Years 4, 5, 6
6 November 2012
1
I think of a number and add 6.
My answer is minus 7, what number did I start with?
Sums and
Things
for Parents
2
minus
13
Well done Lucie.
How did you think that through?
3
Maths – when do we use it?
4
The story so far ……….

Children’s recall of number facts
has become more accurate and faster.
Children are more aware of the strategies
they use to calculate.
 They use vocabulary correctly.
 They are more confident about maths
 Maths is more fun!
5
To succeed in maths in Key Stage 2
children need to be confident in:
•Knowing number bonds for all numbers up to 20, and
complements to 100.
•Partitioning numbers into thousands, hundreds, tens and units.
•Multiplication tables and multiplication and division facts up to
at least 10 x 10.
These all need regular practice, both at school and at home, even once
a child becomes confident in them.
•Understanding place value and when to use zero as a place-holder.
6
What can a numerate child do?
By the age of 11 they should :
 have a sense of the size of number and
where it fits into the number system
 know by heart addition and subtraction
facts to 20, multiplication and division
facts to 10x10, doubles and halves,
complements to 100, multiply and
divide by 10 and 100
 use what they know to figure out
answers mentally
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What can a numerate child do? (cont.)
 calculate accurately
and efficiently, both
mentally and on paper, using a range
of strategies
 recognise when it is appropriate to use a
calculator- and when it is not- and be
able to use one effectively
 explain their methods and reasoning
using correct mathematical terms
 judge whether their answers are
reasonable and have strategies for
checking them where necessary
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The aim
The aim is for children to do mathematics in
their heads, and if the numbers are too
large, to use pencil and paper to avoid
losing track. To do this children need to
learn quick and efficient methods,
including appropriate written methods.
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Learning written methods is not the ultimate aim.
Mathematics is foremost an activity of the
mind, and written calculations are an aid
to that mental activity.
 Maths teaching today aims to develop
children’s mental strategies and then
written methods that derive from and
support mental methods.
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We want children to
ask themselves:
Can I do this in my head?
Can I do this in my head using drawings
or jottings?
Do I need to use an expanded/compact
written method?
Do I need a calculator?
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How do you add and subtract?
61 + 45
7800 – 5600
5735 + 3657
5735 + 3990
83 – 68
5002 – 4996
538 - 295
267 + 267
2.5 + 2.7
5.1 - 2.78
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Addition vocabulary
o altogether
o more than
o count on
o plus
o add
o total
o and
+
13
Mistakes children make:
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…….and more:
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Addition
76 + 47 = 123
+ 10
+ 10
86
+ 10
96
+ 40
+ 10
106
+7
116
123
+7
116
123
16
Addition
358 + 473 = 831
358
358
+ 473
+ 473
11 8 + 3
120 50 + 70
700 300 + 400
831
831
1
1
It is really important in this method
that children understand they are
carrying 10 or 100 and don’t
say/think they are just carrying 1.
17
Your turn!
I have £257 in one bank account and
£468 in another. How much is this
altogether?
A sunflower measures 1.94m. By
Friday it has grown 38cm. How tall is
it now?
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By Year 5
19
And in Year 6 ...
Children should extend the carrying method to numbers
with any number of digits.
20
401.2
26.85
+ 0.71
428.76
21
Subtraction vocabulary
o
o
o
o
o
o
o
o
o
take away
minus
count back
less than
subtract
difference between
decrease
how many left
take from
22
Subtraction
Imran has 43 conkers; he gives 24 away to his
friends. How many does he have left?
43 – 24 =
19 20
-1
23
-3
33
-10
43
-10
19 conkers
23
Subtraction
Sam has saved 93p, Amy has 55p. How much
more money does Sam have than Amy?
93 – 55 =
+5
55
+30
60
+3
90
93
38p more
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Subtraction
8.23 – 4.55 = 3.68
+3
+0.45
4.55
5.00
+0.23
8.00
8.23
To work out calculations such as this, it’s really important that
children know pairs of numbers that make 100.
25
Subtraction
A sports stadium holds 9010 spectators. 5643 people
attend a football match. How many empty seats are
there?
+ 57
5643
+3010
+300
5700
3367 empty seats
6000
9010
5643
5700
57
6000
+300
9010
+3010
3367
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Subtraction using partitioning
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Decomposition
Subtraction using decomposition
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Children should:
•be able to subtract numbers with different numbers of digits;
•using this method, children should also begin to find the difference
between two three-digit sums of money, with or without ‘adjustment’
from the pence to the pounds;
•know that decimal points should line up under each other.
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Your turn!
 There are 83 children on the
playground. 37 go in for their lunch.
How many are left outside?
 There are 7000 spaces in the car park.
3756 cars go in. How many spaces are
empty?
 6.35 – 3.49 =
30
How do you multiply and divide?
57 x 2
78 ÷ 2
43 x 50
742 ÷ 2
36 x 25
700 ÷ 4
18 x 15
65.5  10
8 x 19
17 ÷ 5
34 x 7
5.4 ÷ 6
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Multiplication vocabulary
x
o groups of
o lots of
o times table
o times
o multiplied by
o multiply
o double
32
Mistakes children make:
76
x 8
5648
67
x 54
268
335
101 r 5
603
7 847
33
Multiplication – Grid method
47 x 8 =
x 40
8 320
7
56
376
37 x 46 =
x 30
7
40 1200 280
6 180 42
1480
222
1702
34
TU x TU
(Long multiplication – multiplication by more than a
single digit)
72 x 38
Children will approximate first
72 x 38 is approximately 70 x 40 = 2800
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Using similar methods, they will be able to multiply decimals with one
decimal place by a single digit number, approximating first. They
should know that the decimal points line up under each other.
e.g. 4.9 x 3
Children will approximate first
4.9 x 3 is approximately 5 x 3 = 15
36
HTU x TU
(Long multiplication – multiplication by more than a single digit)
372 x 24
Children will approximate first
372 x 24 is approximately 400 x 25 = 10000
37
Using similar methods, they will be able to multiply decimals with up to two
decimal places by a single digit number and then two digit numbers,
approximating first. They should know that the decimal points line up under
each other.
For example:
4.92 x 3
Children will approximate first
4.92 x 3 is approximately 5 x 3 = 15
38
Your turn!
How many legs do
36 spiders have?
82 x 43 =
34 x 3.72 =
39
Division vocabulary
share
o share equally
o divide
o divided by
o groups
o halve
o half
o
40
Division
In Year 3 ...
Division using an empty number line
How many groups of 5 are there in 25?
25 ÷ 5 = 5
5
0
5
5
5
10
5
15
5
20
25
41
Division in Year 4
42
Chunking - We use repeated
multiplication with
numbers that we are
confident with such as
10, 5 and 2.
43
Integers are whole numbers (positive or negative), not fractions or percentages.
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Your turn!
Try chunking with this division calculation.
144 ÷ 3
48
3 144
- 30
114
- 30
84
- 30
54
- 30
24
-24
0
x10
x10
x10
x10
x8
48
45
Children need to be able to decide what to do after division
and round up or down accordingly. They should make
sensible decisions about rounding up or down after division.
This is needed when solving word problems eg
Yasmin needed 56 plastic cups for her party.
They came in packs of 6. How many packs did
she need?
46
In Year 5 children will continue to use written methods to
solve short division TU ÷ U.
Children can start to subtract larger multiples of the divisor,
e.g. 30x
Short division HTU ÷ U
47
Progression on to long division
972 ÷ 36
27
36) 972
- 720
252
-180
72
- 72
0
20 x
5x
2x
Answer
27
48
Any remainders should be shown
as fractions, i.e. if the children
were dividing 32 by 10, the answer
should be shown as 3 2/10 which
could then be written as 3 1/5 in its
lowest terms.
49
Extend to decimals with up to two decimal places. Children should
know that decimal points line up under each other.
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Written methods are to be used when calculations are too difficult to be
done mentally.
These are some examples of calculations children should be able to do by
the time of their KS2 SATs.
How many sevens are there in six hundred and thirty?
KS2 2008 Mental test level 4
When a number is divided by seven, the answer is three remainder four. What is
the number?
KS2 2007 Mental test level 5
Calculate 848 ÷ 16.
KS2 2006 Paper A level 5
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How you can support your child at home
Look for and talk about
numbers in the environment
Play games
Shopping and giving change.
Number bonds for 10, 20, 100
Doubles/Halves
Times tables
Multiplication facts
Division facts
Practise adding and subtracting
mentally
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Useful websites for practising maths
http://www.mathschamps.co.uk/index.php
http://teachmykids.co.uk/free_resources/
http://www.bbc.co.uk/bitesize/ks2/maths/
http://www.mad4maths.com/kids/
http://resources.woodlandsjunior.kent.sch.uk/maths/timestable/interactive.htm
http://www.bbc.co.uk/schools/websites/4_11/site/numeracy.shtml
http://www.funbrain.com/brain/MathBrain/MathBrain.html
http://www.channel4learning.com/index.html
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