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Strategies – Multiplication and Division
From repeated addition to multiplication as an array
3+3+3+3 4+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.
3
4
4 x 3
Multiplication represented as an area
4
3
3 x 4
3
4
4 x 3 = 12
Multiplication represented as an area
4
3
3 x 4 = 12
14
30
Calculate 30 x 14
Multiplication represented as an area
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
Modelling 38 x 14. Find ?
14
10
4
3038
?
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
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
38X 14 152 380 532
14 x 38 as a calculation
+
Modelling 38 x 142.
142
100
40
30
388
2
30 x 100 8 x 100
30 x 40 8 x 40
30 x 2 8 x 2
Progression in the area model for multiplication
2
x
2 x x
2 (x + 3) = 2x + 6
2 x 3
3
“I know the 2 times and 3 times table. My teacher tells me I can
work out the rest.”
Discuss !
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
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!
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, 8x9One fact of x9 table ie 9x9
20 4 20 4 20 4
20 24 44 48 68 72
3 X 24 = 24 + 24 + 24 Multiplication as repeated addition
20 20 20 4 4 4
20 40 60 64 68 72
3 X 24 = 3 x 20 + 3 x 4 Distributive property of multiplication
Development & Progression 2nd level – ‘ using their knowledge of commutative, associative and distributive properties to simplify calculations’
The ‘distributive’ property for X and ÷
21p21p 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
Show 3 x 24p
= (3 x 20) + (3 x 4)
Using money to illustrate the distributive propertyProgression – Level 2: ‘use their knowledge of ...
distributive properties ...’Multiplication
Show 87p ÷ 3
Using money to illustrate the distributive propertyProgression – Level 2: ‘use their knowledge of ...
distributive properties ...’Division