Transcript Friendship - Westfield School

Westfield Middle School
Visual Calculation Policy
Choosing a method
Addition methods
Subtraction methods
Multiplication methods
Division methods
About this policy
Choosing a method
Can I use a mental strategy?
Can drawings or objects help
me?
Should I use a written
method?
Use this technique
when answering
word problems
Sum
Total
Increase
Add
Addition
More
Plus
Altogether
Count on
Addition – Counting
Divisor
4 + 3
=
7
1. Addition – Counting on
Use numbered number lines to
add, by counting on in ones.
Start with the larger number and
count on.
+1
+1 +1
0 1 2 3 4 5 6 7 8 9 10
6+3=9
2. Addition – Leaping Further
+ 10
63
Use empty number
lines and hundred
squares to build
confidence when
adding 2 digit numbers.
+6
73
79
63 + 16 = 79
3 . Addition – Partitioning
27 + 12 = 39
20
7
+ 10
2
30 + 9 = 39
4. Addition – Expanded Column
Add the
units first in
preparation
for the
compact
method
T U
+ 23
17
10
30
40
H T U
+ 236
73
9
100
200
309
5 . Addition – Compact Column
Move from
expanded
addition to the
compact column
method, adding
units first, and
‘carrying’
numbers
underneath the
calculation.
Th H T U
+ 3517
396
3913
11
Remember this
number is 500 not 5.
Start with the units
Carry any numbers
underneath.
6. Addition – Compact Column
Including decimals
+ 23.59
7.55
31.14
1 1 1
The decimal point
should be aligned in
the same way as
the other place value
columns, and must be
in the same
column in the answer
Take
away
Difference
between
Minus
Subtraction
Less
Count back
Fewer
Subtract
Subtraction – Take away
=
Divisor
9 - 3
=
6
1. Subtraction – Finding the
difference
.
7 is 3 more than 4
2. Subtraction – Counting back
Model subtraction using
hundred squares,
numbered number lines
and practically.
0 1 2 3 4 5 6 7 8 9 10
7–3=4
3. Subtraction – Leaping Back
-1
-1
-10
-1
24 25 26 27
37
47
Partition the second
number and subtract
the tens first
47 – 23 = 24
3. Subtraction – Counting On
+3
+10
89
Start at the
smaller number and
count on in tens
first, then count on
in units to find the
rest of the difference
99
Continue to reinforce
counting on as a strategy
for close together
numbers and also for
numbers that are nearly
multiples of 10, 100,
1000 or £s
102
102 – 89 = 13
4. Subtraction – Expanded column
100
1
200+30+ 8
100+40+ 6
0+90+ 2
=
Once pupils are secure
with the understanding of‘
‘exchanging’, they can use
the partitioned column
method to subtract any 2
and 3-digit numbers.
Use vocabulary
‘steal’ or ‘take’
not ‘borrow’.
238 – 146 = 92
5. Subtraction – Compact Column
Children who are
still not secure
with number facts
and place value will
need to remain on
the partitioned
column method
until ready for the
compact method.
Th H T U
6 1
2754
-1562
1192
6 . Subtraction – Compact Column
with decimals
0 19 1
3 1
105.409
- 39.080
66.329
Empty decimal
places can be
filled with zero to
show the
place value in each
column.
Multiple
Times
Multiplication
Groups
of
Repeated
addition
Product
Lots of
Multiply
Multiplication - Repeated Addition
8
+
8
+
8
= 24
Spiders have 8 legs. How many
legs do 3 spiders have
altogether?
1. Multiplication - Repeated
Addition
There are 3 sweets in a bag and 3
bags of sweets. How many sweets
altogether?
2. Multiplication - Arrays
3 X 7 = 21 or 7 X 3 = 21
3 .Multiplication – The Grid Method
4
300 1200
20
80
7
28
1308
Make sure you do
not add the 4 in
the total
Partition the
number into the
grid
4. Multiplication – Expanded Column
Method
327
X 4
28
80
1200
1308
Short
Multiplication
5. Multiplication – The Grid Method
10
8
Long
Multiplication
10 100 80
180
3
+ 54
30
24
234
18 X 13 = 234
5. Multiplication – Expanded
Column Method
2
X1
2
8
6
2 0
6
4
4
0
0
0
3 6 4
1
Long
Multiplication
6. Multiplication – Decimals
3 . 1 9
x 8 .
2 5 . 5 2
1
7
Include
multiplying more
complex numbers
and decimals.
Remember place
value, make sure
numbers are in the
correct column.
Divisor
Divide
Share
Quotient
Division
Factor
Remainder
Equal
groups of
Halve
1 . Division –Sharing
15 ÷ 3 = 5 15 ÷ 5 = 3
2.Division
Division- Arrays
- Arrays
12 ÷ 4 = 3 12 ÷ 3 = 4
3. Division – On a number line
0 1 2 3 4 5 6 7 8 9 10 11 12
12 ÷ 3 as ‘How
many groups of 3
are in 12?’
This helps to
see the link
between
division and
grouping
4 / 5. Division - Short Division
Remind children
of correct place
value, that 96 is
equal to 90 and
6, but in short
division, pose:
How many 3’s in
9? = 3
1 0 6 1 r4
3
5 5309
Start with one
digit numbers
without
remainders
5/6 . Division – Chunking
2 2
36
7 9 2
- 3 6 0
3 1
4 3 2
- 3 6 0
0 7 2
- 0 7 2
0 0
Circle the groups of 36
you have ‘chunked’ off
the total.
3 6 x 10 = 3 6 0
3 6 x 10 = 3 6 0
36x2=72
Keep
chunking
until there
is less than
36 left
Calculation Policy
This policy aims to clearly show strategies for calculating whilst meeting the
expectations set out in the New Curriculum 2014. The policy is for use of all pupils,
parents and staff in the Westfield community.
The strategies have been organised to show the progression from early
calculation methods such as counting through to written methods involving
decimals. The age expectations have been added to the calculations as a guide of
where children should be working however decisions about when to progress should
be based on the security of pupils understanding and their readiness to progress to
the next stage. Pupils who grasp concepts rapidly should be challenged through
being offered rich and sophisticated problems before any acceleration through new
content.
It is important that any type of calculation is given a real life context or problem
solving approach to help build children's understanding of the purpose of
calculation, and to help them recognise when to use certain operations and methods
when faced with problems. This must be a priority within calculation lessons.
The Maths department will be offering Maths support for parents. Please contact
the office for more information.
Westfield Middle School
Visual Calculation Policy