Year 6 Teaching Sequence summer 7a – Addition and subtraction (including decomposition) (two days)
Prerequisites:
 Use vertical addition to add two numbers with different numbers of decimal places (see spring teaching sequence 7)
 Find a difference between two numbers with different numbers of decimal places, e.g. 5.24 – 3.7, 9.4 – 5.78 (see spring
teaching sequence 7)
 Approximate first when using written methods (see spring teaching sequence 7 and summer oral and mental starter
bank 7)
 Derive quickly pairs of decimals with a total of 10, e.g. 7.8 and 2.2 and with a total of 1, e.g. 0.78 + 0.22 (see spring
teaching sequence 7 and summer oral and mental starter bank 7)
Overview of progression:
Written methods are used to subtract pairs of numbers and to add three numbers with a mix of those with one decimal place
and those with two decimal places: the importance of aligning digits according to place value is emphasised.
Note that some children may feel more confident using expanded addition or decomposition when working with numbers with
decimal places, particularly those with lots of ‘carry’ figures or different numbers of decimal places, even if they are
confident using compact addition/decomposition to add/subtract pairs of whole numbers.
Note that Hamilton main sequences use the method of complementary addition (counting up to find a difference, rather than
decomposition. This is because this method builds on children’s existing mental strategies and has been shown to be more
successful for greater numbers of children. These alternative subtraction sequences are written for schools who wish to
teach decomposition to more able children who are more likely to understand and therefore remember it. Of course, teachers
should always choose the method that fits with the school’s progression and ensures continuity in imagery and procedure. It
is important that decisions about which written methods to use are the whole schools decision to avoid inconsistency in
progression and concomitant confusion for children.
Watch out for children who do not align digits correctly when adding or subtracting numbers, particular those with different
number of digits or decimal places. Typically these are the children who have difficulty writing digits in boxes on squared
paper!
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS7a – Sum – 2days
Objectives:
 Use decomposition to subtract numbers with different numbers of decimal places, e.g. 55.24 – 23.7, 39.4 – 15.78
 Use vertical addition to add several numbers with different numbers of decimal places
Whole class
Group activities
Paired/indiv practice
Resources
Draw the following subtraction on the board:
549.6
- 22.75
31.21
Does this answer look right to you? If you subtract 22
point something from a number bigger than 500 can you
get an answer of around 31? What has gone wrong? Draw
out that the corresponding digits have not been correctly
aligned, and so the wrong digits have been subtracted
from each other. Ask children to lay this subtraction out
properly and work out the answer using decomposition.
Does your answer seem more sensible?
Ask chn to work out 42.34 subtract 37.6 on their
whiteboards, making an approximation of the answer first.
Take feedback on how they arrive at their estimates.
Repeat for 52.2 – 37.69 and 41.78 – 18.2, ensuring that
chn are secure in aligning the corresponding digits.
Group of 4-5 children
Write the following subtractions on
separate Post-it™ notes:
23.44 – 21.65, 23.45 – 21.99,
23.45 – 21.45, 43.25 – 38.76,
40.26 – 38.7, 40.25 – 38.5,
67.35 – 3.73, 67.35 – 5.01,
66.15 – 65.95.
Ask chn to look for a subtraction
which they might work out in their
heads rather using a written
method.
Discuss each subtraction in turn
and sort them into two sets ‘written
method’ and ‘mental method’.
Discuss what those in the mental
method set have in common.
Ask chn to choose at least two from
each set to work out.
Harder: Some chn may be confident
in working more of these out in
their heads than others.
Group of 4-5 children
Write the following additions on
the flipchart:
4.47 + 3.4 + 2.11, 4.29 + 3.4 + 2.56,
3.08 + 2.9 + 4.1, 3.35 + 2.7 + 4.1
Which of these additions will have
answers more than 10? Talk to your
partner. Take feedback. How did
Chn shuffle a pack of 0-9 digit
cards. They take 7 and use them
to make a pair of numbers
between 10 and 100, one with one
decimal place and one with two
decimal places, e.g. 45.6, 27.38 or
45.68, 27.3. They subtract the
smaller number from the larger
using decomposition, estimating
the answer first. They then use
the same seven digits to create
other subtractions.
Harder: Also challenge chn to find
7.125 – 6.995 and 8.235 – 6.779.
 Post-it notesTM
 0-9 digit cards
Chn shuffle a pack of 0-9 digit
cards and use all digits to make
three numbers, two with two
decimal places and one with one
decimal place. They choose
compact or expanded addition to
add the three numbers together,
approximating first. Repeat.
 0-9 digit cards
 Activity sheet
(see resources)
Write the following addition on the board:
40.56 + 32.3 + 7.45
What will the answer be roughly?
One person worked it out like this, and said they didn’t
know where to put the decimal point in the answer:
4 0. 5 6
+ 3 2.3
7.4 5
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS7a – Sum – 2days
5124
1 11
They have aligned both numbers to the right so all the
digits line up, but this isn’t right, why? Draw out how one
number has one decimal place and the others have two,
and so the units are not under the units, the tens under
the tens and so on. Ask chn how they think this sum
should be laid out.
Take feedback and show both expanded and compact
layouts.
40.56
+ 32.3
7.45
0.11
1.2
9
70
80.31
40.56
+ 32.3
7.45
80.31
111
Does this answer seem reasonable? Draw out that 40, 32
and 7 plus some decimal parts of each number are likely to
come to around 80. Which layout do you prefer for this
addition? Discuss that even if chn are happy using the
compact layout for many additions, as this one is a little
more complicated there may be some chn who prefer the
expanded layout for this example.
Repeat with 37.4 + 24.86 + 12.7, asking chn to lay out the
sum on their white boards using their preferred layout.
you decide?
Write 4.29 + 2.4 + 3.23 = 9.56 on
the flipchart.
Is this right? Why not? What error
might the person have made? How
would you explain to them why this
is wrong?
Work with a partner to write three
additions with totals between 9 and
10, and three with totals between
10 and 11. Every number must have
either one or two decimal places.
Easier: Challenge chn to come up
with three sums of money with a
total of £10. Say that each amount
must not be a whole number of
pounds. Discuss how they did this,
discussing what the numbers of
pounds added up to, and the
numbers of pence. Use notes and
coins if necessary.
Repeat.
Easier: Chn add pairs of numbers
with different numbers of
decimal places (see resources).
Harder: Chn are more likely to
use compact addition.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS7a – Sum – 2days