Download MATHS – Calculations policy - Binfield Church of England Primary

Calculations Policy
This policy was reviewed by the Teachers at
Binfield C.E. Primary in September 2012
Binfield C.E. Primary School
Calculation Policy
Subtraction
Multiplication
Addition
Children are encouraged to develop a mental
picture of the number system in their heads to
use for calculation.
They develop ways of recording calculations
using pictures and concrete apparatus etc.
They use number lines, hundred squares and
practical resources to support calculation.
Teachers demonstrate the use of the number
line.
Children begin to use number lines themselves
starting with the larger number and counting
on.
First counting on in tens and ones
34 + 23 = 57
+10
+10
+1 +1 +1
Children are encouraged to develop a mental
picture of the number system in their heads to
use for calculation.
They develop ways of recording calculations
using pictures and concrete apparatus etc.
They use number lines, hundred squares and
practical resources to support calculation.
Teachers demonstrate the use of the number
line.
Children begin to use number lines themselves
to support their calculations.
First counting back in tens and ones
47 - 23 = 24
-1 -1
-1
-10
-10
Children will experience equal groups of
objects, particularly in practical problem solving
activities. They will join in with adults counting
in 2s, 5s and 10s, and become independent.
24 25 26
34
44
54
55
56
57
Then adding the units in one jump
34 + 23 = 57
+10
+10
+3
44
54
57
Followed by adding the tens in one
jump and the units in one jump
34 + 23 = 57
+20
+3
54
Compensation
49 + 73 = 57
+50
57
47
27
37
47
Children will develop their understanding of
multiplication and use jottings to support
calculation.
Repeated addition
3 times 5 = 5 + 5 + 5 = 3 lots of 5 = 5 x 3
Repeated addition can be shown on a number
line:
5x3=5+5+5
+5
+5
+5
0
5
15
Commutativity
Children should also know that 3 x 5 has the
same answer as 5 x 3. This can also be shown
on the number line.
+5
+5
+5
27
47
Counting on
47 – 23 = 24
+7
+10
5
10
15
+3
+3
+3
+3
+3
Arrays
Children should be able to model a
multiplication calculation using an array.
+7
Children will understand equal groups and
share items out in play and problem solving
activities. They will join in with adults counting
in 2s, 5s and 10s and become independent.
Children will develop their understanding of
division and use jottings to support calculation.
Sharing equally
“6 sweets shared between 2 people. How
many do they each get?”
Grouping or repeated addition
“There are 6 sweets. How many children can
have 2 sweets each?”
Repeated subtraction using a number
line
12 ÷ 3 = 4
30
40
0 1 2 3 4 5 6 7 8 9 10 11 12
Repeated subtraction using a number
line including remainders
13 ÷ 3 = 4 r 1
5 x 3 = 15
-1
122 123
10
Children are encouraged to develop a mental
picture of the number system in their heads to
use for calculation.
They develop ways of recording calculations
using pictures and concrete apparatus etc.
0
23
73
37
Followed by subtracting the tens in
one jump and the units in one jump
47 - 23 = 24
-3
-20
24
34
27
Then subtracting the units in one jump
47 - 23 = 24
-3
-10
-10
24
34
Division
Children are encouraged to develop a mental
picture of the number system in their heads to
use for calculation.
They develop ways of recording calculations
using pictures and concrete apparatus etc.
47
3 x 5 = 15
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Using symbols to stand for unknown
numbers
÷ 10 = 8
26 ÷
= 13 24 ÷ 2 =
Binfield C.E. Primary School
Calculation Policy
Children will begin to use informal pencil and
paper methods (jottings) to support, record and
explain partial mental methods building on
existing mental strategies.
Children will begin to use informal pencil and
paper methods (jottings) to support, record and
explain partial mental methods building on
existing mental strategies.
Adding least significant digits first
625 +
148
13
5 +
8
60 20 + 40
700 600 + 100
773
Carrying below the line
587 +
475
1062
Partitioning and decomposition
89
- 57
= 80
50
30
+
+
+
9
7
2
Begin to exchange
60
1
71
- 46
= 70
= 40
20
+
+
+
1
6
5 = 25
Children will begin to use informal pencil and
paper methods (jottings) to support, record and
explain partial mental methods building on
existing mental strategies.
Partitioning
38 x 5 = (30 x 5) + (8 x 5)
= 150 + 40
= 190
Grid Method
x 30
5 150
8
40
= 190
Children will use the grid method to multiply TU
x U, TU x TU, HTU x TU and decimals.
11
Carrying below the line
587 +
475
1062
11
Using similar methods, children will:
Add several numbers using different
numbers of digits;
Begin to add two or more sums of money,
with or without adjustment from pence to
pounds;
Know that the decimal places should line
up underneath each other.
Children should extend the carrying method to
numbers with any number of digits or decimal
places.
Decomposition
6141
754 –
286
468
Using similar methods, children will:
Subtract numbers with different numbers
of digits;
Begin to subtract two or more sums of
money, with or without adjustment from
pence to pounds;
Know that the decimal places should line
up underneath each other.
Children should extend the Decomposition
method to numbers with any number of digits
or decimal places.
Children will develop their use of repeated
subtraction to be able to subtract multiples of
the divisor.
72 ÷ 5
R2 - 5 - 5
-5 -5
- 50
Expanded written method
46 x
32
12
80
180
1200
1472
Compact method
46 x
32
92
1380
1472
Using similar methods, children will:
Know that the decimal places should line
up underneath each other.
Children should extend the Compact method
to multiply decimals with up to two decimal
places by a single digit number, then two digit
numbers.
02
7
12
Chunking
17
22
72
72 ÷ 5 = 14 r 2
-50 (10 x)
22
- 5 (1 x)
17
- 5 (1 x)
12
- 5 (1 x)
7
- 5 (1 x )
2
Compact Method
3
157
471
3
17
15
21
Short Compact Method
157
3
41721
Using similar methods, children will:
Decide what to do after division and
round up or down accordingly;
Express remainders as fractions or
decimals where appropriate.
Children should extend the Compact method
to divide numbers with decimal places.
Binfield C.E. Primary School
Calculation Policy