Maths the Modern Way!!
Addition and Subtraction
St Teresa’s Primary School
with
Essex County Council
The Primary National Strategy
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Basis of teaching since 1999 – based on
extensive research and proven success
Daily entitlement to maths lesson
Key features
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Progression carefully set out
Interactivity – use of models, images, games, practical
activities
Focus on mental skills as well as written
Vocabulary, problem solving, communication, explanation
and reasoning
There is no “right way” to work!!
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Children exposed to a range of methods.
Methods selected will depend upon the situation
and the numbers involved, including when to
use calculators.
Children make decisions about methods and
draw on a range of strategies and approaches
when applying Maths in context.
Children in same class could be using different
methods to others depending on their ability,
confidence and stage of mathematical
development.
Addition

Foundation Stage (Reception)
 Counting
and recognising numbers
 Counting on using number lines or
apparatus
 Recall of facts and number bonds
 Numbers to 10, then beyond.
Key Stage 1

Year 1
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Introduce + and = signs to record
calculations done mentally
Securing bridge over 10s boundary
Mental recall of facts
Numbers extend to 30, 40…
Recognise patterns in 100 square (+10, +1)
Splitting numbers and recombining
The Importance of Place Value
Place Value Runaround!
Key Stage 1

Year 2
 Extension of Year 1
 Introduction of partitioning
 Adding significant digits first
How to Partition
35 + 72
30
5
30 + 70 = 100
5+ 2=
7
100 + 7 = 107
70
2
Try these by partitioning!!
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45+67
154+78
327+198+23
This can work with any size of number – is it
efficient to use this method for this?
 40187+63742+31243
 10005+12010+3000
Key Stage 2
The Numberline!!
67 + 32
67 + 10 + 10 + 10 + 2
67
77
87
97
99
Expanded Addition
(Introduced Year 3)
43+25
43
+ 25
60
8
68
Try this
method with
these!!
254+167
423+541
Standard Method
63+39
63
+
39
12
90
1 02
+
63
39
2
1
63
+
39
1 02
1
You may like to try these problems
using some of the methods that we
have used so far.
623+12
352+231+101
16+746+233
The Roundabouts of Harlow
FINISH
1
1
2
4
11
8
5
9
2
3
5
12
7
6
1
10
START
Subtraction

Foundation Stage (Reception)
 Counting
and recognising numbers
 Counting back using numberlines or
apparatus
 Recall of facts and number bonds
 Numbers to 10, then beyond.
Key Stage 1

Year 1
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Introduce - and = signs to record calculations
done mentally
Mental recall of facts
Subtracting 10 from “teens” number
Recognise patterns in 100 square (-10, -1)
Splitting numbers and recombining
Key Stage 1

Year 2
 Extension of Year 1
 Crossing 10s boundary with numbers to
20,30…. (crossing 100s boundary in Y3)
 May use splitting of
numbers/partitioning to assist in
calculation (e.g. 27–15 = 27–5–2–8)
Key Stage 2
The Numberline!!
67 - 32
67 - 10 - 10 - 10 - 2
-2
35
-10
37
ANSWER!!!
-10
47
-10
57
67
OR….
67 - 32
+10
+10
32
42
+10
52
+5
62
67
10 + 10 + 10 + 5 = 35
+10
+8
32
40
+10
50
10 + 10 + 8 + 7 = 35
+7
60
67
Complementary Addition
+10
+8
32
40
+10
50
10 + 10 + 8 + 7 = 35
67
- 32
8 to 4 0
2 0 to 6 0
7 to 6 7
35
+7
60
67
The Standard Method Decomposition
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Introduced from Year 3
Linked initially with use of images and practical
apparatus to secure understanding of how place
value is being used in the calculation
Lots of stages where children can make errors
Not always the most efficient method to use
If children can obtain an answer using another
method, that is OK.
33 - 17
Can I do
this
mentally?
Shall I
use a
written
method?
Which written
method is most
appropriate to
use for these
numbers?
33 - 17
33
- 17
33 - 17
33
- 17
I’m going
to partition
the
numbers.
33 - 17
33
- 17
=
30 + 3
- 10 + 7
33 - 17
33
- 17
30 + 3
=
- 10 + 7
33 - 17
33
- 17
30 + 3
=
- 10 + 7
I start with the units,
so I need to take
away 7 small cubes.
But I only have 3 of
them.
I’ll break up one of
the 10s into 10 units.
33 - 17
33
- 17
30 + 3
=
20 + 13
- 10 + 7 = - 10 + 7
I’ve now got 2
lots of 10, so
that’s 20, as well
as 13 units, so
let’s write it
down to show
what I am doing.
33 - 17
33
- 17
30 + 3
=
20 + 13
- 10 + 7 = - 10 + 7
Now I can
take away
7!
33 - 17
33
- 17
30 + 3
=
20 + 13
- 10 + 7 = - 10 + 7
6
33 - 17
33
- 17
30 + 3
=
20 + 13
- 10 + 7 = - 10 + 7
6
Now I can
take away
10!
33 - 17
33
- 17
30 + 3
=
20 + 13
- 10 + 7 = - 10 + 7
10 + 6
33 - 17
33
- 17
30 + 3
=
20 + 13
- 10 + 7 = - 10 + 7
10 + 6
=16
Have a Go!
There is some base 10 apparatus in the
tables if you would like to run through using
this to be clear about the process involved.
42 – 27
51 – 29
90 - 36
There will be examples like this…
75 – 32
where no exchange is needed, but partitioning is
still useful as children are more successful at
working with tens and units separately.
-
75
70+5
32
= 30+2
20+3
= 23
Next stages will involve increasing the number of
digits in the numbers (HTU, the ThHTU), working
with apparatus, then without, to ensure children
are secure with place value before moving on to
the final stage. Often this would be taught side
by side with the more expanded method so that
children can see how they relate.
271
200+70+ 1
200+60+11
-158 = 100+50+ 8 = 100+50+
100+10+
6 1
6
1
6
1
8
3=113
6 1
271
2 7 1
2 7 1
2 7 1
2 7 1
-158
- 1 5 8
- 1 5 8
- 1 5 8
-1 5 8
3
1 3
1 1 3
Why the additional steps?
Why the additional steps?
2
1 6 3 0 4
-
3 2 0 7
1
1 6 3 0 4
-
3 2 0 7
1 3 0 0 7
Why the additional steps?
2
1 6 3 0 4
-
3 2 0 7
1
1 6 3 0 4
-
3 2 0 7
1 3 0 0 7
3 0 0 0 5
-
4 8 5 7
3 0 0 0 5
-
4 8 5 7
3 4 8 5 2
Maths the Modern Way!!
Addition and Subtraction
St Teresa’s Primary School
with
Essex County Council