Multiplication and Division Strategies to develop conceptual understanding

3 6 9 12 15 18 21 24 27 30 Twitter : @Count. On.

You can map the stations on the 100 square to see the pattern of

You could continue the pattern as far as you can in the 100 square.

Practice drawing out the 3 x table over and over again. Ask yourself Qs

Lets look into the 3 x table in more depth. 3 6 9 12

1) How many groups of 3 are there? 2) How many dots are there?

3 1) How many groups of 3 are there? 2) How many dots are

Let’s represent that strategy for 14 x 3 in what is called a ‘bar

Use this to work out 26 x 3 3 6 9 12 15 18

Try these questions draw a bar model for each one Extension Set 1) 26

If you like that strategy for multiplying you can use it for division When

Using the bar modelling strategy for division 17 3 30 51 21 7 10

Using the bar modelling strategy for division 18 4 40 72 72 ÷ 4

Using the bar modelling strategy for division 13 7 70 91 91 ÷ 7

Using the bar modelling strategy for division 72 ÷ 3 24 3 30 30

Using the bar modelling strategy for division 12 13 130 156 ÷ 13 26

Using the bar modelling strategy for division 168 ÷ 7 24 7 70 70

Using the bar modelling strategy for division 276 ÷ 12 23 12 120 10

Try these questions. You must draw a bar model for each one. This will

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Multiplication and Division Strategies to develop conceptual understanding

3 6 9 12 15 18 21 24 27 30 Twitter : @Count. On. Us. Ed

1) 2) 3) 4) 5) 6) 3 6 9 12 15 What is 7 x 3 What is 9 x 3 What is 4 x 3 What is 6 x 3 What is 8 x 3 What is 3 x 3 Keep repeatedly asking yourself more Qs about the 3 times table 18 21 1) 2) 3) 4) 24 27 30 Twitter : @Count. On. Us. Ed How many 3 s make 15 What is 30 ÷ 3 What is 6 ÷ 3 What is 3 ÷ 3

You can map the stations on the 100 square to see the pattern of the 3 x table You could continue the pattern as far as you can in the 100 square. Twitter : @Count. On. Us. Ed

You could continue the pattern as far as you can in the 100 square. Twitter : @Count. On. Us. Ed

Practice drawing out the 3 x table over and over again. Ask yourself Qs like 7 x 3, 4 x 3, 9 x 3, …etc Repeat this task for any of the following tables 4, 5, 6, 7, 8 and 9

Lets look into the 3 x table in more depth. 3 6 9 12 15 18 21 24 27 30 Twitter : @Count. On. Us. Ed

3 6 9 12 15 18 21 24 27 30 Twitter : @Count. On. Us. Ed

1) How many groups of 3 are there? 2) How many dots are there? 3) What is 20 x 3? 4) What is 60 ÷ 3? 5) How many 3 s are in 36? 3 6 9 12 15 18 21 24 27 30 Twitter : @Count. On. Us. Ed

3 1) How many groups of 3 are there? 2) How many dots are there? 3) What is 30 x 3? 4) What is 90 ÷ 3? 5) How many 3 s are in 63? 6 9 12 15 18 21 24 27 30 Twitter : @Count. On. Us. Ed

10 x 3 = 30 4 x 3 = 12 3 Use this to work out 14 x 3 = 30 + 12 = 42 6 9 12 15 18 21 24 27 30 Twitter : @Count. On. Us. Ed

Let’s represent that strategy for 14 x 3 in what is called a ‘bar model’ 14 3 30 12 4 10 14 x 3 = 30 + 12 = 42 Twitter : @Count. On. Us. Ed

Use this to work out 26 x 3 3 6 9 12 15 18 21 So 26 x 3 = 30 + 18 = 78 24 27 30 10 x 3 = 30 Twitter : @Count. On. Us. Ed 6 x 3 = 18

26 x 3 = 30 + 18 = 78 26 3 30 30 10 10 Twitter : @Count. On. Us. Ed 18 6

17 x 4 = 40 + 28 =68 17 4 40 28 10 7 Twitter : @Count. On. Us. Ed

16 x 7 = 70 + 42 =112 16 7 70 42 6 10 Twitter : @Count. On. Us. Ed

Try these questions draw a bar model for each one Extension Set 1) 26 x 3 2) 28 x 4 3) 27 x 6 4) 23 x 7 5) 24 x 9 6) 27 x 8 7) 24 x 6 8) 26 x 8 9) 23 x 9 10) 26 x 6 Basic Set 1) 16 x 3 2) 18 x 4 3) 17 x 6 4) 13 x 7 5) 14 x 9 6) 17 x 8 7) 14 x 6 8) 16 x 8 9) 13 x 9 10) 16 x 6 Twitter : @Count. On. Us. Ed

If you like that strategy for multiplying you can use it for division When dividing we just need to understand that each number has a key number When dividing by 3 the key number is …. 30 When dividing by 4 the key number is …. 40 When dividing by 8 the key number is …. 80 When dividing by 6 the key number is …. 60 When dividing by 13 the key number is …. 130 Twitter : @Count. On. Us. Ed

Using the bar modelling strategy for division 17 3 30 51 21 7 10 51 ÷ 3 When dividing by 3 the key number is …. 30 If the first bit is the key number of 30 the other bit must be 21 As 30 + 21 = 51 Divide 30 and 21 by 3 separately 30 ÷ 3 = 10 So 51 ÷ 3 = 17 21 ÷ 3 = 7 Twitter : @Count. On. Us. Ed

Using the bar modelling strategy for division 18 4 40 72 72 ÷ 4 32 8 10 When dividing by 4 the key number is …. 40 If the first bit is the key number of 40 the other bit must be 32 As 40 + 32 = 72 So 72 ÷ 4 = 18 Twitter : @Count. On. Us. Ed

Using the bar modelling strategy for division 13 7 70 91 91 ÷ 7 21 3 10 When dividing by 7 the key number is …. 70 If the first bit is the key number of 70 the other bit must be 21 As 70 + 21 = 91 So 91 ÷ 7 = 13 Twitter : @Count. On. Us. Ed

Using the bar modelling strategy for division 72 ÷ 3 24 3 30 30 10 10 12 4 When dividing by 3 the key number is …. 30 We can fit 30 into 72 twice So 72 ÷ 3 = 24 Twitter : @Count. On. Us. Ed

Using the bar modelling strategy for division 12 13 130 156 ÷ 13 26 2 10 When dividing by 13 the key number is …. 130 So 156 ÷ 13 = 12 Twitter : @Count. On. Us. Ed

Using the bar modelling strategy for division 168 ÷ 7 24 7 70 70 10 10 28 4 When dividing by 7 the key number is …. 70 We can fit 70 into 168 twice So 168 ÷ 7 = 24 Twitter : @Count. On. Us. Ed

Using the bar modelling strategy for division 276 ÷ 12 23 12 120 10 10 36 3 When dividing by 12 the key number is …. 120 We can fit 120 into 276 twice So 276 ÷ 12 = 23 Twitter : @Count. On. Us. Ed

Try these questions. You must draw a bar model for each one. This will help strength the understanding and help you remember long term. Basic Set 1) 42 ÷ 3 2) 56 ÷ 4 3) 84 ÷ 6 4) 48 ÷ 3 5) 64 ÷ 4 6) 85 ÷ 5 7) 91 ÷ 7 8) 54 ÷ 3 9) 96 ÷ 6 10) 72 ÷ 4 Intermediate Set 1) 104 ÷ 8 2) 126 ÷ 9 3) 112 ÷ 7 4) 108 ÷ 6 5) 107 ÷ 9 6) 136 ÷ 8 7) 168 ÷ 14 8) 204 ÷ 17 9) 128 ÷ 8 10) 154 ÷ 11 Extension Set 1) 72 ÷ 3 2) 92 ÷ 4 3) 114 ÷ 6 4) 78 ÷ 3 5) 135 ÷ 5 6) 161 ÷ 7 7) 84 ÷ 3 8) 156 ÷ 6 9) 112 ÷ 4 10) 135 ÷ 3 Post your answers to the Twitter Count On Us Facebook or twitter page : @Count. On. Us. Ed