Number & place value
Introduction to Negative Numbers
Year 3 · Year 4 · Year 5 · Year 6
- ✓By the end of this lesson students will be able to identify and understand negative numbers in real-life contexts.
- ✓By the end of this lesson students will be able to count forwards and backwards with positive and negative whole numbers, including through zero.
- ✓By the end of this lesson students will be able to order and compare positive and negative numbers using a number line.
- ✓By the end of this lesson students will be able to solve simple problems involving negative numbers in practical situations.
Key concepts
Negative numbers are numbers that are less than zero. They are always shown with a minus sign (-) in front of them. We use negative numbers in everyday life to describe things like temperatures below freezing, depths below sea level, or money owed (debt). For example, -5°C means five degrees Celsius below zero.
A number line is a straight line with numbers placed at equal intervals along it. Zero is usually in the centre. Positive numbers are to the right of zero, and negative numbers are to the left of zero. The further a number is to the right, the greater its value. The further a number is to the left, the smaller its value.
When you count backwards from a positive number, you will eventually reach zero, and then continue into the negative numbers. For example, 3, 2, 1, 0, -1, -2, -3. Similarly, when you count forwards from a negative number, you will pass through zero to reach the positive numbers. For example, -3, -2, -1, 0, 1, 2, 3.
To compare negative numbers, remember that the number further to the left on the number line is always smaller. This means that a negative number with a larger digit (like -5) is actually smaller than a negative number with a smaller digit (like -2). For example, -5 is smaller than -2 because -5 is further to the left of zero on the number line.
Key facts to remember
- 1Negative numbers are numbers less than zero.
- 2All negative numbers have a minus sign (-) in front of them.
- 3Zero is neither positive nor negative.
- 4On a number line, numbers increase in value as you move to the right and decrease as you move to the left.
- 5The further a negative number is from zero (to the left on a number line), the smaller its value.
- 6Real-life examples of negative numbers include temperature, depth below sea level, and financial debt.
Worked examples
Example 1
Start at 2 and count back 5. What number do you land on?
Answer
-3
Visualising this on a number line is very helpful.
Example 2
Order these numbers from smallest to largest: 3, -4, 0, 1, -2.
Answer
-4, -2, 0, 1, 3
Remember that negative numbers with a larger digit are smaller in value.
Example 3
The temperature in London was 4°C. Overnight, it dropped by 6°C. What was the new temperature?
Answer
-2°C
Think of the number line as a thermometer.
Common mistakes
- ✗Confusing the magnitude of a negative number with its value (e.g., thinking -5 is 'bigger' than -2 because 5 is bigger than 2). Remember -5 is smaller than -2.
- ✗Incorrectly counting through zero (e.g., 2, 1, 0, 1, 2 instead of 2, 1, 0, -1, -2).
- ✗Forgetting to include the minus sign when writing negative numbers.
- ✗Misplacing negative numbers on a number line, especially when ordering a mixed set of positive and negative numbers.
Exam tips
- ★Always use a number line to help you visualise and solve problems involving negative numbers, especially when counting or ordering.
- ★Think of real-world examples like a thermometer or a lift in a building to help understand the concept of moving through zero.
- ★Pay close attention to the minus sign; it completely changes the value of a number.
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