Age 12 guide to negative numbers

Quick answer

Negative numbers are numbers less than zero, like -1, -2, -3, and so on. You can think of them as going backwards or going below zero on a number line. You'll learn how to use them in real life, like when it's freezing outside or when you're counting down to a party.

Learning outcome

By the end of this page, you will be able to understand what negative numbers are, how they work on a number line, and how to use them in everyday situations like temperatures, money, and directions.

• You can place negative numbers on a number line
• You can compare negative numbers using the < and > symbols
• You can solve simple problems involving negative numbers
• You can explain where you see negative numbers in real life

Why this matters

Negative numbers help us describe things that go below zero. You use them when it's freezing outside, when you owe someone money, or when you're counting down to a big event. Understanding negative numbers helps you solve problems in maths, science, and real life.

How it works

Negative numbers are like the opposite of positive numbers. They are less than zero and go to the left on a number line.

1. Think of a number line with zero in the middle
2. Numbers to the right of zero are positive
3. Numbers to the left of zero are negative
4. Each step to the left is one less than the last
5. For example: -1, -2, -3, -4, -5

Examples you can see

Here are some examples of negative numbers in real life:

Let's imagine you are at a ski resort where the temperature is -5°C. This means it is 5 degrees colder than zero. If you go 10 steps backwards, you are at -10. If you go 5 steps forwards from -10, you are at -5.

Try it as a mini adventure

Adventure: The Treasure Hunt

You are on a treasure hunt in a cave. The cave is 10 steps below the entrance. You go down 3 steps, then go up 5 steps. Where are you now?

1. You start at 0 steps
2. You go down 3 steps: 0 - 3 = -3 steps
3. You go up 5 steps: -3 + 5 = 2 steps
4. You are now at 2 steps above the entrance

Try this with your family! Draw a number line and act out the steps.

Common mistakes

• Mistake: Thinking -5 is bigger than -2
• Why it happens: Confusing negative numbers with positive numbers
• Fix: Remember that -5 is further to the left on the number line than -2

• Mistake: Adding two negative numbers and getting a positive answer
• Why it happens: Not understanding that adding negatives makes the number smaller
• Fix: -3 + (-2) = -5, not 5

• Mistake: Thinking that -10 is smaller than -5
• Why it happens: Mixing up the direction of negative numbers
• Fix: On the number line, -10 is further to the left than -5, so -10 is smaller

Parent and carer guide

Help your child understand negative numbers by:

1. Using real-life examples like temperature or money
2. Playing number line games
3. Encouraging them to explain their thinking
4. Reinforcing that negative numbers are just the opposite of positive numbers
5. Practicing with simple problems

Ask questions like: "What does -5°C mean?" or "If you owe someone £5, how can you show that?"

Remember to be patient. It's normal for children to get confused at first. Practice makes progress!

Practice questions

1. Which number is smaller: -3 or -7?
2. What is -4 + (-3)?
3. Where would you place -6 on a number line?
4. If the temperature drops from 2°C to -3°C, how much did it drop?
5. What is -10 - (-5)?

Answers:

1. -7 is smaller than -3
2. -4 + (-3) = -7
3. -6 is 6 steps to the left of zero
4. It dropped 5 degrees (2 - (-3) = 5)
5. -10 - (-5) = -5

FAQ

What are negative numbers?

Negative numbers are numbers that are less than zero. They are written with a minus sign (-) in front of them. For example, -1, -2, -3, etc.

Where do we see negative numbers in real life?

You see negative numbers in temperatures (like -5°C), money (owing someone money), depths (like -20 metres below sea level), and in games or sports when counting backwards.

How do I add negative numbers?

To add negative numbers, you move further to the left on the number line. For example, -3 + (-2) = -5 because you start at -3 and move 2 more steps to the left.

Can you subtract a negative number?

Yes! Subtracting a negative number is the same as adding a positive number. For example, 5 - (-3) = 5 + 3 = 8.

Why do we need negative numbers?

Negative numbers help us describe things that go below zero, like freezing temperatures, owing money, or depths below sea level. They make our maths more complete and useful for real life.