Maths Multiplication and Division Workshop 12th November 2014

Aims of the Workshop Aims of the Workshop To raise standards in maths by working closely with parents. To outline the expectations of the new National Curriculum in mathematics To provide parents with a clear outline of the key features of maths teaching at Provost Williams Primary School. 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.

The new National Curriculum in Maths Fluency Mathematical reasoning Problem solving through applying their mathematics A mastery curriculum which broadens and deepens pupils knowledge rather than accelerate them into new curriculum content.

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. 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.

Multiplication

Multiplication Practical Multiplication - 2 x 4 2 lots of 4. 2. Repeated addition 4 x 5 = 5 + 5 + 5 + 5 = 20 or 4 + 4 + 4 + 4 + 4 = 20 3. Use of arrays 4 x 5 0 5 10 15 20 This is an array.

13 x 3 = x 10 3 30 9 30 + 9 = 39

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

Have a go! Can you do these sums using the grid method? 6 x 15 23 x 54

10 5 6 60 30 60 + 30 = 90 50 4 20 1000 80 3 150 12 1000+ 80 +150+12 = 1242

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

Division

To divide successfully, children need to be able to: understand the relationship between multiplication and division understand and use multiplication and division as inverse operations. recall multiplication and division facts to 10 × 10 and recognise multiples of one-digit numbers know how to multiply single digits by multiples of 10 or 100 know how to find a remainder working mentally - for example, find the remainder when 48 is divided by 5;

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. 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

Division cont ……… 5. Using Chunking with larger numbers. 6. Leading to sums using decimals. 875÷24 = 36 r 11 24 875 - 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 Useful Multiples 1 x 24 = 24 2 x 24 = 48 4 x 24 = 96 8 x 24 = 192 10 x 24 = 240

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.