Which is bigger, -5 or -2?

-2 is bigger. It is further to the right on the number line, and a temperature of -2 degrees C is warmer than -5 degrees C.

How do I find the difference between 4 and -3?

Count from -3 to 0 (3 steps), then from 0 to 4 (4 steps). 3 + 4 = 7.

What number comes before 0?

-1. When counting backwards, 2, 1, 0, -1, -2.

Do negative numbers always have a minus sign?

Yes. A number without a sign is positive, and a number below zero must have the minus sign in front.

Year 4 negative numbers lesson to download as PDF

This Year 4 negative numbers lesson is written for pupils aged 8-9 and follows the National Curriculum. In short, it shows you how to count through zero and order positive and negative numbers in the context of temperature. Before you start, it helps to revise place value to 10 000 and Roman numerals, because this lesson builds on it.

Table of Contents

Year 4 negative numbers lesson: what you will learn

Hello, I am Otto! Have you ever seen a thermometer that shows a temperature below zero, or pressed a button for a floor underneath the ground in a lift? Those are negative numbers. In this chapter you learn to read, order and compare negative numbers, to count through zero and to find the difference between temperatures.

Starter activity

Look at a freezer thermometer. It shows −18 °C. Is that warmer or colder than 0 °C, the temperature at which water freezes? It is much colder, because it is 18 degrees below zero. Now imagine the temperature outside is 3 °C in the morning and falls by 5 degrees by the evening. What is the temperature in the evening? To answer, you have to count down through zero. Let us learn how!

What are negative numbers?

Definition: negative number

A negative number is a number that is less than zero. We write it with a minus sign in front, for example −3. We say "minus three" or "negative three". Positive numbers are bigger than zero, such as 3. Zero is neither positive nor negative.

We meet negative numbers in many places. On winter nights in the UK the temperature can fall to −5 °C. In a lift in a shopping centre, button 0 is the ground floor and button −1 is the car park below. A diver who is 10 metres under the sea is at a height of −10 m compared with sea level. And in football, a team can have a goal difference of −2 if it lets in more goals than it scores.

The thermometer shows −4 °C. The scale goes up in steps of 5 degrees. The red liquid is below the 0 mark, so the temperature is below freezing.

The number line

Key fact: negative numbers on the number line

Zero is in the middle. Positive numbers are to the right of zero and negative numbers are to the left.
The further left a number is, the smaller it is. So −7 is smaller than −2.
The numbers get bigger as you move to the right: −3, −2, −1, 0, 1, 2, 3.

This number line goes from −6 to 6. The red dots show −3 and 2. The number −3 is to the left of 2, so −3 is less than 2.

Watch out

Many people think −7 is bigger than −2 because 7 is bigger than 2. This is wrong! With negative numbers the opposite is true. −7 is 7 below zero, which is colder and lower than −2. Think of the number line: −7 is further to the left, so −7 < −2.

Example 1

Which is colder, −3 °C or −7 °C?

On the number line −7 is further to the left than −3, so −7 is smaller. A smaller temperature means a colder temperature, so −7 °C is colder.

Ordering and comparing

Method: ordering numbers that include negatives

Sketch a quick number line, or imagine one.
Put the negative numbers on the left. Among negative numbers the one with the biggest digit part is the smallest, for example −9 is smaller than −4.
Put zero in the middle and then the positive numbers on the right.
Read the numbers from left to right for smallest first.

Example 2

Put these numbers in order, smallest first: 3, −5, 0, −1, 6, −8.

The negative numbers are −8, −5 and −1. The smallest is −8, then −5, then −1. Next comes 0. Then the positive numbers 3 and 6. The order is −8, −5, −1, 0, 3, 6.

Key fact: comparing with signs

We use > for "is greater than" and < for "is less than". For example, −2 > −6 because −2 is to the right of −6 on the number line. And −4 < 1 because every negative number is less than every positive number.

Counting through zero

When you count up from a negative number you get closer to zero, you pass through zero and carry on into the positive numbers. When you count down from a positive number you pass through zero and go into the negative numbers. A number line is a great tool for this.

Method: counting on and back using a number line

Mark the starting number on the number line.
To count up, move right. To count down, move left.
Count each step carefully, and remember that there is a step from 1 to 0 and from 0 to −1.
Write down the number where you land.

Starting at 3 and counting back 5 steps gives 2, 1, 0, −1, −2. So 3 − 5 = −2.

Example 3

The temperature is 2 °C at 6 pm. It falls by 6 degrees overnight. What is the temperature in the morning?

Start at 2 and count back 6: 1, 0, −1, −2, −3, −4. So the temperature in the morning is −4 °C.

Example 4

A lift starts at floor −2 and goes up 5 floors. At which floor does it stop?

Start at −2 and count up 5: −1, 0, 1, 2, 3. So the lift stops at floor 3.

Finding the difference

Method: the difference between two temperatures

Draw a number line or use a thermometer.
Count the steps from the lower number up to the higher number.
The number of steps is the difference. Remember that you count the steps from the negative number to zero, and then from zero to the positive number.

Example 5

The temperature in London is 4 °C and in Edinburgh it is −3 °C. What is the difference?

From −3 up to 0 is 3 steps. From 0 up to 4 is 4 more steps. Add: 3 + 4 = 7 degrees. London is 7 degrees warmer than Edinburgh.

Example 6

The temperature on Monday is −2 °C and on Tuesday it is −9 °C. By how many degrees has it fallen?

Both are negative. From −9 up to −2 is 7 steps (−8, −7, −6, −5, −4, −3, −2). So it fell by 7 degrees. Check: −2 − 7 = −9.

Did you know?

The coldest temperature ever measured on Earth was about −89 °C, in Antarctica in 1983. In the UK the coldest ever temperature was −27.2 °C, recorded in Scotland in 1995. Some freezers go down to −24 °C. Water freezes at 0 °C and boils at 100 °C. The Celsius scale is named after the Swedish scientist Anders Celsius.

Otto’s tip

Always draw a quick number line when you are not sure. Put 0 in the middle, negatives on the left and positives on the right. Then count the steps one by one. And remember: a bigger digit after the minus sign means a smaller number, so −10 is smaller than −1!

How to use this Year 4 negative numbers lesson

First, read the key points so that you know where the Year 4 negative numbers lesson is going. Then work through each definition and worked example, and cover the solution before you read it. After that, practise with the negative numbers worksheet and check every question with the worksheet answers. When you feel ready, test yourself with the multiple choice questions or the quick quiz. Finally, sit the negative numbers test and mark it with the test answers.

Also, the starters are a good warm-up, so you can keep the key facts fresh. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday. In short, this Year 4 negative numbers lesson gives you everything you need for the chapter.