Year 5 · Negative numbers
Understand what a negative number means
Learn how to read negative numbers, count through zero, put positive and negative numbers in order, and find the difference between numbers either side of 0.
Definition
A negative number is a number less than zero, written with a minus sign in front, like -3. You meet them on cold days, when the temperature drops below 0°C. On a number line, negative numbers sit to the left of zero and mirror the positive numbers on the right. The further left a number sits, the smaller it is.
Why Do I Have to Learn This?
Negative numbers describe things below zero, like freezing temperatures or owing money. They let us measure in both directions.
Key Rules:
- 1. A negative number is less than zero and is written with a minus sign in front, like -3.
- 2. On a number line, negative numbers sit to the left of zero, and moving left always makes numbers smaller.
Remember:
- •Zero is not a wall: the number line carries straight on through it, and further left always means smaller.
Don’t Forget...
- •Thinking -7 is bigger than -2 because 7 is bigger than 2. On the number line -7 sits further to the left than -2, so it is smaller: with negative numbers, a bigger digit means a smaller number.
- •Skipping zero when counting through it, jumping from 1 straight to -1. Zero is a number on the line in its own right, so counting back from 1 goes 1, 0, -1.
- •Finding the difference between -4 and 7 as 3, by working out 7 - 4. -4 is 4 below zero, not 4 above it, so the gap is the 4 below zero plus the 7 above it, which is 11.
Directed number
A number with a sign, so positive or negative.
−3 and +5 are directed numbers. On a number line, −3 sits three steps to the left of zero.
Worked Example:
The temperature was -4°C at dawn and 7°C by the afternoon. By how many degrees did the temperature rise?
Picture a number line with 0 in the middle, -4 to the left and 7 to the right.
Count from -4 up to 0: that jump is 4.
Count from 0 up to 7: that jump is 7.
Add the two jumps: 4 + 7 = 11.
Answer: The temperature rose by 11°C.
Why It Works:
The number line runs in one unbroken order and zero is a point on it, not a barrier, so counting and ordering work the same on both sides of it. Splitting a jump at zero is valid because the two parts of the jump add up to the whole distance.
Another Example:
Start at 6 and count back in steps of 2. Write the next five numbers.
Take away 2 each time: 6, 4, 2.
From 2, taking away 2 lands exactly on 0.
Keep going past zero: 0 take away 2 is -2, and -2 take away 2 is -4.
Answer: 4, 2, 0, -2, -4
Animated Example:
Free Understand what a negative number means Worksheet
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Next: Directed number (Year 7)
Let’s Practise the Concept
Step 1 of 3
Order the data
Tap the values from smallest to largest.
In order so far: nothing yet