Year 5 Teaching Sequence Summer 1 - Ordering negative and positive numbers (three days)
Prerequisites:
 Use negative numbers in context, e.g. temperature (see Year 4 spring teaching sequence 7 and oral and mental starter
bank 1)
 Count on and back in steps of constant size, e.g. 25, including beyond zero to -100 for example (see Year 4 summer
teaching sequence 7 and oral and mental starter bank 1)
Overview of progression:
Children compare temperatures (above and below zero degrees Celsius) and calculate rises and falls in temperature. They
order pairs of negative and positive numbers and then count on and back in steps of constant size including through zero.
Note that the vertical scale of the thermometer is used as a context for negative numbers, and so negative numbers out of
context are shown on a vertical scale to start with to link with this image. Later we switch to a horizontal scale. Children
need to understand that both ‘minus’ and ‘negative’ are used to describe these numbers.
Watch out for children who think that temperatures such as -7°C are warmer than -3°C because 7 is higher than 3.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y5 Maths TS1 – Sum – 3days
Objectives:
 Count on and back in steps of a constant size, extending beyond zero
 Order negative and positive numbers on a number line and temperature scale
 Calculate a rise/fall in temperature
Whole class
Group activities
Launch the ITP Thermometer, and choose a range of -10
to 10. At what sort of temperature might we get ice
outside? Why? Agree that as water freezes at 0
degrees Celsius the temperature will be less than this,
e.g. minus one, two. Ask chn to label some of these
temperatures on the thermometer. Which of these
temperatures is the coldest?
During one day it was 5 degrees Celsius. During the night
the temperature fell to minus 5 degrees Celsius. Move
the slide to 5, then -5 on the thermometer.
Group of 4-5 children
Use an internet site to find
temperatures in cities around the world
(e.g. www.bbc.co.uk/weather) including
countries where the temperature is
below zero and record them on Postits™. Ask chn to put them in order
from the warmest to the coldest. Find
the cities on a globe. Ask questions
such as:
Which is colder, Reykjavik or Helsinki?
What is the difference in
temperature? Sketch a vertical number
line to help. What happens to
temperatures generally as you move
further away from the equator? Why
do you think this is?
Easier:/Harder: Adapt your questions
as appropriate, for example asking chn
to find narrower or wider differences.
How many degrees has the temperature fallen? How
many degrees had it fallen when it got to zero? Draw a
hop of 5 to 0. And then? Draw hop of 5 to -5. Click on
change to check. Move the slider up to 3°C. The next day
the temperature rose, but it was colder than the
previous day. How much has the temperature gone up by?
Draw a hop of 5 to 0°C, and then a hop of 3 to 3°C.
Paired/indiv practice
Chn order temperatures and
calculate rises and falls in
temperature (see resources).
They sketch vertical lines to
help if necessary.
Easier: Chn are given a
thermometer picture to help
them work out falls in
temperature.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Resources
 ITP
Thermometer
 Access to the
internet
 Globe
 Activity sheets
(see resources)
Y5 Maths TS1 – Sum – 3days
Repeat with similar questions.
Close the ITP and display the following table:
Maximum
Minimum
temperature temperature
Monday
7°C
-2°C
Tuesday
5°C
-3°C
Wednesday
1°C
-2°C
Thursday
2°C
-4°C
Friday
0°C
-5°C
These are the temperatures recorded at a school
weather station. When do you think they might have
been recorded? What was the highest temperature
recorded? And the lowest? On which day was there the
greatest difference between maximum and minimum
temperature? By how much did the temperature fall?
Sketch a vertical line from -2°C to 7°C to help chn to see
this. Which day has the smallest difference between
maximum and minimum temperature? What was the
drop? Sketch a vertical line to help chn see this.
Show chn a counting stick so that it is vertical. Let's
count back in ones from five. Start at the top end of the
counting stick as chn see it. 5, 4, 3, 2, 1, 0, what comes
next? Continue saying negative one, negative two…
Remind chn that numbers less than zero are called
negative numbers, and numbers more than zero are called
positive numbers. When might we use negative numbers?
Agree examples such as temperature, depth below sea
level, and, especially, overdrafts. When we owe money,
we talk about having negative or minus amounts of money.
Point out that we often say ‘minus’ rather than ‘negative’.
Write 0, -2 and -4 on Post-its™. Point to the top of the
counting stick. If this is 5 and we count down in ones,
Group of 4-5 children
Write numbers from -20 to 20 on
separate cards and shuffle them. Deal
them face down to the children. Turn
over a sand timer. Can everyone order
their cards before the sand runs out?
Reshuffle and repeat.
Show me a card between -5 and 0.
Show me a card less than -10.
Show me a card greater than -6.
Show me a card between -2 and 2.
Repeat with similar questions.
Easier: Give each pair a set of shuffled
Give a set of -10 to 10 cards to
each pair. They shuffle and
then arrange them in order
from -10 to 10.
They reshuffle them, each
select three cards and write
them in order from the least
to the greatest.
Repeat.
Easier: Chn practise ordering
cards -10 to 10 several times.
They then take a card and
write down the number before
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Counting stick
 ITP Number
Line
 -20 to 20
cards
 One minute
sand timer
 -10 to 10 cards
Y5 Maths TS1 – Sum – 3days
where should we stick 0? And negative 2? And negative
4?
Turn the counting stick so that it is horizontal.
Point to the left, as chn see it. This is -5. We’re going to
count from -5 to 5. Count on, speeding up as you pass
zero, and then count back again. Ask chn to place the
Post-its™ on the stick in the correct places.
Launch the ITP Number Line and choose a range from
-20 to 20. Click so that the numbers are not displayed on
the tags and move them to -2 and -8. What numbers are
labelled? How did you work it out?
Which number is bigger? Record -2 > -8. Write a number
in-between on your whiteboards. Repeat with other pairs
of numbers including mixes of negative and positive
numbers.
Show chn the counting stick so that it is horizontal.
Point to the left, as chn see it. This is -10. We’re going
to count on in twos. Where do you think we will get to?
Count on in twos, speeding up as you pass zero, and then
count back again.
Repeat, this time starting at -40 counting in fives,
starting at -100 counting on in tens and finally starting
at -200 and counting on in 25s.
-5 to 5 cards and ask them to put them
in order before the sand runs out. Ask
similar questions when they have all
their cards in order.
it, the number on the card and
the number after it.
Group of 4-5 children
Write numbers from -10 to 10 on
separate cards and shuffle them. Ask
chn to help you to put them in order.
If we have 3 subtract 4, we’d normally
say we can’t do it, but we can if we use
negative numbers. What do you think 3
subtract 4 is? Count back 4 from 3
Give each pair a sheet of -20
to 20 number lines (see
resources). They roll a dice
and count back in steps of that
size from 20 until they pass 20, recording each hop as they
do so. E.g. they roll a 6 and
count back in steps of 6: 20,
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Counting stick
 ITP Number
Line
 -10 to 10 cards
 -20 to 20
number lines
(see resources)
 1-6 dice
Y5 Maths TS1 – Sum – 3days
Launch the ITP Number Line and choose a range from
-20 to 20. This time we’re going to count back in 3s.
Together count back in 3s, recording the jumps on the
number line as you do so. Take particular care when
crossing zero.
Repeat, this time counting back in 6s.
using the cards. Together make up
other subtractions with a negative
answer.
Discuss situations in ‘real life’ where
these sorts of subtractions are
possible, e.g. falls in temperature,
descending below sea level, and perhaps
going overdrawn, although not to be
recommended!
Easier: Mark zero on the middle of the
counting stick and use this vertically to
support counting back through zero
when subtracting.
14, 8, 2, -4, -10, -16, -22. If
they roll one, they roll again.
Easier: Chn count back in 2s,
4s, 5s and 10s from 20 to -20.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y5 Maths TS1 – Sum – 3days