Supporting your child in Maths Multiplication and Division
The aims of this morning: To share the methods we use to teach multiplication and division calculations at school; To explore the practical methods that children use to support their learning in Maths; To provide activities that you can use to support your children at home in a way that encourages enthusiasm for the subject.
Supporting your child in Maths Multiplication and Division
What the children said... It was fun being with your parents doing maths. Now my mum and dad know how to do it.
I enjoyed having maths with my mum because I got to be like the teacher and show her how to use a number line.
I enjoyed being with my mum and dad and showing them my talent.
Supporting your child in Maths Multiplication and Division
Place Value As with addition and subtraction, understanding of place value is key to the understanding of multiplication and division. Being able to break a number down into smaller parts means that we can break a calculation into smaller steps.
Children are taught how to partition numbers from KS1 and throughout the school.
Supporting your child in Maths Multiplication and Division
Times Tables Mental recall of times table facts begins to be more formally taught in KS2. In KS1 the emphasis is placed on counting in steps, a skill which is required for carrying out calculations with all four mathematical operations.
10x 4x
8x
Supporting your child in Maths Multiplication and Division
Multiplication Children are first introduced to the idea of multiplication in school through setting up groups in role-play. This is done using a number of different models and images: Putting 5 flowers in each vase.
This practical method would also be used to introduce the concept of doubling as finding ‘2 lot’s of’.
Supporting your child in Maths Multiplication and Division
Multiplication Once the use of role-play has begun to develop the understanding of the very idea of what multiplying is, children will begin to use arrays to represent multiplication problems. At first this would be done using a variety of practical equipment.
Peg Boards Counters
Supporting your child in Maths Multiplication and Division
Multiplication Once the use of role-play has begun to develop the understanding of the very idea of what multiplying is, children will begin to use arrays to represent multiplication problems. At first this would be done using a variety of practical equipment. 3 x 5 = 15 3 5
Supporting your child in Maths Multiplication and Division
Multiplication Once the use of role-play has begun to develop the understanding of the very idea of what multiplying is, children will begin to use arrays to represent multiplication problems. 3 x 5 = 15 3 5
As their understanding deepens further children will be expected to create jottings of these arrays using dots, on their whiteboards or in their books, to help them calculate such questions independently.
Supporting your child in Maths Multiplication and Division
Multiplication Alongside using arrays to represent their calculations visually children will continue to link multiplication to finding ‘lots of’ by counting on. Children may be supported in this by using number lines to count-on in steps. These may be numbered tracks: 3 x 5= 15 +5
+5
+5
___________________________________ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Or blank lines that the children would be expected to number themselves: 3 x 5= 15 +5
+5
+5
___________________________________ 0 5 10 15
Supporting your child in Maths Multiplication and Division
Multiplication As children move through KS2 the use of arrays and their knowledge of place value will be used to introduce the grid method. This method can be used to multiply numbers of any size by breaking the calculation down into smaller steps. 4 x 24 = 96 x
By using arrays inside the grids initially children are encouraged to link the grid method to previous use of arrays.
Supporting your child in Maths Multiplication and Division
Multiplication As children move through KS2 the use of arrays and their knowledge of place value will be used to introduce the grid method. This method can be used to multiply numbers of any size by breaking the calculation down into smaller steps. 4 x 24 = 96 x
4
20
80
4
16
= 80+ 16 = 96
The children then use the method themselves, writing in the numerical solutions to each part of the calculation
Supporting your child in Maths Multiplication and Division
Multiplication The grid method can then be developed to multiply bigger numbers: U x HTU
TU x TU
3 x 124
72 x 38
x
3
x
30
8
100
300
70
2100
560
20
60
2
60
16
4
12
= 300 + 60 + 12 = 372
= 2100 + 560 + 60 + 16 = 2736
Supporting your child in Maths Multiplication and Division
Multiplication The final stage is to link the grid method to an expanded vertical method: 7 x 38 x
7
30
210
8
56
= 210+ 56 = 266
38 7 x -------210 (30 x 7) 56 (8 x 7) ------266
Supporting your child in Maths Multiplication and Division
Multiplication As they near the end of KS2 some children may be shown the full vertical method: 136 x 24 2 712 0 41224 312 6 4
Supporting your child in Maths Multiplication and Division
Division As with all the other operations we have looked at, children will first meet division in practical ways. There are two ways that children are encouraged to think about division. Sharing If 6 apples are shared between 2 people, how many would they have each?
3
Grouping There are 6 apples. How many people could have 2 each?
3
Supporting your child in Maths Multiplication and Division
Division As with all the other operations we have looked at, children will first meet division in practical ways. There are two ways that children are encouraged to think about division.
The idea of grouping as talking away ‘lots of’ is then used to introduce the use of repeated subtraction....
Grouping There are 6 apples. How many people could have 2 each?
3
Supporting your child in Maths Multiplication and Division
Division The idea as grouping as repeated subtraction is first taught through numerous practical methods, using counters and other practical equipment to represent calculations. 12 ÷ 3 = 4
After this children would be shown how to use the vertical number line to carry out division problems more independently:
12 11 10 9 8 7 6 5 4 3 2 1 0
3
3
3
3
Supporting your child in Maths Multiplication and Division
Division This method can be built upon once the children are confident in using blank lines which they number themselves And here we 13 12 ÷ 3 = 4 12 13 ÷ 3 = 4 r 1 see why we 3 3 now count 10 back on our 9 3 3 number 7 lines... 6 ..remainders! 3 3
3 3 0
4 3 1 0
Supporting your child in Maths Multiplication and Division
Division The vertical number line method can be used to divide with larger numbers, and with greater efficiency: 52 ÷ 4 = 10 + 3 = 13
126 ÷ 4 = 10 + 10 + 10 + 1 r2 = 31 r 2 126
52
10 x 4 86 10 x 4
10 x 4 46
10 x 4
12
6 3x4
0
1x4 2 0
Supporting your child in Maths Multiplication and Division
Division From this point children would be expected to use the vertical number line method if they are finding a calculation difficult. However they may be shown the chunking method as an introduction to short division: 72÷3 = 10+10+4 = 24 3 72 - 30 (10x3) 42 - 30 (10x3) 12 - 12 (4x3) 0
Supporting your child in Maths Multiplication and Division
Division As they near the end of KS2 some children may be shown the full bus stop method: 644÷7 0 9 2 7 6 64 14
Supporting your child in Maths Multiplication and Division
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Talking about Maths
As some of you will remember from the addition and subtraction morning, there are many ways you can build maths into the time you spend with your children at home. There are further ideas in the leaflets on your chairs for you to take away from this morning.
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Supporting your child in Maths Multiplication and Division
In the classrooms.... You may spend time in your child’s classroom until approximately 10.10, at this point the children will be getting ready for assembly. If you have more than one child please feel free to move from one room to the other in your own time. Lessons are being taught as normal and the teachers attention will be with the other children in the classroom. We would appreciate it if you did not take away from this valuable input by asking questions of the teacher yourself. You may ask questions of Miss Everton or Miss Godbold who will both be available in the entrance after the session has finished. Space will be tight and we apologise that we can not accommodate seating in the classrooms for you.
