Table of Contents
This blog focuses on the key elements of negative numbers that need to be taught in key stage 2 and to help teachers deliver lessons.
Teaching negative numbers can be made easier by bearing a key principle in mind.
Students need to be comfortable with the language around negative numbers and the concept of negative numbers before doing any calculations.
If you are following a CPA (concrete, pictoral, abstract approach), the most popular pictoral representation of negative numbers is one is the number line.
The history of negative numbers is quite interesting and may be useful for cross curricular purposes.
This paper by Stanford University includes an explanation about how negative numbers were adapted by the Chinese to solve simultaneous equations. They would represent the positive numbers with red rods and the negative numbers in black rods.
Negative and Positive Numbers on the National Curriculum
count backwards through zero to include negative numbers
interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero
use negative numbers in context, and calculate intervals across zero
Using the number line, pupils use, add and subtract positive and negative integers for
measures such as temperature.
Pupils draw and label a pair of axes in all four quadrants with equal scaling. This extends their knowledge of one quadrant to all four quadrants, including the use of negative numbers.
These are the essential learning points and the order of the concepts, students need to grasp to be comfortable with negative numbers in key stage 2:
- To understand that negative numbers exist and to be able to talk about negative numbers (for example in relation to temperature or money).
- To be able to recognise how negative numbers are representated differently from positive numbers.
- To be able to represent negative and positive numbers on a number line and to be able to do basic calculations with negative numbers.
1. Negative Numbers Exist and Talking About them.
I believe to talk about negative numbers in an understandable way, we need to look at where they come from.
Why do we need negative numbers? When do we need negative numbers?
What happens when the temperature goes below 0 degrees? How do represent how much colder than 0?
What would your students do to represent:
- freezing (at 0 degrees),
- a little bit colder than freezing (say -5 degrees)
- a lot colder than freezing (say -100 degrees!)
They could do numbers in red (or blue!). They could use a symbol (like -) to represent less than zero.
Could your students draw a number line showing how they would represent numbers less than zero?
Would their systems work for less than “zero money”?
Reveal the system we use i.e. “-” and see what they think.
Is it confusing with the take away sign? Why might it be a good system?
2. Representing Negative & Positive Numbers
So we have establish that there are negative numbers and those are presented with a “–” sign.
(A top tip is to remind students that positive numbers can actually have a “+” before the number, but they are not shown, whereas negative numbers always show the “-“.)
After students have understood how to represent negative and positive numbers, you can start helping them get used to an extended number line.
3. Number Lines and Negative Numbers
Students need to know how to identify a negative number on the number line and then as always to add we go right; and to subtract we go left.
Negative Numbers in Real Life
There are some good opportunities to introduce negative numbers in a few cross curricular areas:
- Money – overdrafts & borrowing money. How big would my overdraft be if I spent another £100.
- Temperature – below freezing. How much is 10 degrees colder?
- Time differences – if New York is 5 hours behind and it is 10am here, what time is it in New York?
Negative Number Activities
Some other activities which can aid the progress of understanding negative numbers are:
Playing Ladders: On the floor set up a number line, this could be imaginary. Have students go to the number of your choice.
Sequences: You could also draw some sequences on the board and ask students to tell you if the sequences are correct or not by using their mathematical knowledge. You can also illustrate numbers on the board and ask students to put them in order.
Negative Number Worksheets
We have prepared two worksheets for your students to practise the number line and recognise negative and positive numbers. Simply click the button to download!
Negative Number Game
If your student enjoys learning through games, we suggest taking advantage of Emile’s free trial access. You can find many games such as, adding and subtracting, including negative numbers, which your students will love playing. They can compete against one another, collect outfits for their virtual Emile and see their progress.