Addition
By the end of Foundation
Stage
Understand concept and vocabulary of plus, sum
total, add, altogether and through practical activities
in meaningful contexts within 5 and 10
• Songs – 1,2,3,4,5
Once I caught a fish alive.
• Count on, altogether, one more etc
• Matching numbers to objects
• Illustrate number stories with number sentences
• Counting on fingers in a consistent way
• Counting forwards in 1’s, 2’s and 10’s, up to 100,
20, 100 respectively (Ext 5’s) on a number line,
number square and with coins
Y1
Y2
Through practical activities in meaningful
contexts and informal written methods
• Develop partitioning/bonds to 20 and within
20 (separate a group of objects into 2 groups)
e.g. 8 is 5 and 3. Reinforce with Numicon.
• Use of number sentences and mathematical
language - count on / altogether / one more/
two more
•
• Use of number lines within 10 / Ext 20
Drawing jumps on prepared lines
Through practical activities and meaningful
contexts and informal written methods
• Fluent recall of bonds to 20 and within 20
• Derive fact families up to 100
13 + 7 = 20
7 + 13 = 20 (and link to subtraction)
20 = 7 + 13
20 – 7 =13
20 - 13 = 7
• Constructing own lines- partitioning the
smallest number
8 + 7 = 15
6+3
0 1 2 3 4 5 6
7
8
9
0 1 2 3 4 5 6 7
10
Relationships/Related Facts including symbols
+ and = various positions in number sentence:
•
=5+4
0
2
4
6
8
• Pictures and Marks – 1 more / 2 more
There are 3 cars in the garage. 1 more came
along
5+
=9
+4=9
= 5+4
+
3
5+ 4=
1
+
=9
Partitioning 14 = 10 + 4 (Numicon)
Use Numicon
+
=
4 + 1 =
5
Terry has 3 apples and Tony has 2 apples. How
many altogether?
+
• Begin to work on number bonds to 20.
• Money – use Numicon to help recognition value
of coins and simple addition e.g. 5p + 2p
(Blu tack on)
• Money and addition up to 20p
+2
8 9
10
+5
11 12 13 14 15
(Allow children to make choices when
partitioning the smaller number, not all children
will need to partition the smaller number, some
will count in 1s.)
• Partitioning into tens and units and using
number lines e.g. 61+14
+4
61
+10
71
75
(Teach children to add units first to ensure)
consistency when moving onto column
method
• Use Numicon to help partitioning and
re-combining
61 + 14 =
(Blu tack Numicon to coins)
60 + 1
10 + 4
70 + 5
• Count in 2’s, 5’s and 10’s
61 + 14 =
1+4=5
60 + 10 =70
70 + 5 = 75
• Addition of money up to £1.00 – using coins
Extension
•
Adding to multiples of 10
5 + 10
5 + 20
3 + 30
• Count on in 2’s, 5’s and 10’s from different
numbers e.g. 3, 9, 16, within 100.
• Visualisation of the 100 square
• Adding three numbers
2 + 8 + 4 = 14 or 1 + + 5 = 9
• Extend to questions such as 14 + 5 = 10 +
National Curriculum requirement -pupils
should be taught to:
Add 1 digit and 2 digit numbers up to 20
National Curriculum requirement -pupils
should be taught to:
Add within 100
To add successfully, children need to be
able to:
• Recall all addition pairs to 9 + 9 and
know number bonds to and within
10/20/100
• Add mentally a series of one-digit
numbers, such as 5 + 8 + 4
• Add multiples of 10 (such as 60 + 70)
and 100 (such as 600 + 700) using
the related addition fact, e.g. 6 + 7,
and their knowledge of place value
• Partition two-digit and three-digit
numbers into multiples of 100, 10 and
1 in different ways.
e.g. 52 = 50 + 2, 40 + 12, 30 + 22
Note:
It is important that children’s mental
methods of calculation are practised and
secured alongside their learning and use
of an efficient written method for
addition.
Key Stage Two – Addition
Y3
Y4
TO
23
+ 42
65
No ‘carrying’
HTO
315
+ 624
939
2. Extra digit in answer
TO
HTO
94
561
+ 73
+ 718
167
1279
3. Carrying U to T
TO
HTO
47
237
+25
+ 516
72
753
1
1
NB. Emphasise value of digit e.g. 2 tens and 3 units
Continue to use number lines and partitioning method.
Use resources to model/aid. Write calculations horizontally.
Emphasise as a school, we will ‘carry’ over the digits at the bottom for all column addition.
Carry digits are recoded below the line using the words ‘carry 10’ or carry ‘100’ and not ‘carry 1’.
National Curriculum requirement -pupils should be taught to:
Add numbers up to 3 digits
5. Carrying T to H. 6. Carrying O to T and T to H 7. Different number of Digits
HTO
HTO
ThHTO
371
376
2388
+ 485
+ 485
+ 1124
856
861
3512
1
1 1
1 1
Money and Decimals
A. £3.25
£1.53
£4.78
When introducing a new written strategy
it should be introduced alongside the
previous strategy taught so that children
can explicitly see the connection.
In Y3 and Y4 (and beyond where
appropriate) the children should
record their written calculations
using H T O. t h to reinforce the
place value of each digit in the
calculation.
1.
B. £4.21
+ £3.87
£8.08
1
Y5
£1.85 + 48p (written horizontally)
C. £1.85
+ £0.48
£2.33
1 1
National Curriculum requirement -pupils should be taught to:
Add numbers up to 4 digits
Addition using Th, H, T, O
Addition of decimals TO.t h
including more than two numbers
D. 1463
E. 14.1 + 3.89
+ 921
759
14.10
3143
+ 3.89
211
17.99
Real life problems involving money or measures.
National Curriculum requirement -pupils should be taught to:
Add numbers with more than 4 digits
Y6
Reinforce and securing all of the above.
National Curriculum requirement -pupils should be taught to:
Add numbers with more than 4 digits
Subtraction
By the end of Foundation Stage
Y1
Y2
Understand concept and vocabulary of -,
difference, subtraction, less, minus, take away
through practical activities in meaningful contexts
within 5 and 10
• Songs such as 5 little ducks went swimming
one day...
Through practical and meaningful contexts
• Find the difference within 20,
e.g. The difference between 7 and 11 using
towers/Numicon/Cuisenaire rods
• Drawing jumps on using vertical number lines
• Find difference by counting up (only when the
difference is small)
Through practical and meaningful contexts
• Counting back by partitioning second number.
Eg 46 - 18
46 – 10 - 8
14 – 12 = 2
•
•
•
•
(using images such as pegs)
e.g. 1 less than 5 (cover 1 peg up)
1 less , 2 less
Counting on from a smaller number
Counting back through practical activities in
meaningful contexts
Pictures/ Marks
We made 6 cakes. We ate 2 of them.
How many cakes are left?
Link to vertical number line 6 – 2 =
6
5
4
3
2
1
0
Use Numicon
5
-
3 =
9
10
11
12
13
The difference between
2 and 4
Ext: Begin to understand inverse of number
bonds to 10. e.g. 10 – 8 = 2
-10
36
14
-8
• Subtract multiples of 10 e.g. 50 – 20 = 30
• Record using – and =
Relationships/ Related Facts
5 - 2 =
=5-2
5 - =3
3 =-2
 -2 =3
3 = 5-
 - =3
3 = -

• Continued use of Numicon
12 – 8
28
• Find the difference (subtraction) by counting
on and add only when the difference is small.
Use of balance
example 1
5–2=
• Consolidate inverse of number bonds to 20
2
46
e.g. 10 – 3 = 7
10 – 7 = 3
• Consolidate inverse of number bonds within
20
e.g. if 6 + 2 = 8
8–2=6
8–6=2
• Add and subtract one digit and two digit numbers
to 20
including 0.
National Curriculum requirement -pupils
should be taught to:
Subtract 1 digit and 2 digit numbers up to 20.
23 – 18 = 5
+1
+1
+1
+1
15 16 17 18 19 20 21 22 23
Use Numicon to support
• Inverse bonds fluently to 20 and within 20
e.g. 20 – 18 = 2
20 – 2 = 18
16 minus 4 =12
16 subtract 12 = 4
• Derive and use related facts up to 100
e.g. 10 – 7 = 3 so 100 – 70 = 30
National Curriculum requirement -pupils
should be taught to:
Subtract within 100
To subtract successfully, children need to be able
to:
• Recall subtraction facts to 20 and within 20
• Subtract multiples of 10 (such as 160 – 70)
using the related subtraction fact 16 – 7 and
their knowledge of place value
• Partition two-digit and three-digit numbers
into multiples of hundreds, tens and
ones/units in different ways (e.g. partition 74
into 70 + 4 or 60 + 14).
Note:
It is important that children’s mental methods of
calculation are practised and secured alongside
their learning and use of an efficient written
method for subtraction.
Key Stage Two – Subtraction
Y3
Y4
When introducing a new written strategy it should
be introduced alongside the previous strategy
taught so that children can explicitly see the
connection.
In Y3 and Y4 (and beyond where
appropriate) the children should record
their written calculations using H T O.t h
to reinforce the place value of each digit in
the calculation.
Y5
1. No adjustment
2. Adjustment / Exchange T and O
TO
HTO
T O
4 5 11
47
864
Use base
- 23
- 621
- 3 6 10 to help
24
243 Ext
1 5
• Consolidation of using number lines, counting forwards and backwards within 100.
• Emphasise value of digit, e.g. 4 tens subtract 2 tens = 2 tens
• Use the correct language for subtraction i.e. exchange rather than borrow.
National Curriculum requirement -pupils should be taught to:
Subtract numbers up to 3 digits
3. Adjustment H to T
4. Adjustment H to T and T to O
H TO
H T O
34 13 7
34 123 12
- 1 8 2
- 1 8 7
2 5 5
2 45
5. Noughts
H TO
H T O
Check using inverse
56 910 14
4 6 7 10
Extend to subtracting numbers up to 4 digits
-1 4 2
- 3 4 7
3 28
2 5 7
A. £4.35
B. £5.3415
C. £ 23.159
- £1.23
- £2. 2 9
- £ 1.7 3
£3.12
£3. 1 6
£ 1. 86
National Curriculum requirement -pupils should be taught to:
Subtract numbers up to digits
Subtraction involving Th, H, T O and use of number lines (including
decimals also)
9
Y6
A. £ 45.12315 B. £ 3.7810
C. £ 34.10 10
D. £ 78.108
- £ 2. 8 7
- £ 1. 3 9
- £ 1. 3 5
- £ 2. 71
£ 2. 4 8
£ 2. 4 1
£ 2. 6 5
£ 5. 37
Real life problems involving money or measures.
National Curriculum requirement -pupils should be taught to:
Subtract numbers with more than 4 digits.
Reinforce and securing all of the above.
National Curriculum requirement -pupils should be taught to:
Subtract numbers with more than 4 digits.
Multiplication
Y1
Y2
Through practical activities and meaningful contexts using concrete
objects, pictorial representations and arrays with the support of the
teacher
•
Doubles
7
+
7
Through practical activities and meaningful contexts using concrete objects,
pictorial representations and arrays
• Double numbers (by partitioning and recombining)
17 + 17
=14
10 + 10
7 + 7
• Understand multiplication as repeated addition/ groups/ lots.
• Read arrays
Make connections between arrays, number patterns and
counting in 2’s, 5’s to 50 and 10’s to 100
• Number Lines
•
2x4 (2, 4 times)
0
1
2
3
4
5
6
•
“100
•
There are 2 sweets in one bag. How many sweets are there in 5
bags?
Square”
7
8
9
to
10 11 12 13
count
14
in
2’s,
5’s
and
10’s
• Repeated addition on a number line
2 + 2 + 2 + 2
0
•
1
Counting multiples of coins: 2p, 5p, 10p
2p +
2p
+
2p
2
3
4
0
1
2
4
+
3
4
5
6
7
(4 groups of 2, 2 four times, 2 x 4)
8
4
5 6
9
10
(2 groups of 4, 4 two times, 4x2)
7
8
9 10
• Know the times tables and division facts for 2, 5 and 10
• Calculate mathematical statements within the multiplication tables using
the multiplication (x) and equals (=) signs
• Show that the multiplication of two numbers can be done in any order
(commutative)
Key Stage Two – Multiplication
Y3
• Know Times Tables for 3,4,8
• Continue to use arrays and number lines/Cuisenaire rods/ for x 3,4,8
• Write and calculate mathematical statements for multiplication using the multiplication tables that they know, including for 2 digit numbers x 1
digit numbers, using mental and progressing to formal written methods
• Introduce grid model
X 10
4
(Link to image of partitioning array/ place value arrow cards)
5
50
20 = 70
10
4
5
Progressing to expanded method of multiplication
•
X
Y4
14
5
20
50
70
National Curriculum requirement -pupils should be taught to:
2 digits x 1 digit
• Know Times Tables and division facts up to 12x12 (including multiplying x0 and 1)
• Continue using partitoning method
• Short Multiplication
Ext
Carrying
Noughts
5
38
202
x 4
X
7
x 4
2 2
266
808
5
Y5
National Curriculum requirement -pupils should be taught to:
2 digit x 1 digit
3 digit x 1 digit
Use Grid Method to introduce TO x TO then introduce Long Multiplication
HTO
X
20
3
800
225
47
40 800 120 = 920 OR
120
X 5
x 23
7 140
21 = 161
140
1125
141
+
1081
+ _ 21
2 12
9 40
1081
1 1 081
Extend to ThHTO x TO
National Curriculum requirement -pupils should be taught to:
• 2 digit x 1 digit
• 3 digit x 1 digit
• 4 digit x 1 digit
Y6
•
•
•
•
2 digit x 2 digit
3 digit x 2 digit
4 digit x 2 digit
Whole numbers and decimals by 10,100, 1000)
Use Grid Method to introduce HTOxTO then introduce Long Multiplication
286x
HTO X TO
29
X
200
80
6
2574
20 4000 1600 120 =
5720
5 5 77 2
0
9 1800
720
54 = + 2574
1 1 8
294
8294
1
1
Introduce multiplying decimals using grid method and column O.t x O and O.t h x O
1.3 x 4 =5.2
3.65 x 5 = 18.25
National Curriculum requirement -pupils should be taught to:
Multiply up to 4 digits by 2 digits
•
Y1
Y2
Through practical activities in meaningful contexts
• Division as Sharing
Share equally
Share a bag of 15 sweets between 5 children
– one for you, one for you, one for you, one for
you, one for me
•
Through practical activities in meaningful contexts
•
•
Recognise relationship between x and ÷
Division as Grouping, 2’s, 5’s and 10’s
Eg: A bag of sweets, how many children can have 2 sweets each? - Put
into groups of 2
Eg: 15 children get into teams of 5 to play a game. How many teams are
there?
•
Use Numicon and hands to help with how many groups of 5 in 15?
How many 5’s have been counted?
•
Use of Numicon and Numicon Number Lines
Introduce halving even numbers up to 10
Using multilink, counters etc.
Half of 4
0
10
How many 2’s in 10 and 5’s in 20?
•
Introduce number sentences using ÷ sign
Understanding 8 ÷ 2 as half of 8
Using number lines to answer questions such as
20 ÷ 2 linking to how many 2’s in 20?
20
18
16
14
12
10
8
6
4
2
0
Use Cuisenaire rods and number track.
Know related division facts for 2 x 5 x 10 x tables
Record using ÷ and = signs
Key Stage Two – Division
Y3
Know division facts for 3,4, and 8 times tables
Introduce repeated subtraction on a numberline INSERT IMAGE
Y3
Know division facts for 3,4, and 8 times tables
Introduce repeated subtraction on a numberline INSERT IMAGE
Division questions based on multiplication tables they know
Eg 30÷10, 18÷2
Introduce grouping method before short division
13
5) 65
- 50 5 x 10
15
- 15 5 x 3
0 13
Create fact box
to encourage
efficient
grouping eg
not always
groups of 10
1x
2x
5x
10x
20x
50x
100x
Introduce short division
No remainder, no carrying
23
3 ) 69
Encourage children to estimate answers before attempting calculation Continued use of Cuisenaire and number lines to model.
National Curriculum requirement -pupils should be taught to:
Divide 2 digits by 1 digit, progressing to formal written methods (statutory)
Y4
Know all division facts for all times tables (including dividing by 1)
No remainder, carrying
1 5
3 ) 4 15
Remainder, carrying
1 4 1 r1
3 ) 4 12 4
Placing of quotient (answer)
41
7 ) 2 28 7
Zeros in quotient
204
4 ) 8 1 16
National Curriculum non statutory guidance -pupils should be taught to:
Divide 2 digits by 1 digit and 3 digits by 1 digit becoming fluent with formal written method of short division with exact answers
The National Curriculum statutory requirements for Year 4 are not clear therefore our guidance for Year 4 has been based on the skills
required to access Year 5 statutory requirements
Y5
Consolidate the use of the formal written method of short division
1 1 7 1 r1
8 ) 9 1 3 56 9
National Curriculum requirement -pupils should be taught to:
• 2 digit ÷ 1 digit
• 3 digit ÷ 1 digit
• 4 digit ÷ 1 digit
Children interpret the remainders appropriately for the context
eg as fractions, decimals or by rounding
98÷4 = 98/4 =24r2=24 ½ =24.5 rounded to 25
Divide whole numbers and those involving decimals by 10, 100, 1000
Y6
Consolidate short division.
Children should be able to interpret remainders as whole number remainders, fractions or by rounding, as appropriate for the context.
•
•
•
2 digit ÷ 2 digit
3 digit ÷ 2 digit
4 digit ÷ 2 digit
Introduce long division
Y6
Consolidate short division.
Children should be able to interpret remainders as whole number remainders, fractions or by rounding, as appropriate for the context.
•
•
•
2 digit ÷ 2 digit
3 digit ÷ 2 digit
4 digit ÷ 2 digit
Introduce long division
N.B: The above examples are taken from the National Curriculum for Mathematics appendix
National Curriculum requirement -pupils should be taught to:
• Divide numbers up to 4 digits by a 2 digit number using the formal written method of short division where appropriate
• Divide up to 4 digits by a 2 digits whole number using the formal written method of long division
• Interpret remainders as whole number remainders, fractions or by rounding, as appropriate for the context