Slide 1Years 4, 5, 6
I think of a number and add 6.
My answer is minus 7, what number did I start with?
Sums and Things
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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.
Maths is more fun!
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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.
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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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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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61 + 45 7800 – 5600
5735 + 3657 5735 + 3990
83 – 68 5002 – 4996
538 - 295 267 + 267
2.5 + 2.7 5.1 - 2.78
831
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.
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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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with any number of digits.
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401.2
26.85
+ 0.71
428.76
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Subtraction
Imran has 43 conkers; he gives 24 away to his friends. How many does he have left?
43 – 24 =
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Subtraction
Sam has saved 93p, Amy has 55p. How much more money does Sam have than Amy?
93 – 55 =
4.55
+0.45
5.00
8.00
+3
+0.23
8.23
3.68
To work out calculations such as this, it’s really important that children know pairs of numbers that make 100.
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Subtraction
A sports stadium holds 9010 spectators. 5643 people attend a football match. How many empty seats are there?
5700
9010
6000
5643
+ 57
+300
+3010
5643
5700
6000
9010
57
+300
+3010
3367
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.
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 =
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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32
8 320 56 376
72 x 38
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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
37
372 x 24
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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:
How many legs do 36 spiders have?
82 x 43 =
34 x 3.72 =
How many groups of 5 are there in 25?
25 ÷ 5 = 5
0 5 10 15 20 25
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Integers are whole numbers (positive or negative), not fractions or percentages.
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144 ÷ 3
144
30
114
30
84
30
54
30
24
24
0
3
x10
x10
x10
x10
x8
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48
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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?
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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
972 ÷ 36
5x
2x
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Answer
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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.
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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.
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Look for and talk about numbers in the environment
Play games
Doubles/Halves
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