Stage 6 Advanced Additive

Solve 53 - 29

Summary of StrategiesTidy numbers using

Compensation

53 - 30 + 1

53 - 29

Place Value Partitioning

53 - 20 - 9

Equal Additions54 - 30

Reversibility29 + ? = 53

53 - 29Tidy Numbers using Compensation

53 - 30 + 1= 24

53 - 29Place Value Partitioning

53 - 20 - 3 - 6 = 24

53 – 29 Reversibility

29 + 1 + 20 + 3 = 53

53 - 29Equal Additions

5329

1

1

5430

= 24

53 - 29Equal Additions

5329

30 54

Summary of StrategiesTidy numbers using

Compensation

53 - 30 + 1

53 - 29

Place Value Partitioning

53 - 20 - 9

Equal Additions54 - 30

Reversibility29 + ? = 53

Possible Multiplicative Strategies

Place Value 5 x 30 = 150.

And 5 x 6 = 30.So 150 + 30 = 180

Doubling and Halving.

Double 5= 10, half 36= 18.

So 10 x 18 = 180

Written Form 36X 5 180

5 x 36 =

Tidy NumbersI know 5 x 40 = 200.

200 - (4x5) = 180.

Stage 7 Advanced Multiplicative

Solve 3 x 18

3 x 18

Types of Advanced Multiplicative Part-Whole Strategies 3x18

• Rounding –(20x3)-(2x3)• Adding – (12x3)+(6x3)• Doubling – 2x(9x3)• Proportional adjustment (e.g. doubling

and halving) (9x6)• Place vale partitioning (10x3) +(8x3)

3 x 18

10101010 1010

3 x 20 = 6060 - (3 x 2) = 54

Tidy Numbers using Compensation

3 x 18

1010 10

3 x 10 = 30

Place Value Partitioning

3 x 8 = 2430 + 24 = 54

3 x 18

3 x 9 3 x 9

Proportional Adjustment

6 x 9 = 54

3 x 18

6 x 9

x 2 ÷ 2

0- (3 x 2)

3 x 20

0

3 x 10 3 x 8

Using Number Lines 3x18

30 54

54 60

0 9 9 9 9 99 54

18 1818

54

Proportional Adjustment

Place value

Tidy Numbers

A

B

C

Possible Multiplicative Strategies

Place Value 5 x 30 = 150.

And 5 x 6 = 30.So 150 + 30 = 180

Doubling and Halving.

Double 5= 10, half 36= 18.

So 10 x 18 = 180

Written Form 36X 5 180

5 x 36 =

Tidy NumbersI know 5 x 40 = 200.

200 - (4x5) = 180.

• Possible multiplicative part-whole strategies for the wheels problem include:

• 80 4 = 2- so 72 4 = 20 – (8 4) = 18 (compensation)

• 10 x 4 = 40. 72 – 40 = 32, 8 x 4 = 32, 10 + 8 = 18, so 18 x 4 = 72 (reversibility and place-value partitioning);

• 9 x 8 = 72 20 18 x 4 = 72 (doubling and halving) (Ministry of Education, 2005a)

Diagnostic Interview – Car Problem