Ministry of Education

Secondary Numeracy Project

Algebra in Multiplication

Kevin Hannah

Central Auckland Airport Hotel

23-24 February 2005

Algebra in Multiplication

Computing using the distributive law Recognising structure in numbers Exploring algebraic expressions

7 x 98

What’s the answer?

How did you do it?

7 x 98 = 7 x 100 - 7 x 2

597 x 5

What’s the answer?

How did you do it?

597 x 5 = 600 x 5 - 3 x 5

407 x 8

What’s the answer?

How did you do it?

407 x 8 = 400 x 8 + 7 x 8

Are these correct?

3x(400-8) = 3x400 - 3x8

597 x 11 = 600 x 11 - 3 x 7

915 x 8 = 900 x 8 + 15 x 8

7 x 98 = 7 x 100 - 7 x 2

Are these correct?

12x40 - 8x12= 8x(40-12)

79 x 11 = 70 x 11 +9x9

80 x 7 - 5 x 7 = 85 x 7

8 x 300 - 7 x 8 = 8 x 293

What’s missing?

5x(70-2) =5x70 - 5x 12

6 x 600 + 7 x 6 = 6 x 607

58 x 13 = 50 x 13 + 8 x 13

80 x 6 - 6 x 6 = 74 x 6

Fill in the gaps

5(y-2) =5y - 10

6 ( m + 7) = 6m + 42

7 ( m + 9 ) = 7m + 63

8c - 48 = 8(c - 6)

Expand

5 ( y + 6) = 5y + 30

7(x - 10) = 7x - 70

4 ( 2m + 3 ) = 8m + 12 6(3r-9) = 18r - 54

Factorise

3 ( n + 2) = 3n + 6

8(x - 4) = 8x - 32

5 ( 4p + 3 ) = 12p + 15 7(6 - 5y) = 42 - 35y

a(b ± c) = ab ± ac

Recognising Structure