more deeply about the maths.

Practice questions

  1. What is -3 + 7?
  2. If x – 4 = 9, what is x?
  3. What is the ratio of 4 apples to 6 oranges?
  4. What is the probability of rolling a 4 on a dice?
  5. What is 3 times 8?
Answers:
  1. 4
  2. 13
  3. 2:3
  4. 1/6
  5. 24

FAQ

What are negative numbers?

Negative numbers are numbers less than zero. They are used to show things like temperatures below zero, money owed, or floors below ground level.

What is algebra?

Algebra is using letters like x or y to represent unknown numbers. It helps us solve problems by creating equations.

What is a ratio?

A ratio compares two amounts. For example, if there are 3 red sweets and 5 blue sweets, the ratio of red to blue is 3:5.

How do I work out probability?

Probability is the chance something will happen. It is worked out by dividing the number of ways something can happen by the total number of possible outcomes.

Why do I need to learn these skills?

These skills help you solve puzzles, understand money, plan trips, and even win games. They are used in science, cooking, art, and many other areas!