2
Addition
3
Partitioning
35+ 28=
35= 30 5
This method
can also be
used for HTU
28= 20 8
30+ 20= 50
5+8= 13
50+ 13= 63
4
Using a Number Line to Add Two
Digit Numbers
Start by adding the tens number, then adding the units number. This
is first introduced on number line with all the numbers shown. If you
do not have one of these at home use a ruler. Once a child is
confident with the method, there is no need to write out all the
numbers on the line.
+ 10
22
+2
32
22 + 12 = 34
34
5
Column Addition with Carrying
from Units to Tens
+
2 3 4
3 5 7
5 9 1
It is important that
numbers are lined
up in columns
carefully. We
always work from
right to left. Any
carrying is placed
below the bottom
line.
1
6
Column Addition with 3 Digit
Numbers, Carrying from all Columns
8 3 4
+
4 6 7
1 3 0 1
1
1
7
Column Addition with Numbers
with One Decimal Place
8 3 ∙4
+ 4 6 ∙7
1 3 0∙ 1
1
1
It is important to
line up the
decimal point in
each number
when setting out
the sums.
Remember to
place a decimal
point in the
8
answer.
Subtraction
9
Using a Number Line to Subtract
2 Digit Numbers
Start by subtracting the tens number, then subtract the units
number. This is first introduced on a number line with all the
numbers shown. If you do not have one of these at home use a
ruler. Once a child is confident with the method, there is no need to
write out all the numbers on the line.
-2
- 10
34-12 = 22
22
24
34
10
Column Subtraction with Exchange
from Tens to Units Column
7
5 8 4
3 5 7
2 2 7
1
-
11
Column Subtraction with
Exchange from all Columns
5 8 4
4
17
1
-
3 9 7
1 8 7
12
Column Subtraction with Decimal Numbers
with One Decimal Place and Exchange from all
Columns
5 8 ∙4
4
∙
17
1
3 9 ∙7
1 8 7
It is important
to line up the
decimal points
when setting
up calculations
with decimal
numbers
13
Multiplication
14
Using the Grid Method to
Multiply by a Single Digit
First draw out a grid. It is only really necessary to draw out the red lines
below. The grid can be used for numbers with any amount of digits
e.g. 23x7
x
20
7
140
3
+ 21 = 161
15
Using the Grid Method to
Multiply by Two Digits
First draw out a grid. It is only really necessary to draw out the red lines
below. The grid can be used for numbers with any amount of digits
e.g. 23x37
x
20
30
600
7
140
Your child may wish to use
this standard way to multiply
numbers with more than one
digit once they understand
how numbers are partitioned.
Of course, they may prefer to
continue using this grid
method instead.
3
+ 90 = 690
+
+ 21 = 161
851
16
Using Column Multiplication
3 4 6
X
5
1 7
3
2
0
3
Once confident
and with an
understanding of
how numbers are
partitioned when
multiplying, your
child will be
encouraged to
use this standard
way to multiply
single digit
numbers
17
Using Column Multiplication
when Multiplying by a Two Digit
Number Your child may wish
to use this standard
3 4 6
way to multiply
X
2 5
1
+6
8
7
9
2
3 0
2 0
3
numbers with more
than one digit once
they understand how
numbers are
partitioned. However,
they may prefer to
continue using this
grid method instead.
1
6
5 0
1
18
Using Column Multiplication with
Decimal numbers
3 4 6•
X
5
1 7
3 • 0
2
3
19
How many groups are
in..?
Division
20
Sharing a Number
8 divided by 4 = 2
21
Chunking
72 divided by 3
0
10x3
10x3
3
3
3
3
72
22
Using Arrays
An array is an arrangement of a number or counters represented as
a rectangle. The number of rows and columns show the numbers it
can be divided by. For example, let’s consider the number 12. It
can be visually represented in an array like this:
So, 12 ÷ 2 = 6
23
Interpreting Arrays
By showing division in this way and by
ringing columns rather than rows, it is
very clear to see that 12 ÷ 6 = 2
By ringing columns instead of rows the
introduction to thinking of division as
grouping can be made
12 divided by 2= 6
24
Locating Division Facts from a
Multiplication Square
x
1
2
3
4
5
6
7
8
9
10
11
12
1
1
2
3
4
5
6
7
8
9
10
11
12
2
2
4
6
8
10
12
14
16
18
20
22
24
3
3
6
9
12
15
18
21
24
27
30
33
36
4
4
8
12
16
20
24
28
32
36
40
44
48
5
5
10
15
20
25
30
35
40
45
50
55
60
6
6
12
18
24
30
36
42
48
54
60
66
72
7
7
14
21
28
35
42
49
56
63
70
77
84
8
8
16
24
32
40
48
56
64
72
80
88
96
9
9
18
27
36
45
54
63
72
81
90
99
108
10
10
20
30
40
50
60
70
80
90
100
110
120
11
11
22
33
44
55
66
77
88
99
110
121
132
12
12
24
36
48
60
72
84
96
108
120
132
144
To find the answer to 42 ÷ 7:
1. Look across the top for
the 7 column
2. Go down the x7 column
until you find 42
3. Read across to see how
many groups of 7 made
42
25
Standard Division
(no remainders)
2
2
3
2
4
6
4
4
We always work
from left to right
8
26
Standard Division
(with a remainder in the answer)
2
2
3
2
4
6
4
4
r
1
9
Place the
remainder
after the letter
‘r’ at the end of
the answer
27