5 Children are more aware of the strategies they use to calculate. 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 mathsMaths is more fun!
6 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.
7 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 systemknow 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 100use what they know to figure out answers mentally
8 What can a numerate child do? (cont.) calculate accurately and efficiently, both mentally and on paper, using a range of strategiesrecognise when it is appropriate to use a calculator- and when it is not- and be able to use one effectivelyexplain their methods and reasoning using correct mathematical termsjudge whether their answers are reasonable and have strategies for checking them where necessary
9 The aimThe 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.
10 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.
11 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?
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.
30 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 cars go in. How many spaces are empty?6.35 – 3.49 =
31 How do you multiply and divide? 57 x ÷ 243 x ÷ 236 x ÷ 418 x 108 x ÷ 534 x ÷ 6
33 Mistakes children make: 76x 8564867x 54268335603101 r 57 847
34 Multiplication – Grid method 47 x 8 = x37 x 46 =x1702
35 TU x TU(Long multiplication – multiplication by more than a single digit)72 x 38Children will approximate first72 x 38 is approximately 70 x 40 = 2800
36 Using similar methods, they will be able to multiply decimals with one decimal place by a single digit number, approximating first. Theyshould know that the decimal points line up under each other.e.g x 3Children will approximate first4.9 x 3 is approximately 5 x 3 = 15
37 HTU x TU(Long multiplication – multiplication by more than a single digit)372 x 24Children will approximate first372 x 24 is approximately 400 x 25 = 10000
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 3Children will approximate first4.92 x 3 is approximately 5 x 3 = 15
39 Your turn!How many legs do 36 spiders have?82 x 43 =34 x 3.72 =
40 Division vocabulary share equally divide divided by groups halve half
41 Division In Year 3 ... Division using an empty number line How many groups of 5 are there in 25?25 ÷ 5 = 5
43 Chunking - We use repeated multiplication withnumbers that we areconfident with such as10, 5 and 2.
44 Integers are whole numbers (positive or negative), not fractions or percentages.
45 Your turn! Try chunking with this division calculation. 48 3 144 30 114845424144 ÷ 3x10x848
46 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 egYasmin needed 56 plastic cups for her party. They came in packs of 6. How many packs did she need?
47 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. 30xShort division HTU ÷ U
48 Progression on to long division 972 ÷ 3627972- 720252-18072- 7220 x5x2x27Answer
49 Any remainders should be shown as fractions, i. e 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.
50 Extend to decimals with up to two decimal places Extend to decimals with up to two decimal places. Children should know that decimal points line up under each other.
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?KS Mental test level 4When a number is divided by seven, the answer is three remainder four. What is the number?KS Mental test level 5Calculate 848 ÷ 16.KS Paper A level 5
52 How you can support your child at home Look for and talk about numbers in the environmentPlay gamesShopping and giving change.Number bonds for 10, 20, 100Doubles/HalvesTimes tablesMultiplication factsDivision factsPractise adding and subtracting mentally