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Published byTeresa Hoover Modified over 2 years ago

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Strategies – Multiplication and Division

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From repeated addition to multiplication as an array 3+3+3+34+4+4 4 groups of 3 = 4 x 3 3 groups of 4 = 3 x 4 4 x 3 does not represent the same as 3 x 4 but it has the same value.

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3 4 4 x 3 Multiplication represented as an area 4 3 3 x 4

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3 4 4 x 3 = 12 Multiplication represented as an area 4 3 3 x 4 = 12

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14 30 Calculate 30 x 14 Multiplication represented as an area

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14 10 4 30 30 x 10 = 300 30 x 4 = 120 30 x 14 = (30 x 10) + (30 x 4) = 300 + 120 = 420 Multiplication as an area

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Modelling 38 x 14. Find ? 14 10 4 30 38 ? 38 x 14 = (30 x 10) + (? x 10) + (30 x 4) + (? x 4) = 300 + ? + 120 + ? = ? 30 x 10? x 10 30 x 4 ? x 4

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Compare these models! 10 4 30 30 x 10 = 300 30 x 4 = 120 14 x 38 as an area 8 x 10 = 80 8 x 4 = 32 8 30 x 10 = 300 + 8 x 10 = 80 + 30 x 4 = 120 + 8 x 4 = 32 14 x 38 = 532 Area model for multiplication 38 x 14 38 X 14 152 380 532 14 x 38 as a calculation +

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Modelling 38 x 142. 142 100 40 30 38 8 2 30 x 1008 x 100 30 x 40 8 x 40 30 x 2 8 x 2

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Progression in the area model for multiplication 2 x 2 x x 2 (x + 3) = 2x + 6 2 x 32 x 3 3

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0.10.20.30.40.50.60.70.80.91.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Representation of 0∙3 Progression in the area model to multiplying decimal fractions

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0∙3 = 0.12 x 0∙4 Extending area model to multiplying decimal fractions 0.10.20.30.40.50.60.70.80.91.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

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“I know the 2 times and 3 times table. My teacher tells me I can work out the rest.” Discuss !

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Multiplication facts from the 2 times and 3 times tables. Using x2 table x4 and x8 (by doubling) Using x3 x6 (x2 x3 or x3+x3) and x9 (x3 x3) Using x2 and x3 tables x5 (x2+x3) Using x3 and x4 x7 (x3+x4) x10 (x5+x5) deserves special attention. So, I can work out all the times tables up to x10??? you can derive the

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Learning multiplication facts Hints and tips for helping with 7x8, 8x9, 9x9 etc When they have mastered the early multiplication facts eg x2, x3, x4, x5, x10, children have only 10 more x facts to learn! Discuss!

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Learning multiplication facts Use commutative properties, e.g. 3 x 4 = 4 x 3 So, when learning 6x table children already know facts up to 6 x 5 (from the x5 table) which leaves only four facts to learn: That leaves only six more facts to master on the x7, x8 and x9 tables, ie : 6x6, 6x7,6x8,6x9 Why? Three facts of x7 table ie 7x7, 7x8, 7x9 = Two facts of x8 table ie 8x8, 8x9 One fact of x9 table ie 9x9

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204 4 4 2444486872 3 X 24 = 24 + 24 + 24Multiplication as repeated addition 20 444 4060646872 3 X 24 = 3 x 20 + 3 x 4Distributive property of multiplication Development & Progression 2 nd level – ‘ using their knowledge of commutative, associative and distributive properties to simplify calculations’ The ‘distributive’ property for X and ÷

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21p 3 x 21p = (3 x 20p) + (3 x 1p) Using money to illustrate the distributive property Progression – Level 2: ‘use their knowledge of... distributive properties...’ Multiplication

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Show 3 x 24p = (3 x 20) + (3 x 4) Using money to illustrate the distributive property Progression – Level 2: ‘use their knowledge of... distributive properties...’ Multiplication

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Show 87p ÷ 3 Using money to illustrate the distributive property Progression – Level 2: ‘use their knowledge of... distributive properties...’ Division

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8 x 15 = 4 x 30 = 2 x 60 = 1 x 120 = 120 An effective strategy for multiplication halving and doubling example halvingdoubling

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204 ÷ 4 = 102 ÷ 2 = 51 ÷ 1 = 51 example An effective strategy for division halving and halving halvingdoubling

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