1. Stage 6 Advanced Additive
Solve

2. 53 - 29 Summary of Strategies Tidy numbers using Compensation
Place Value Partitioning
Reversibility
29 + ? = 53
Equal Additions

3.
Tidy Numbers using Compensation
= 24

4.
Place Value Partitioning
= 24

5. 53 – 29 Reversibility
= 53

6.
Equal Additions 1 54 30 53
= 24 29

7.
Equal Additions 53 29 30 54

8. 53 - 29 Summary of Strategies Tidy numbers using Compensation
Place Value Partitioning
Reversibility
29 + ? = 53
Equal Additions

9. Possible Multiplicative Strategies
Tidy Numbers
I know 5 x 40 = 200.
200 - (4x5) = 180.
Place Value
5 x 30 = 150.
And 5 x 6 = 30.
So = 180
5 x 36 =
Written Form 36
X 5
180
Doubling and Halving.
Double 5= 10, half 36= 18.
So 10 x 18 = 180

10. Stage 7 Advanced Multiplicative
Solve 3 x 18

11. 3 x 18

12. 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)

13. 3 x 18 Tidy Numbers using Compensation 3 x 20 = 60 60 - (3 x 2) = 5410
3 x 20 = 60
60 - (3 x 2) = 54

14. 3 x 18
Place Value Partitioning 10
3 x 10 = 30
= 54
3 x 8 = 24

15. 3 x 18
3 x 9
3 x 9

16. Proportional Adjustment
6 x 9 = 54
3 x 18
6 x 9
x 2
÷ 2

17. Using Number Lines 3x18 Proportional Adjustment Place value
Tidy Numbers 54 A 30 54 B 54 60 C

18. Possible Multiplicative Strategies
Tidy Numbers
I know 5 x 40 = 200.
200 - (4x5) = 180.
Place Value
5 x 30 = 150.
And 5 x 6 = 30.
So = 180
5 x 36 =
Written Form 36
X 5
180
Doubling and Halving.
Double 5= 10, half 36= 18.
So 10 x 18 = 180

19. Diagnostic Interview – Car Problem
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 = 32, 8 x 4 = 32, = 18, so 18 x 4 = 72 (reversibility and place-value partitioning);
9 x 8 = x 4 = 72 (doubling and halving) (Ministry of Education, 2005a)