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Years 4, 5, 6 6 November 2012 1

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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

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minus 13 Well done Lucie. How did you think that through? 3

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4 Maths when do we use it?

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The story so far . Childrens 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

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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. 6

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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 7

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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 8

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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. 9

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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 childrens mental strategies and then written methods that derive from and support mental methods. 10

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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? 11

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How do you add and subtract? 61 + 457800 5600 5735 + 36575735 + 3990 83 685002 4996 538 - 295267 + 267 2.5 + 2.75.1 - 2.78 12

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Addition vocabulary + o altogether o more than o count on o plus o add o total o and 13

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Mistakes children make: 14

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.and more: 15

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Addition 76 + 47 = + 10 + 7 8696106116123 116123 + 40 + 7 16

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358 + 473 831 358 + 473 831 11 11 8 + 3 120 50 + 70 700 300 + 400 Addition 358 + 473 =831 It is really important in this method that children understand they are carrying 10 or 100 and dont say/think they are just carrying 1. 17

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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? 18

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By Year 5 19

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And in Year 6... Children should extend the carrying method to numbers with any number of digits. 20

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401.2 26.85 + 0.71 428.76 21

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Subtraction vocabulary - o take away o minus o count back o less than o subtract o difference between o decrease o how many left o take from 22

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Subtraction Imran has 43 conkers; he gives 24 away to his friends. How many does he have left? 43 24 = 4333 -10 23 -10 20 -3 19 19 conkers 23

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Subtraction Sam has saved 93p, Amy has 55p. How much more money does Sam have than Amy? 93 55 = 55 60 +5 93 +3 90 +30 38p more 24

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Subtraction 8.23 4.55 = 4.55 +0.45 5.008.00 +3 +0.23 8.23 3.68 To work out calculations such as this, its really important that children know pairs of numbers that make 100. 25

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Subtraction A sports stadium holds 9010 spectators. 5643 people attend a football match. How many empty seats are there? 570090106000 5643 + 57+300 +3010 5643 5700 6000 9010 57 +300 +3010 3367 3367 empty seats 26

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27 Subtraction using partitioning

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28 Decomposition Subtraction using decomposition

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29 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

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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 31

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32 Multiplication vocabulary o groups of o lots of o times table o times o multiplied by o multiply o double x

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76 x 8 5648 Mistakes children make : 67 x 54 268 335 603 101 r 5 7 847 33

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Multiplication Grid method 47 x 8 =x 407 8 32056376 37 x 46 = x 30 7 40 1200 280 1480 6 180 42 222 1702 34

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35 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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36 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

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37 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

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38 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

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How many legs do 36 spiders have? 82 x 43 = 34 x 3.72 = Your turn! 39

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40 Division vocabulary o share o share equally o divide o divided by o groups o halve o half

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Division In Year 3... Division using an empty number line How many groups of 5 are there in 25? 25 5 = 5 5 5 5 5 5 0 5 10 15 20 25 41

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Division in Year 4 42

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Chunking - We use repeated multiplication with numbers that we are confident with such as 10, 5 and 2. 43

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Integers are whole numbers (positive or negative), not fractions or percentages. 44

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Your turn! Try chunking with this division calculation. 144 3 144 - 30 114 - 30 84 - 30 54 - 30 24 -24 0 3 x10 x8 48 45

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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? 46

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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 47

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Progression on to long division 972 36 36)972 - 720 252 -180 72 - 72 0 20 x 5x 2x 27 Answer 48

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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. 49

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Extend to decimals with up to two decimal places. Children should know that decimal points line up under each other. 50

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51 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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52 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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53 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.woodlands- junior.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