Welcome! Maths Workshop 2017   St. Mary's C. of E. Primary School   ‘Through God’s love, we strive to be the best we can be’.

Aims of the Workshop To raise standards in maths by working closely with parents. To provide parents with a clear outline of the key features of maths teaching at St Mary’s School. To help parents to support their child’s maths development at home. We’re very good at developing the well rounded child, our children have lots of opportunities to develop socially, work independently and creatively, but what we now need to do is raise the standards in maths throughout the school. This is a key school improvement priority, identified by parents, teachers, the county, the school and we want to work with you to succeed. The only way we can work with you is to share; us giving you a clear outline of what we’re doing in school and you sharing your needs at home. So tonight our 2 aims there show we want to show you what we are doing and also provide you with materials to take away and use at home.

Maths in the past! In the 1960s, a lot of time was given to practising methods. Research shows that despite this some children found certain methods difficult, forgot them rather quickly or made persistent errors. Sometimes, the result was a dislike of the subject, which could persist into adult life. With the 1970s bringing the introduction of calculators, people began to debate what calculating skills are actually needed in life. So what was maths like for you at school. Maybe you loved maths. Maybe you hated it. Well if you’re like most people, when somebody mentions maths to adults, they immediately think back to the time they were at school and if we just briefly look at what maths was like 30/40 years ago, it was very much about teaching methods. Certainly when I was at school, I remember spending a lot of time completing row of sums, I used to queue up at the teachers desk and either look forward to getting lots of red ticks when I got the addition but the moment we went onto subtraction and decomposition, my book looked a bit like Paul’s. And when we went onto long multiplication and division, I remember praying that I was sitting next to someone who knew what they were doing. If your experience was not like mine, then I’m happy for you but research shows that despite endless practising, many children found methods difficult and didn’t really understand what they were doing. Consequently many adults now have a dislike for the subject and this is passed on to their children. How many people do you know today who say. Oh no not maths. I was terrible at maths at school. I always found it difficult. Well interestingly in the 1970s wit the introduction of calcuators, the debate about the usefulness of rows of sums was discussed and people started to think about what calculating skills children need in life. Even today people still debate what children need to learn in maths. You’ll be pleased to know that after years of debate, researchers and educationalist have now come to a conclusion about what learning in maths should be about. This is what they say.

Concrete – Pictorial - Abstract Start with concrete – resources that the children can handle and count Move on to pictoral – using pictures to represent items, instead of concrete Progress to abstract – using mental and written methods to replace pictures The CPA sequence is followed in all year groups to ensure full understanding of concepts taught. Two points are clear about what mathematical skills children need in life. Educationalists say that children today need to learn 2 key skills. The ability to calculate mentally and the ability to estimate. Mental calculation skills are vital. Just have a think how often you use mental maths in your own lives. Shopping- working out change. Working out how many packets of biscuits or crisps you need to buy for a children’s birthday party. Working out how long it is before you need to leave to pick up children from school. Working out how many days left to do all your Christmas shopping? A lot of maths in life is done in your head. But within that I hope that you’re also estimating. When working out how long you have until you need to come to school, you round to the nearest hour or half hour. So in school, we encourage children to estimate. If they are faced with a problem. I have 18 sweets in 1 bag and 33 in another bag. How many in total? Children in maths lessons today would be encouraged to round to the nearest 10 in their head and work out 20 add 30 to approximate an answer. Alongside the ability to estimate, Educationalists today also say that children need to develop other key skills in maths. Childrern need to learn maths in a context. Therefore in school we aren’t just giving children lists of sums to complete. We are asking them to really think. Research shows that many children who can tell you what 7 x 7 = 49 cannot answer a question in a real life context. E.g. There are 7 fields, each has 7 sheep in them. How many sheep are there altoghether. Children need to be able to explain. What they are doing. You may well say well what about the written calculations. Well these are still taught, but there is a balance. At St Luke’s we certainly would expect children by the time they leave school to know, understand and use a written strategy for more complex maths calculations but emphasis early on is placed on mental calculations. If we look at the next slide, this will hopefully illustrate the point in hand.

Good practice in Maths today! Mental calculation skills are vital. Children need the ability to estimate. e.g. If I have 18 sweets in one bag and 33 sweets in another bag, how many do I have altogether. Children can estimate by adding 20 and 30 and know that roughly the answer should be around 50. Two points are clear about what mathematical skills children need in life. Educationalists say that children today need to learn 2 key skills. The ability to calculate mentally and the ability to estimate. Mental calculation skills are vital. Just have a think how often you use mental maths in your own lives. Shopping- working out change. Working out how many packets of biscuits or crisps you need to buy for a children’s birthday party. Working out how long it is before you need to leave to pick up children from school. Working out how many days left to do all your Christmas shopping? A lot of maths in life is done in your head. But within that I hope that you’re also estimating. When working out how long you have until you need to come to school, you round to the nearest hour or half hour. So in school, we encourage children to estimate. If they are faced with a problem. I have 18 sweets in 1 bag and 33 in another bag. How many in total? Children in maths lessons today would be encouraged to round to the nearest 10 in their head and work out 20 add 30 to approximate an answer. Alongside the ability to estimate, Educationalists today also say that children need to develop other key skills in maths. Childrern need to learn maths in a context. Therefore in school we aren’t just giving children lists of sums to complete. We are asking them to really think. Research shows that many children who can tell you what 7 x 7 = 49 cannot answer a question in a real life context. E.g. There are 7 fields, each has 7 sheep in them. How many sheep are there altoghether. Children need to be able to explain. What they are doing. You may well say well what about the written calculations. Well these are still taught, but there is a balance. At St Luke’s we certainly would expect children by the time they leave school to know, understand and use a written strategy for more complex maths calculations but emphasis early on is placed on mental calculations. If we look at the next slide, this will hopefully illustrate the point in hand.

Good practice in Maths today! All children need to learn maths in a real life context. As well as knowing 7x7=49. Children need to be able to do the following: There are 7 fields, each field has 7 sheep in them. How many sheep are there in total? Children need to be able to explain how they have calculated something using a method that suits them. If they can’t explain it, they don’t fully understand it. Written calculations, are taught but when children are ready. Two points are clear about what mathematical skills children need in life. Educationalists say that children today need to learn 2 key skills. The ability to calculate mentally and the ability to estimate. Mental calculation skills are vital. Just have a think how often you use mental maths in your own lives. Shopping- working out change. Working out how many packets of biscuits or crisps you need to buy for a children’s birthday party. Working out how long it is before you need to leave to pick up children from school. Working out how many days left to do all your Christmas shopping? A lot of maths in life is done in your head. But within that I hope that you’re also estimating. When working out how long you have until you need to come to school, you round to the nearest hour or half hour. So in school, we encourage children to estimate. If they are faced with a problem. I have 18 sweets in 1 bag and 33 in another bag. How many in total? Children in maths lessons today would be encouraged to round to the nearest 10 in their head and work out 20 add 30 to approximate an answer. Alongside the ability to estimate, Educationalists today also say that children need to develop other key skills in maths. Childrern need to learn maths in a context. Therefore in school we aren’t just giving children lists of sums to complete. We are asking them to really think. Research shows that many children who can tell you what 7 x 7 = 49 cannot answer a question in a real life context. E.g. There are 7 fields, each has 7 sheep in them. How many sheep are there altoghether. Children need to be able to explain. What they are doing. You may well say well what about the written calculations. Well these are still taught, but there is a balance. Research shows that teaching children written procedures at too early a stage in their mathematical development can have an adverse effect upon their ability to operate mentally. In line with many other countries, mental calculation skills are being taught and focussed upon, and the introduction of written methods are delayed until children are ready. At St Luke’s we certainly would expect children by the time they leave school to know, understand and use a written strategy for more complex maths calculations but emphasis early on is placed on mental calculations. If we look at the next slide, this will hopefully illustrate the point in hand.

Mental and concrete before written I’m only five but I’ve gone right off the idea of maths! We need to first develop a sense of number.

Examples of written calculations which should be done mentally in Year 1 to Year 4! Here a child who in the past would traditionally have written rows of sums would now be able to calculate the answers to these questions in their head.

So how do children learn in maths? Counting of objects and mental counting. Early stages of calculation with learning of addition and subtraction number facts, with recording. 5 + 8 = or 13 = + 5 Work with structured number lines Work with larger numbers, unstructured number lines and informal jottings. e.g. 47 + 26 0 1 2 3 4 5 6 7 8 9 10 So where do we start in maths. The first thing we do is to teach children to count. They count real things. The count forwards and backwards. They counting in ones, twos, fives and then tens. In this way, children are really gaining a sense of number. They then move on to learn number facts. Then we would ask children to learn number facts. By that I mean children would get to know pairs of numbers that make 10. 5+5=10, 7+3 =10. 10-3=7. Structured number lines already have the numbers on them. Unstructured number lines are blank and children fill in numbers. +3 +20 47 50 70 73 73

I must remember to add the least significant digit first Informal written methods, first with whole numbers and decimals. Formal written methods. Use of calculators for more difficult calculations in year 5/6 or for checking answers With any calculation, teach children to consider first whether a mental method is appropriate and remembering to estimate first. I must remember to add the least significant digit first Remember to partition 76 + 47 = 76 + 40 +7 = 116 + 7 = 123 (8+3) (60+90) (300+400) Partitioning is a key tool that all children are encouraged to use whether adding, subtracting, multiplying or dividing. When children are ready, they move to using informal written methods- horizontal first and then in the vertical layout. If and when they are ready, they can move to the more formal compact written method. In terms of the numbers that your child uses within this process, refer to year group objectives to find the sort of numbers for each year group.

What does a maths lesson look like? Oh look, these numbers make a lovely pattern. Before we go on to look at addition, subtraction, multiplication and division, lets watch some numeracy teaching in practice.

Remember to put the largest number first Addition Practical addition of real objects. Mental addition of number facts. Use of a structured number line to add. Partitioning to add. Use of an unstructured number line. 37 + 48= 0 1 2 3 4 5 6 7 8 9 10 + + 100 20 3 100 20 3 = 100 20 3 48 78 68 80 58 +10 +5 +2 85 Remember to put the largest number first Note: the units jump can be broken down to make it easier to count on through a multiple of 10

Addition cont ……… Beginning to record vertically.                   Beginning to record vertically. Adding the least significant digit first. 126 +57= Estimate: 126 +57 is nearly 130 + 60 so estimate answer should be near 190.                                                             126 + 57 13 (6+7) 70 (20+50) 100 (100+0) 183

Addition cont ……… Standard vertical method involving carrying. When children are confident working with larger numbers using the previous strategies, they will be introduced to ‘carrying’ digits. Usually this is during Year 5 and 6. 2856+1095 Estimate: 2900+1100 =4000 Answer should be less as I have rounded up. 2856 +1095 3951 1 1

Addition cont ……… Adding decimals This is first introduced through money and measures. As with all vertical methods, children should know how to line up place value columns and the decimal point under each other. £5.75 + £3.18 = Estimate: £6.00 + £3.00 = £9.00 £5.75 + £3.18 0. 13 (0.05+0.08) 0. 80 (0.70+0.10) 8. 00 (5.00+3.00) £8.93 £5.75 +£3.18 £8.93 1

Subtraction Practical subtraction of real objects. Mental subtraction of number facts. Use of a structured number line to subtract. Use of an unstructured number line. 123 - 47= Estimate first 120 - 50 = 70 Counting back- (most significant digit first, in this case tens, then units) or 0 1 2 3 4 5 6 7 8 9 10 -4 -3 -3 -10 -10 -10 -10 Start here. 76 80 83 93 103 113 123 -30 -20 +3 73 76 103 123

Add the numbers on top of the number line to get the answer. Subtraction cont ……… Counting on (Complimentary addition) How shopkeepers counted out change (before the till took over!) Children will be taught to find the difference by counting on in the following ways. 533 – 187 = Estimate : 530 – 190 = 340 (carried out mentally as 530 – 200 + 10 = 340) The difference is: 3 + 10 + 300 +30 +3 or 300 + 40+6 = 346                 +300 +3 +10 +30 +3 187 190 200 500 530 533 Start at this end. Add the numbers on top of the number line to get the answer.

Subtraction continued… Children learn to exchange and regroup 564 – 127 = ? Hundreds Tens Units Bank

This first vertical method is again based on counting up. Subtraction cont ……… Towards standard vertical subtraction When children are confident in finding the difference between larger numbers using number lines, they will begin to be introduced to a more efficient vertical procedure.                            533 - 187 13 (to make 200) 300 (to make 500) 33 (to make 533) 346 This first vertical method is again based on counting up.

Subtraction cont ……… 7. Subtraction by decomposition                            7. Subtraction by decomposition Children will then be shown decomposition; they must really understand place value to do this.                             Ten is taken from 80 and added to the three. 83 80 + 3 - 55 is the same as 50 + 5 This can be rewritten as 70 + 13 - 50 + 5 20 + 8 = 28 A hundred is taken from 500 and added to 20. 533 500 + 30 + 3 500 + 20 + 13 - 187 is the same as -100 + 80 + 7 -100 + 80 + 7 A hundred now needs to be moved as well. 400 + 120 + 13 - 100 + 80 + 7 300 + 40 + 6 = 346

Subtraction continued… 500 30 3 100 80 7 + 500 20 13 100 80 7 + 400 120 13 100 80 7 + 533 -187 = = = = 346 H T U

Subtraction cont ……… 8. Subtraction by decomposition                            8. Subtraction by decomposition      Only when children are completely secure in this we will teach them standard vertical subtraction using decomposition.                        5 3 3 - 1 8 7 3 4 6 Not all children will ever reach this stage. 4 12 1

Multiplication Practical Multiplication - 4 x 2 2 lots of 4. 2. Use of arrays 4 x 5 3. Repeated addition 4 x 5 = 5 + 5 + 5 + 5 = 20 or 4 + 4 + 4 + 4 + 4 = 20 This is an array.

Number lines can be used to do the addition part! Multiplication cont ….. 4. Repeated addition can also be done on a number line. 4 x 5 5. Partitioning – Simple recording 17 x 3 = (10 x 3) + (7 x 3) 30 + 21 = 51 0 5 10 15 20 Number lines can be used to do the addition part! 30 51 21 +

Add the numbers inside the grid together to get the answer. Multiplication cont ….. 4. The Grid Method This is our key strategy for beginning to formally record multiplication. 17 x 3 = (10 x 3 ) + (7 x 3 ) 30 + 21 = 51 5. Multiplying two 2 digit numbers 18 x 23 Estimate 20 x 20 = 400. 200 + 160 + 30 + 24 = 360 + 54 360 + 54 = 414 X 10 7 3 30 21 Add the numbers inside the grid together to get the answer. Try to add the numbers together mentally. If not, use a written method. X 10 8 20 200 160 3 30 24 360 + 54 4 110 300 414

Multiplication cont ….. 6. 3 digit by 2 digit 156 x 25 = Estimate 160 x 20 = 3200 7. 3 digit by 3 digit 152 x 385 Estimate 150 x 400 = 60000. x 100 50 6 20 2000 1000 120 5 500 250 30 3120 + 780 3900 1 x 100 50 2 300 30000 15000 600 80 8000 4000 160 5 500 250 10 45 600 + 12 160 760 58 520 1 1

Multiplication cont ….. 8. Once children are confident with the grid method, they will be introduced to the following strategies for recording. Short multiplication 17 x 3 9. Long multiplication 184 x 32 Estimate 180 x 30 = 5400. leads to 17 x 3 51 2 17 x 3 21 (7x3) 30 (10 x 3) 51 184 + 32 368 (184 x 2) 5520 (184 x 30) 5888

Division Sharing or Grouping – Division is initially represented pictorially. 6 sweets shared between 2 people. How many each? There are 6 people in a room. Put them into groups of 2. How many groups can you make? 2. Using a number line to show division. 6 ÷2 = 3 Sharing and grouping are two totally different concepts that children need to understand. 21 ÷7 = 3 -7 7 14 21

Start with 90 and take away multiples of 5. And then decimal remainder Division cont ……… 3. Using Multiples of the Divisor - Chunking. 4. Short division 90 - 50 (10 x 5) 40 - 40 (8 x 5) 0 90÷5 = 18 Start with 90 and take away multiples of 5. 4 87 - 40 (10 x 4) 47 - 40 (10 x 4) 7 - 4 (1x4) 3 87÷4 = 21 r 3 Next step: Fraction remainder 21 ¾ And then decimal remainder 21.75

Division cont ……… 875÷24 = 36 r 11 Using Chunking with larger numbers. 4 875 - 240 (10 x 24) 5 1 635 - 240 (10 x 24) 395 - 240 (10 x 24) 155 - 120 (5 x 24) 35 - 24 (1 x 24) 11

Daily counting Supports with mental calculation of all operations Example of counting objectives from National Curriculum: Year 2 To count on in tens from any given number (with and without a hundred square).

Remember what is important in maths! A focus on mental calculations. The ability to estimate. To use maths in a real life context. To ask children to explain how they have calculated something using a method that suits them. Teach children written calculations, but only when children are ready.

Useful Maths Websites www.bbc.co.uk/bitesize/ correct Key stage: EYFS = N&R , KS1- Y1-2, Years 3-6 are KS2, www.woodlands-junior.kent.sch.uk/maths/ www.mathszone.co.uk www.supermathsworld.com www.coolmath.com coolmaths4kids.com www.crickweb.co.uk/ks2numeracy.html www.educationquizzes.com www.free-training-tutorial.com/ordering-numbersgames.

Thank you for coming! Maths Workshop 2017   St. Mary's C. of E. Primary School   ‘Through God’s love, we strive to be the best we can be’.