Maths Morning 2018 This presentation is intended to explain the mental and written calculation process to parents, drawing on the mental skills and strategies children use and the recording used to support their thinking. It will enable parents to help their children. It is based on the LEA recommendations for Pencil and Paper procedures published November 2002 that is available on this website. It covers Y1-9. There is associated guidance, including a booklet for parents and ‘Homework Helps’ to support this work. It is vital that schools have agreed their policy on recording calculation in order to establish continuity and progression. Title slide Explain that you hope the presentation will enable parents to find out about the mathematics their children are doing, particularly the way they calculate and record calculations and also enable them to help their children at home. Include a ‘fun’ mental/oral starter here so that the parents get to ‘do some maths’ straightaway. Try one where they can work with a partner and talk, perhaps using mini-whiteboards.

Using three darts can you make 50? 20 22 12 33 25 18

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 How do you add and subtract? Ask the parents to decide how they would tackle each calculation. Use individual whiteboards and pens. Tell them they can work with a partner and encourage talk. Take feedback. All the calculations can be tackled mentally using a variety of strategies apart from 5735 + 3657 (for most people), which lends itself to a written method. Outline some of the strategies that may be used. Emphasize looking at the numbers and then deciding, not just automatically doing ‘sums’. If parents are puzzled by the last example get them to think about it in the context of money and ‘counting on’. Tell the parents have just been using the problem-solving approach to calculation – making decisions after looking at the numbers. Possible strategies (there are more!): 61 + 45 7800 – 5600 count on 40 then 5 add 50 to 78, then add 6, replace zeros 5735 + 3657 5735 + 3990 vertical algorithm add 4000, then adjust 83 – 68 5002 – 4996 count on 2, to 70 then add 13 count on 4, then 2 538 - 295 267 + 267 subtract 300, then adjust double 26, adjust place value, then add 14 2.5 + 2.7 5.1 - 2.78 double 2.5, then add 0.2 ‘money’ – count on from 2.78 to 5.10

Addition 76 + 47 = 86 +10 96 +10 106 +10 116 +10 123 +7 76 116 76 + 40 123 + 7 Now say you are going to demonstrate the recording methods used for each of the operations in turn. (animated slide) Addition The number line models the counting on that children may be doing in their heads. It supports their thinking. You will see this type of recording in children’s books from KS1 onwards. The second example illustrates moving towards a more efficient method. Something that the parents may have done in their calculations earlier. To fit in with your school’s policy you need to chose one of the next 2 slides and delete the other: Addition using the vertical expansion Addition using the horizontal expansion

Addition Moving on to… 67 + 56 = 60 + 50 = 110 7 + 6 = 11 121

Addition 358 + 473 = 358 + 473 358 + 473 831 1 700 120 (Animated slide) Addition using the vertical expansion Stress the importance of the correct vocabulary..eight add three, fifty add seventy…3 hundred add 4 hundred Here the least significant digits are added first. If your policy uses the intermediate step of adding the most significant digits first you will need to amend this slide. 11 831

Subtraction – KS1 Imran has 43 conkers; he gives 24 away to his friends. How many does he have left? 43 – 24 = 43 -1 19 20 -3 23 -10 33 -10 (Animated slide) This slide demonstrates to parents the process of using an empty number line to support children’s thinking in subtraction. It might well be how they (the parents) would work this mentally using an imaginary number line. Children will experience this type of recording from Y2. The jumps are below the line to show ‘counting back’. 19 conkers

Subtraction Sam has saved 93p, Amy has 55p. How much more money does Sam have than Amy? 93 – 55 = 60 +5 90 +30 93 +3 55 (Animated slide) Another subtraction calculation, this time involving difference. Here the child has counted on from 55 to 93, recording the jumps on a number line. Having a visual image like this supports the child with what is going on in their head. The big jump of 30 may initially be made with three jumps of 10. 38p more

Subtraction 8.23 – 4.55 = 3.68 +0.23 +0.45 +3 The same method but using decimals. Counting on or complementary addition is used. This is one of the reasons that children work on complements, as mentioned earlier. Putting one number underneath the other would result in many children giving an answer of 4.12. 4.55 5.00 8.00 8.23

Subtraction A sports stadium holds 9010 spectators. 5643 people attend a football match. How many empty seats are there? + 57 +300 +3010 5643 5700 6000 9010 3010 300 57 3367 (animated slide) The same method but using large numbers. Counting on or complementary addition is used again. Some children may begin to record the jumps vertically without using a line. If you have time let the parents have a go. 3367 empty seats

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 How do you multiply and divide? As before ask the parents to decide how they would tackle each calculation. Use individual whiteboards and pens. Tell them they can work with a partner and encourage talk. Take feedback. All the calculations can be tackled mentally using a variety of strategies. Outline some of the strategies that may be used. Emphasize looking at the numbers and then deciding, not just automatically doing ‘sums’. Tell the parents they were using the problem-solving approach to calculation. Possible strategies (there are more!): 57 x 2 78 ÷ 2 Partition, double 50, double 7, recombine partition, halve 70, halve 8, recombine 43 x 50 742 ÷ 2 X100, then halve partition, halve 700, halve 42, recombine 36 x 25 700 ÷ 4 X100, then 4 halve, and then halve again 18 x 15 65.5  10 18x10, halve answer, then move digits one place to right, (NOT decimal point to left) Add 18x10 to 18x5 use this opportunity to explain how to x and ÷ by 10, 100 8 x 19 17 ÷ 5 8x20 then subtract 8 17 ÷ 10, then double 34 x 7 5.4 ÷ 6 Partition, 30x7, add 4x7 tables facts, 6x9=54

Multiplication 47 x 8 = x 40 7 8 320 56 376 37 x 46 = x 30 7 40 1200 280 1480 6 180 42 222 1702 Children are now taught to use the grid method for multiplication. The numbers are partitioned, multiplied and then recombined. If you have time let the parents have a go. Children have experienced great success with this method of recording. It has also helped enormously when they move into KS3 with algebra. If you have worked with your High School or other primaries on a recording policy it is important to mention this to parents. All High Schools and Upper Schools have been informed about the policy by KS3 consultants and are being encouraged to adopt it.

……… leading to algebra (a + b)2 = (a + b) x (a + b) x a b a a2 ab a2 + ab b ab b2 ab + b2 a2 + 2ab + b2 (animated slide) Remember these! The expansion of brackets. Here the grid method demonstrates this quite clearly, rather than ‘eyebrows’ and ‘smiley faces’. (a + b)2 = a2 + 2ab + b2

Arrays 3 x 3 = 9 4 x 5 = 20 5 x 15 = 75 7 x 5 = 35

47  8 8 47 375  43 43 375 Division (animated slide) 8 47 (animated slide) These are examples of the ‘gozinter’ method that show how it doesn’t really get you anywhere. Try them! 375  43 43 375

…or ‘chunking’ So we now teach a method that children can understand. It involves repeated subtraction. The opposite of multiplication which is repeated addition.

18 ÷ 3 = 6 We look carefully at the divisor and jump to the target number on a number line. Then count how many jumps. +3 +3 +3 +3 +3 +3 ____ 0 3 6 9 12 15 18

Moving on to… 78 ÷ 5 = 15 r 3 78 50 25 r3 5 x 10 5 x 5

Mastery speedy teacher intervention to prevent gaps challenge provided by going deeper not accelerating  focused, rigorous and thorough teaching more time on teaching topics – depth and practice

Make sure maths is fun! How can you help? Use school methods Talk about how you do maths Be positive Ask your child to explain Give praise and encouragement (Animated slide) Final slide and how parents can help at home. Encourage parents to talk to the teachers. LEA publications: Sums and things for parents Helping your child with maths Useful websites for parents: www.leics.gov.uk/education/ngfl/numeracy www.standards.dfes.gov.uk Make sure maths is fun!