Year 4 Teaching Sequence Spring 6 - Subtraction including find a difference and counting back (four days)
Prerequisites:
 Find a difference between near multiples of 100, e.g. 304 – 296 (see autumn teaching sequence 6)
 Use complements to 100 to find differences between two- and three-digit numbers, e.g. 137 – 72 (see autumn
teaching sequence 6)
 Derive quickly pairs of two-digit numbers with a total of 100, e.g. 72 + = 100 (see autumn teaching sequence 6 and
spring oral and mental starter bank 6)
 Count on and back in 1s, 10s, 100s or 1000s from four-digit numbers to add and subtract (see autumn teaching
sequence 7 and spring oral and mental starter bank 6)
Overview of progression:
Children subtract pairs of three-digit numbers either side of a multiple of 100, e.g. 524 – 478 by counting up (find a
difference) and subtract three-digit numbers on either side of neighbouring multiples of 100, e.g. 524 – 389, using pairs to
100 and place value to help. Contexts of distance and height are used. Children use pairs to 100 and ENL jottings to find out
what needs to be added to multiples of 50 to make 1000, and then use this to find differences between multiples of ten on
either side of 1000. Counting back in 100s and 10s is used to subtract three-digit multiples of 10 from four-digit numbers,
and then children choose whether to count back or on or count on (find a difference) to solve subtractions such as 1250 –
420 and 1340 – 650.
Note that chn use both counting back (take away) and counting up (finding a difference) this sequence. When you want
children to decide which strategy to use, it is helpful to read the – sign as subtract, as this doesn’t suggest one or the
other.
Watch out for children who draw jumps from 700 to 730 and then a hop to 734 to find the difference between 700 and
734 as this shows that they are not using three-digit place value to help. Watch out for children who are not secure about
the two contexts of subtraction: take away and difference.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y4 Maths TS6 – Spr – 4days
Objectives:
 Count up to subtract near-multiples of 100, e.g. 524 – 478, 524 – 389, using pairs to 100 and place value to help, drawing own empty
number line
 Derive quickly pairs of multiples of 50 with a total of 1000, e.g. 850 +  = 1000, and use to subtract three- and four-digit multiples
of 50, e.g. 1250 – 850
 Subtract three-digit multiples of 10 by counting back in 100s and 10s, e.g. 1250 – 310
 Choose whether to subtract by counting back or counting up, bridging the 100s
Whole class
Group activities
Paired/indiv practice
Resources
Two groups of cyclists cycling from John
O’Groats in northern Scotland to Lands End in
Cornwall. The distance is 874 miles! One group
plan to take 10 days to complete the ride, and
the other group (who are less experienced at
long distance cycling) are planning to take 14
days. Both are raising money for charity. On
day 9, the first group have cycled 789 miles.
How far have they got to cycle on their last
day? How could we work this out? Draft a
number line from 789 to 874. What important
number lies between these two? 800 will be
quite a landmark for them! What’s the
difference between 789 and 800? How did you
work that out? And between 800 and 874?
That's easy, we can use place value! So what’s
the difference between 789 and 874? Work it
out, making a jotting on your whiteboards if it
helps. Agree that they have 85 miles left to
cycle. What subtraction could we write? What
strategy have we used to find the difference?
We are targeting 100s to find a difference
and so we can call this T100.
Ask children to work in pairs to use T100 to
Group of 4-5 children
Display the following list of prices, but with a
fourth column headed ‘reduction’:
Item
Old
Sale
price
price
DVD
£9.25
£7.69
CD
£7.25
£5.99
Book
£6.50
£4.89
Paint set
£8.45
£7.79
Drawing pad
£3.79
£2.45
Drawing pencils
£4.25
£3.49
All these items have been reduced in the
sale. Which item do you think has been
reduced by the most? And the least? How
much has the DVD been reduced by? How can
we work this out? Together draft a line from
£7.69 to £9.25. What are the important
amounts between £7.69 and £9.25? What is
the difference between £7.69 and £8? £8
and £9? £9 and £9.25? Mark these on the
ENL jotting. So what’s the reduction? Put
this in the table. Ask children to work in
pairs to find the other reductions.
Easier: Use the following table:
Ask chn to practise targeting 100
(bridging 100) by working through the
following: 523 – 489, 425 – 378, 615 –
586, 672 – 584, 565 – 448, 756 – 637,
745 – 688, 634 – 569, 925 – 867, 826
– 782, 537 – 473.
Ask them to sketch ENLs to show
their steps.
Easier: Children find differences
either side of a multiple of 100, and
have beaded, then landmarked lines
for support initially (see resources).
They may need to draw a hop to the
next multiple of ten from the smaller
number, and then a jump to 100.
Harder: Ask chn to do every other
question.
Challenge chn to find numbers
between 400 and 600 with a
difference of 48.
 Activity
sheet of
differences
with number
line support
(see
resources)
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y4 Maths TS6 – Spr – 4days
find the answers to 524 – 478 and 324 – 289,
drawing jottings on their whiteboards. Take
feedback.
Another group of cyclists are cycling from
John O’Groats to lands End. So far they have
cycled 625 miles. How far have they got to
cycle during the next 5 days? Draft a line to
show 625 & 874. What important numbers lie
between 625 and 874? This time there are
two multiples of 100. Ask a child to mark on
700 & 800. How can we use this to find the
difference? Ask children to find the
difference between 625 & 700, between 700
& 800, then between 800 & 874. So this time
we have 3 jumps to add up. What subtraction
can we write? And what does each number in
this subtraction mean? Agree that they
represent distance they have cycled already,
the target distance, and distance left to cycle.
So roughly how many miles a day do they need
to cycle?
Ask children to work in pairs to use T100 to
find the answers to 524 – 378 and 524 – 389,
drawing jottings on their whiteboards. Take
feedback.
Item
Old
Sale
price
price
DVD
£8.25
£7.69
CD
£6.25
£5.99
Book
£5.50
£4.89
Paint set
£8.45
£7.79
Drawing pad
£3.29
£2.45
Drawing pencils
£4.25
£3.49
Group of 4-5 children
Write the following subtractions on the
board:
518 - 347, 567 - 392, 548 - 329
Ask chn to discuss in pairs which they think
will have the greatest answer and which will
have the least. How did you decide? Draw out
strategies such as rounding to the nearest
multiple of ten and then subtracting.
Give each pair a set of digit cards. Work with
a partner to think of three additions with
answers between 100 and 200, where every
digit is different. They find the exact answer
to check. Take feedback asking chn to explain
how they came up with the two numbers.
Easier: Children compare subtractions: 518 –
397, 567 – 492 and 548 – 429. They find
subtractions with answer of less than 100.
Ask chn to practise targeting 100
(bridging 100) by working through the
following:
745 – 588, 723 – 489, 535 – 378, 615
– 476, 762 – 584, 755 – 448, 756 –
437, 634 – 469, 925 – 767, 826 – 682,
537 – 373. Ask them to sketch ENLs
to show their steps.
Easier: Children find differences
either side of a multiple of 100 from
the previous main practice session, and
have landmarked lines for support
initially (see resources). They may
need to draw a hop to the next
multiple of ten from the smaller
number, and then a jump to 100.
Harder: Ask chn to do every other
question. Some children may be able to
find the large difference by drawing
just two jumps, e.g. solving 745 – 588
by drawing a jump from 588 to 600,
then one large jump from 600 to 745.
Challenge chn to find numbers
between 300 and 600 with a
difference of 148.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 1-9 digit
cards
 0-1000
landmarked
line (see
resources)
Y4 Maths TS6 – Spr – 4days
Show a 0-1000 line (100s labelled, see
resources). Ask a child to mark on 850. What
do you add to 850 to make 1000? Record 850 +
150 = 1000. What do you think you might add
to 750 to make 1000? What do you add to 75
to make 100? Does that help? Ask a child to
mark on 750, and point out the 50, the 200
needed to make 1000. Work with a partner to
find other pairs to 1000. Write the following
on the board:
50 +
= 1000
150 +
= 1000
250 +
= 1000
650 +
= 1000
Ask questions about the list. So what is 1000
subtract 250? Subtract 350? What is the
difference between 450 and 1000?
Write the following subtractions on the board:
1200 – 850, 1350 – 900 and 1150 – 650.
Talk to your partner about how we might find
the answers to these subtractions. Take
feedback and sketch a line from 850 to 1200.
What important number is between 850 and
1200? And what is the difference between
850 and 1000? And between 1000 and 1200?
So what is 1200 subtract 850?
Ask children to work in pairs to use ENL
jottings to find the answers to the other two
subtractions.
Group of 4-5 children
Display the following table of heights of
some of the mountains in the UK.
Mountain
Ben Nevis, Scotland
Cairn Gorm, Scotland
Snowdon, Wales
Cadair Idris, Wales
Scafell Pike, England
Helvellyn, England
Slieve Donard, NI
Height to the
nearest 10m
1340
1240
1090
890
980
950
850
What is the difference in height between the
highest mountain in England and the highest
mountain in Wales? How could we find out?
Sketch a vertical line from 980 up to 1090.
What important height is in between? What
is the difference in height between 980 and
1000? And between 1000 and 1090?
And what is the difference in height between
the highest mountain in Scotland and the
highest mountain in England? Sketch a
vertical line to help.
Repeat with other pairs of mountains whose
heights are either side of 1000m.
Harder: Use the following table instead:
Mountain
Ben Nevis, Scotland
Cairn Gorm, Scotland
Snowdon, Wales
Cadair Idris, Wales
Scafell Pike, England
Helvellyn, England
Slieve Donard, NI
Ask children to write additions of
three–digit numbers ending in 50 with
a total of 1000.
They then use this to help solve the
following:
1050 – 850, 1200 – 650, 1350 – 450,
1300 – 550, 1650 – 750, 1500 – 850,
1400 – 550, 1100 – 350. Suggest
children sketch ENL jottings to help.
Harder: Children may not need to
sketch jottings but may be able to
work out the answers in their heads.
 0-1000
landmarked
line (see
resources)
Height to the
nearest m
1344
1244
1085
893
978
950
852
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y4 Maths TS6 – Spr – 4days
Write 1250 - 300 on the board. How could we
work this out? Discuss this with your partner.
Take feedback and draw out how we could
either count up to find the difference
between 300 and 1250 as in the previous
session, or we could count back in 100s from
1250. Draft an ENL jotting to show 1250, a
jump back of 100 to 1150, a jump back to 1050,
and then 950.
How could we work out 1250 subtract 310?
Agree that we could count up from 310 to
1250 or we could count back in 100s to
subtract 300, and then subtract 10. Ask
children to work in pairs to use both
strategies. Which was easier? Quicker? Share
any jottings children have drawn to help keep
track of counting back 300, then 10.
Ask children to repeat with 1250 – 420, and
then 1250 – 470.
Group of 4-5 children
Annie has scored 1300 points on a computer
game. But, disaster! She loses 970 points!
How many points does she have left? What
do we need to do to the numbers in this word
problem? What calculation can we write?
Agree that we can write 1300 – 970. How
would you normally work out this subtraction?
(Count up to find a difference.) But the
problem asks us to take the number away?
Use both counting up and counting back to
find the answer. The answer is the same, so
even if it looks like we are taking away, if it’s
easier to count up we can do that!
Write the following problem on the flipchart:
Ben has scored 1550 points, Annie has now
scored 420 points. What’s the difference
between their scores?
What calculation can we write to solve this
problem? And how would you prefer to work
out this subtraction, by counting up or by
counting back? Use both, conclude both give
the same answer and ask children which they
found easier/quicker for this calculation.
Write similar problems on the flipchart and
ask chn to discuss whether they would find it
easier to use counting back or counting up to
answer them.
Easier: Some chn might not be ready for this
idea, so just use word problems where the
strategy suggested in the problem is the
most efficient to solve it, i.e. just use this
session to set ‘take away’ and ‘difference’ in
context.
Children practise counting back in
100s, then 10s to work out the
following drawing ENL jottings where
necessary:
1750 – 220, 1530 – 310, 1350 – 410,
1270 – 320, 1180 – 210, 1450 – 520,
1870 – 350, 1290 – 450.
They then choose to count back or to
count up (find a difference) to work
out the following:
1420 – 580, 1250 – 420, 1340 – 650.
Easier: Children draw ENL jottings to
count back 100s, then 10s for the
first set of calculations only.
Harder: Ask children also to think of
two more calculations that they would
solve by counting back and two for
which they would count up.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y4 Maths TS6 – Spr – 4days