Download Calculation Policy - Broadmead Lower School

Broadmead Lower School
Calculation Policy
2015
Introduction
Children are introduced to calculation through practical, oral and mental activities. As children begin to understand the underlying ideas they
develop ways of recording to support their thinking and calculation methods. They use particular methods that apply to special cases and learn
to interpret and use the signs and symbols involved. Over time children learn how to use models and images, such as empty number lines, to
support their mental and informal written methods of calculation. As their mental methods are strengthened and refined, so too are their informal
written methods. These methods become more efficient and succinct and they lead to efficient written methods that can be used more generally.
By the end of year 4 we aim that children are equipped with mental, written and calculator methods that they understand and can use correctly.
When faced with a calculation, children are able to decide which method is most appropriate and have strategies to check its accuracy. At
whatever stage in their learning and whatever method is being used, it must still be underpinned by a secure and appropriate knowledge of
number facts, along with those mental skills that are needed to carry out the process and judge if it was successful.
The overall aim is that children leave Broadmead Lower School with the ability to
 have a secure knowledge of number facts and a good understanding of the four operations
 are able to use their knowledge and understanding to carry out calculations mentally and to apply general strategies when using one-digit
and two-digit numbers. Their knowledge will be extended particular strategies to include special cases involving bigger numbers
 make use of diagrams and informal notes to help record steps and part answers, when using mental methods that generate more
information than can be kept in their heads
 have an efficient, reliable, compact written method of calculation for each operation, that can be applied with confidence when
undertaking calculations that they cannot carry out mentally
 using their mental skills to monitor the process, check the steps involved and decide if the numbers displayed make sense.
Progression is designed to be fluid so as to ensure children consolidate where necessary and move on when ready. Methods are not confined to
any particular year group, however it is a National Curriculum expectation that children will be ready to start on formal column methods in
year 3.
ADDITION
To add successfully, children need to be able to:
 recall all addition pairs to 9 + 9 and complements in 10
 add mentally a series of one-digit numbers, such as 5 + 8 + 4
 add multiples of 10 (such as 60 + 70) or of 100 (such as 600 + 700) using the related basic addition fact, 6 + 7 and their knowledge of
place value
 partition two-digit and three-digit numbers into multiples of 100, 10 and 1
It is important that as children learn and use an effective method of calculation for addition, they continue to secure and practise mental
methods for this operation.
Addition
Stage 1
Stage 2
3+2=5
Drawing and Practical
methods using
equipment.
Number lines and
Hundred Squares.
Pupils will use printed
number lines to record
jumps, for example for
3+2, before recording
on blank number lines.
At later stage 2,
Children may jump in
steps of 10 initially,
rather than the whole
multiple of 10.
48 + 36
+
=
23 + 8 =
+7
+1
23
30
31
57 + 26
+10
57
+10
67
+6
77
83
Jottings to support
mental methods.
Eg. Partitioning
46 + 63 = 109
Stage 3
100
Vertical methods
(expanded)
Stage 4
+
8
+
5
1
1 3
1 4
9
3
9
2
0
2
= 109
Formal written column
addition
Stage 5
6 4 7
+
3 9 4
1 0 4 1
1
1
SUBTRACTION
To subtract successfully, children need to be able to:
 recall all addition and subtraction facts to 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 one hundred, ten and one in different ways (e.g. partition 74 into 70 + 4 or
60 + 14).
It is important that as children learn and use an effective method of calculation for subtraction, they continue to secure and practise mental
methods for this operation.
Subtraction
Drawing and Practical methods
using equipment
Stage 1
5–3=2
Either by moving the objects or (on paper) crossing them out.
Counting backwards using
number lines or hundred
squares
19 – 4 = 15
-1 -1 -1 -1
Stage 2
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Stage 3
Stage 4
Number lines or 100 squares
Using number lines counting
back in tens and ones, then
more efficient, larger jumps.
Number lines
Counting on from the smallest
number to the largest. This is
especially good with small
gaps between numbers or those
close to a ten.
35 – 25 = 10
-5
-10
-10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
33 - 28
+5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
Stage 5
Stage 6
The expanded layout
The number line method may
be developed into a vertical
method by finding what to add
to make the next multiple of 1,
10, 100 etc. Initially the
number line and then the
vertical method will be
recorded side by side.
Formal column methods
More able can be challenged
with larger numbers and
decimals
36
-
12
8
10
6
24
20
30
36
MULTIPLICATION
To multiply successfully, children need to be able to:
 recall all multiplication facts to 10 × 10
 partition number into multiples of one hundred, ten and one
 work out products such as 70 × 5, 70 × 50, 700 × 5 or 700 × 50 using the related fact 7 × 5 and their knowledge of place value
 add two or more single-digit numbers mentally
 add multiples of 10 (such as 60 + 70) or of 100 (such as 600 + 700) using the related addition fact, 6 + 7 and their knowledge of place
value
It is important that as children learn and use an effective method of calculation for multiplication, they continue to secure and practise mental
methods for this operation.
Multiplication
Stage 1
solve one-step problems
involving multiplication,
by using concrete objects,
pictorial representations
and arrays with the
support of the teacher.
Arrays
There are three football players. How many legs altogether?
Repeated addition.
4 + 4 + 4 = 12
3 + 3 + 3 + 3 = 12
3x4 =12
Stage 2
Multiplication on a
printed/
6 x 5 = 30
+5
blank number line
+5
+5
+5
+5
+5
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
14 x 3 =
Stage 3
10 x 3
4x3
0
30
Grid Method
23 x 9 =
x
9
20 1 8 0
3
1 8
Stage 4
180 + 18 = 198
33
36
39
42
short multiplication OR
TU x TU using grid
method.
Stage 5
Long Multiplication
Stage 6
DIVISION
To carry out written methods of division successfully, children need to be able to
 understand division as grouping and sharing
 understand division as repeated subtraction
 count in multiples
 have knowledge of multiplication tables
 estimate how many times one number divides into another eg how many sixes there are in forty seven, or how many twenty threes there
are in ninety two
 multiply a two-digit number by a single-digit number mentally
 understand division and multiplication as inverse operations
It is important that as children learn and use an effective method of calculation for division, they continue to secure and practise mental methods
for this operation.
Division
Stage 1
Equal groups and
sharing
Children will
understand sharing out
items in play and
problem solving.
Sharing equally.
6 sweets are shared
between 3 children.
How many do they get
each?
6÷2=3
Stage 2
Grouping or repeated
subtraction (by
removing the objects in
groups of the same
amount)
Stage 3
Division on a number
line. Children use the
number line method so
they are able to
recognise the
relationship between
division and
multiplication.
Moving on to
calculations with a
remainder
12÷ 4= 3
9÷3= 3
-3
0
-3
3
-3
6
9
Using known facts to
arrive at an answer
97 ÷ 9 =
We know that 10 x 9 = 90 with a remainder of 7
Stage 4
So 97÷ 9 = 10 r7
Division by chunking –
using knowledge of
tables
6
-
1
1
9
2
7
6
1
1
6
0 (2 0 x 6)
6
0 (1 0 X 6)
6
2 ( 2 X 6)
4
3
2
r
Stage 5
-
4
Formal written
methods short division
and long division
Stage 6
Addition and subtraction of fractions (KS2)
Stage 1
add and subtract fractions with the same
denominator within one whole
Stage 2
add and subtract fractions with the same
denominator
Stage 3
add and subtract fractions with the same
denominator and denominators that are
multiples of the same number
Eg:
5/7 + 1/7 = 6/7
6/8 – 2/8 = 4/8
Eg:
4/7 + 5/7 = 9/7 (1 and 2/7)
7/4 – 3/4 = 4/4 (1)
Eg:
3/6 + 4/12 = 10/12
Addition
add, more, and, plus, make, sum, total, altogether, score, double, near
double,
one more, two more, ten more one hundred more
how many more to make _ ?
how many more is _ than _ ?
Vocabulary
Subtraction
take (away), leave
-, subtract, subtraction, take (away), minus, leave, how many are left/left over?
how many are left/left over?
how many have gone?
how many fewer is _ than _ ?
difference between
one less, two less, ten less, one hundred less
how much less is _?
Both
is the same as
=, equals, sign, is the same as
tens boundary
number bonds
compliment to 100
inverses
Multiplication
lots of, groups of, times, multiply, multiplied by, multiple of, once, twice,
three times, ten times,
times as (big, long, wide and so on)
repeated addition
array
row, column
double,
multiple of, product
once, twice, three times ten times
times as (big, long, wide, and so on)
squared
square root
Both
inverse
lots of
Division
halve
share, share equally
one each, two each, three each
group in pairs, threes, tens
equal groups of
divide, divided by, divided into
left, left over
lots of,
remainder
divisible by
fraction
parts of
quarter
factors