A Positive Experience Teaching Negative Numbers!
Negative Numbers can be a challenge at first for students.
It’s not so much the complexity of the learning objective
that is the teaching and learning challenge. It’s simply
that negative numbers are initially an abstract concept to
many children. How can we present this new learning so
that children “really get it”?
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Children have learned to recognise numbers, count on
and add and subtract numbers beyond zero. They
have yet to discover that negative numbers exist.
Start with a ‘safe’ scaffold. My class are used to counting
on to the right of zero, finding difference and recognising
numbers on a number line from 0 to 20. They are the
whole numbers we are used to. I introduce the term
‘positive numbers’.
0
1
2
3
4
5
-6
-5
-4
-3
-2
positive
-1
0
1
2
3
4
-7
-6
-9
We look at the positive number line and establish that the
further we go to the left, the smaller the positive number.
This helps us understand the concept that the further we
go into the negative the smaller the numbers are.
6
Now, the new concept that the number line can also
extend to the left of zero. I introduce the term ‘negative
numbers’ and we learn that zero is the special number that
separates positive and negative numbers.
negative
-3
5
6
An important teaching point here is to insist on children
using the correct language. We will learn that the first
numbers to the left of zero on the numberline are ‘negative
1’, ‘negative 2’ etc. It is important to distinguish that the symbol is attached to the number value, and not the same
as “minus, take away, subtract”. We learn that numbers
are either positive or negative, and that we call them
integers.
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Using a number line to order negative numbers really
helps with our understanding of their place value. For
instance, we can quickly see that -2 is a higher number
than -5 because it is further to the right on the number
line. This is an important visual, because one of the
learning misconceptions we will encounter if this idea is
not embedded early on is children who think that -5 is a
bigger number than -2 because they apply their previous
learning of “it’s a bigger number so it must be greater”.
At this point, I often include > < challenges. Start safely
with positive number cards and ask the children to
compare using > < symbols. Extend by comparing positive
and negative numbers in this way and then focus your
learning outcome on correctly comparing two negative
numbers.
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TEACHING TOOLS: A Positive Experience Teaching Negative Numbers!
count back
Once we have used the number line to establish place
value concepts, we can deal with the curriculum objectives
of counting forward and backward through zero. The
numberline is the ideal scaffold to demonstrate counting
back through zero at Year 4. Start at 4, count back 7. It
provides a clear visual.
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
At Year 5, we begin to count forward and backwards
through zero and the number line is the perfect tool once
more.
Have fun with Negative Numbers!
Create a giant number line that extends into the negative
across the classroom floor using masking tape. Let the
children explore the place value of negative numbers using
number cards. Children throw or place two bean-bags on
the number line. They can find the difference by “jumping
along the number line”.
Capture forecasts from a “chilly” part of the world and use
webcams of the conditions to bring the meaning of the
negative numbers to life.
Chalk out these same concepts on the playground. Let
them explore through play.
Traditional board games start at zero. Put a twist on this
and play games starting at negative 20. Build in counting
on and back rules.
Bring your number line to life. Turn-it into a class tower
block and let the children create art content for each level.
Enjoy the level of problem solving engagement that
follows!
5
4
3
2
1
0
-1
-2
-3
-4
-5
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So have lots of fun with negative numbers!
Visit our Pinterest page:
for more negative number activities & games
Useful resources:
Counting stick, negative number squares and editable
board games
Useful websites:
Use the excellent negative number resource bank at
nrich.maths.org
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Class golden time? Rather than earning 20 merits a week
starting from zero, start the children off at negative 20 with
the golden time target of zero. Make it real to them!