Multiplication and Division Calculating efficiently and accurately.
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Transcript of Multiplication and Division Calculating efficiently and accurately.
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Multiplication and Division
Calculating efficiently and accurately
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• Counting• Doubling and halving
• Multiplication as repeated addition, describing an array and scaling
• Division as grouping and sharing• Understand that multiplication and division are inverses
• Recall of multiplication and division facts• Multiply two / three-digit numbers by 10 / 100
Progression for multiplication and division
context
Dice race game
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Counting in context How many 10p coins are here?
How much money is that?
How many toes are there on 2 feet?
How many gloves in 3 pairs?
If Sarah counts in 2s and Nigel counts in 5s, when will they reach the same number?
How many lengths of 10m can you cut from 80m of rope?
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Doubling and halving in context
There are 8 raisins. Take half of them.How many have you taken?
One snake is 20cm long. Another snake is double that length.How long is the longer snake?
I double a number and then double the answer. I now have the number 32. What number did I start with?
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94 65 48 30 71
28 36 56 97 32
12 24 51 82 19
77 63 44 53 28
60 96 75 17 43
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2 x 3 or 3 x 23 plates, 2 cakes on each plate
(Children could draw a picture to help them work out the answer)
2 x 3 or 3 x 23 plates, 2 cakes on each plate
(Children could use dots or tally marks to represent objects – quicker than drawing a picture)
Multiplication
pictures
symbols
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Number tracks and number lines(modelled using bead strings)
2 x 3 or 3 x 2
4 620
[two, three times] or [three groups of two]
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Arrays
5 x 3 or 3 x 5
14 x 2 = 28
x 10 42 20 8
Array creator
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XX 10 3
4
X 10 3
4 40 12Answer = 52
13 x 4 = 52
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43x 6
2581
40 x 6 = 240
3 x 6 = 18
X 40 3
6 240 18
43 x 6
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27 x 34
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Multiplication grid ITP
Approximation: Answer lies between 600 (20 x 30) and 1200 (30 x 40) or 30 x 30 = 900
27 x 34
108 (27 x 4) 810 (27 x 30)
918
Extend to HTU x U, U.t x U and HTU x TU
27 x 34
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6 ÷ 2 6 cakes shared between 2
6 cakes put into groups of 2
(Children could draw a picture to help them work out the answer)
pictures
Division
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6 ÷ 2
6 cakes shared between 2
6 cakes put into groups of 2
(Children could use dots or tally marks to represent objects – quicker than drawing a picture)
symbols
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Number tracks and number lines - grouping(modelled using bead strings)
8 ÷ 2 = 4
6 ÷ 2 = 3
0 2 4 6
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Number lines / Arrays
15 ÷ 5 = 3
0 5 10 15
Grouping ITP
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Number dial ITP
67 ÷ 4 = 16 r 3
67 ÷ 4
4 x 10 = 40
4 x 6 = 24 [64]
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97 ÷ 9 = 10 r 7
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Efficient methods . . . .
Answer = 125 r 4
Approximation: Answer lies between 100 (600 ÷ 6) and 150 (900 ÷ 6)
754
- 600 (6 x 100)
154
- 120 (6 x 20)
34
- 30 (6 x 5)
4
Extend to U.t ÷ U and HTU ÷ TU
754 ÷ 6
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Efficient methods . . . . Short division
291 ÷ 3 = 97
Estimation: 270 ÷ 3 = 90 3 291
972
7 43.4
6.21
43.4 ÷ 7 = 6.2
Estimation: 42 ÷ 7 = 6
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A Challenge for you!
Domino Magic Imagine a domino Add the two numbers together Multiply by five Double Add the larger of the two numbers.
What is your number?