Year 3 Teaching Sequence 5 - Adding two-digit numbers (three days)
Prerequisites:
 Know addition facts for all pairs of single digits (see teaching sequence 3 and oral and mental starter bank 5)
 Use addition facts for all numbers up to 10 to find pairs of multiples of 10, e.g. use 5 + 2 to find 50 + 20 (oral and
mental starter bank 5)
 Use partitioning and combining to add pairs of two-digit numbers (where the ones digits totalled less than 10, and the
tens less than 100) (see Year 2 summer teaching sequence 10)
 Add two-digit numbers by adding multiples of ten and one (e.g. add 45 and 23 by adding 20, then 3) (see Year 2
summer teaching sequence 5)
Overview of progression:
Children revise using J10 (Jump 10, adding on tens, then the units (also called ones)) to add on a two-digit number, and
revise how to use Splits (partitioning and recombining) to add pairs of two-digit numbers (where the ones digits totalled less
than 10, and the tens less than 100). They move on to use J10 and Splits to add pairs of two-digit numbers where the ones
digit total more than 10. They sort calculations according to whether they prefer to use J10 or Splits. When using J10 they
choose which number line to use (0-100 beaded, landmarked or draft their own ‘empty’ number line); these are used to
record steps in mental calculations in the Year 2 sequences.
Note that J10 and Splits are terms used in Year 2 sequences. If children have not met these sequences, you will need to
decide whether to use these terms or others that they know. It is helpful for all teachers and teaching assistants in a
school to use the same terms for consistency. Having abbreviations for strategies can be very useful as they become easy
labels for children to use to describe their strategies: they are ‘shorthand’ for previous teaching.
Watch out for children who are not fluent in counting on in tens, or who do not have the necessary addition facts to use
strategies efficiently.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y3 Maths TS5 – Aut –3 days
Objectives:
 Revise two-digit +/- 20, 30, 40, 50, then use to add 22, 23, 32, 33 etc.
 Add any pair of two-digit numbers (totals less than 100) by partitioning and recombining
 Choose whether to partition and recombine or to count on in tens and ones
Whole class
Group activities
Paired/indiv practice
Resources
Revise adding multiples of ten to two-digit numbers.
Ask chn to make 45 using place value cards. What is
45 add 20? Which card will you change? Repeat with
45 + 30, 52 + 30, 52 + 40.
Show a jotting of 43 + 24 on a beaded line (see
resources). What calculation has this person done?
How have they done it? Point out that they have
added 20 and then added the 4. This strategy can be
described as J10: Jump 10, counting on in tens, then
adding the units. Repeat with jotting of 35 + 31 on a
landmarked line and jotting of 65 + 24 on an empty
number line (see resources).
When we learnt to double numbers like 34, what did
we do? Could we use this method to add 65 and 24?
Remind chn how they used Splits in Year 2 to add
pairs of two-digit numbers. Ask chn to work in pairs
to each make one of the two numbers 65 and 24
using place value cards. Mimic this process using the
ITP Place value. Move the tens together. How much
have we got here? Move the units or ones card
together. And here? And altogether?
Record on the board:
65 + 24 = 60 + 20 + 5 + 4
= 80 + 9
= 89
Group of 4-5 children
Write the following additions on the flipchart
and ask children to use both J10 and Splits to
find the answers:
56 + 31, 45 + 34, 62 + 26
Discuss each in turn and ask children which
strategy they preferred and why. Stress that
different children are likely to have different
preferences.
Draw a set (unlabelled) and write the following
additions in it: 64 + 21, 75 + 22, 53 + 31 and in a
separate set: 65 + 34, 55 + 25, 63 + 26.
Someone has sorted these additions into two
sets, J10 and Splits. Can you guess which is
which? Why do you think that?
Harder: Chn each think of an extra calculation
to go in each set.
Write 45, 52 and 65 on the
board. Chn add 23 and 32 to
them using J10 choosing
beaded, landmarked lines or
drafting their own empty
number line. They practise
using Splits (partitioning and
recombining) to add pairs of
two-digit numbers (see
resources).
Harder: Chn also choose three
additions from the activity
sheet to answer using both
J10 and Splits and discuss
which strategy in pairs which
they prefer for each.
 Jotting of 43 +
24 on a beaded
line (see
resources)
 Jotting of 35 +
31 on a
landmarked line
(see resources)
 Jotting of 65 +
24 on an empty
number line
(see resources)
 Place value
cards
 ITP Place value
 Beaded and
landmarked
lines (see
resources)
 Activity sheet
to practise
Splits
(partitioning
and
recombining)
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y3 Maths TS5 – Aut –3 days
Discuss how we can use J10 (Jump 10, adding on tens,
then the units to add 24 as 20 then 4), or we can use
Splits (split both numbers, add the tens, add the
ones and then put them back together again).
Explain that today we are going to practise adding
pairs of two-digit numbers where the units’ digits
come to a total of more than 10.
Write 57 + 25 on the board. Ask a child to label 57
on the beaded line and then to draw jumps to add 20
(either two jumps of 10 or one jump of 20). What’s
going to happen when we add 5? Draw out that we are
going to cross the next multiple of ten. What might
be a good way to add 5 to 77? Agree that it would be
helpful to target 80, splitting 5 into 3 and 2. Draw a
hop of 3 to 80 labelling it +3, and a hop of 2 to 82,
labelling it + 2. So we’re using J10 and T10!
Repeat with 48 + 34 and 56 + 37.
Ask chn to work in pairs to each make one of the two
numbers 57 and 25 using place value cards. Mimic
this process using the ITP Place value. Move the tens
together. How much have we got here? Move the
units or ones card together. And here? And
altogether?
Record on the board:
57 + 25
= 70 + 12
= 82
Point out the extra small step in adding 70 and 12 as
7 and 5 came to more than ten.
Repeat with 48 and 34, 56 + 37.
Write: 55 + 23
= 50 + 20 + 5 + 3
= 70 + 8
= 78
on the flipchart, and use a Post-it™ to cover
23. On another sheet write:
56 + 27 = 50 + 20 + 6 + 7
= 70 + 13
= 83
and cover up 27. Can you guess what number is
covered up?
Repeat with: 48 + 37
= 70 + 15
= 85
this time covering the 37. Did you notice that
all of the multiples of tens in these additions
add up to 70? But some had answers greater
than 80! Why is that?
Write the following additions on cards and
discuss which will have totals of more than 80:
46 + 32, 45 + 37, 58 + 26, 45 + 43, 52 + 25.
Sort them into two groups >80 and <80,
discussing what is common in each group.
Harder: Miss out the second line of the first
two additions (= 50 + 20 + 5 + 3 and = 50 + 20 +
6 + 7). Challenge chn to make up additions with
totals between 70 and 80.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Write 48, 57 and 69 on the
board. Chn add 24 to them
using J10 choosing to use
beaded, landmarked lines or
drafting their own empty
number line. Chn practise
using Splits (partitioning and
recombining) to add two-digit
numbers where the ones
digits have a total of more
than 10 (see resources).
Easier: Children just use
Splits.
 Beaded and
landmarked
lines (see
resources)
 Place value
cards
 ITP Place value
 Activity sheet
to practise
Splits
(partitioning
and
recombining)
Y3 Maths TS5 – Aut –3 days
Write the following calculations on the board: 65 +
21, 46 + 37, 48 + 32, and 54 + 35.
Work in pairs to use J10 and then Splits to find the
answer to each.
When chn have worked out all four additions using
both strategies, ask them which they preferred for
each addition. Discuss how adding on 21 for example
is really easy using J10, whereas more chn may have
preferred using Splits to work out 46 + 37 as
counting on 37 is trickier. Some chn may have used
Splits to add 48 and 32 as they spotted the 8 and 2
to make 10. There may be no consensus about 54 +
35, explain that this is fine as different chn will
favour one strategy more than the other.
Write the following additions on cards (or separate
text boxes on the IWB):
51 + 37, 72 + 11, 48 + 28, 44 + 44, 56 + 32, 62 + 35
and labelled two sets J10 and Splits. Ask chn to
discuss how they would prefer to work out 51 + 37 in
pairs, take feedback and ask chn to vote. Put the
calculation in the most popular set. Repeat with the
other additions. Choose at least one from each set to
work out.
Group of 4-5 children
Draw a set (unlabelled) and write the following
additions in it: 64 + 21, 35 + 22, 53 + 31 and in a
separate set: 45 + 34, 35 + 25, 36 + 27.
Someone has sorted these additions into two
sets, J10 and Splits. Can you guess which is
which? Why do you think that? Label the sets.
Underneath write the numbers 42, 56, 21, 11,
38, 47, 32, 28.
Ask chn to use two of numbers to create an
addition they would use J10 to solve. Write
their suggestions in the J10 set. Any others?
Repeat, this time making additions for the
Splits category.
Easier: Work together as a group to solve each
of the six additions using both strategies and
see if they agree with person who sorted them.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Chn sort calculations
according to their preferred
strategy for each, and then
choose at least three from
each set to solve (see
resources). They choose 0100 beaded lines, landmarked
or draft their own empty
number lines to solve those
using J10.
Easier: Chn choose five
additions to work out. They
use both strategies and
decide which they preferred.
Give chn beaded lines (see
resources) to help them to
use J10 and place value cards
if necessary to use Splits.
Harder: Chn think of other
additions to write in each set.
 Activity sheet
of additions to
sort (see
resources)
 0-100 beaded
numbers lines
 0-100
landmarked
lines
 Place value
cards
Y3 Maths TS5 – Aut –3 days