Multiplicative Thinking Diagnostic

This short assessment is all about multiplication reasoning. Answer each question carefully to the very best of your knowledge. There is no time limit.


Phase 1 – Equal groups

1. Which picture shows 3 groups of 4?

2. There are 4 groups of 2 counters. How many counters altogether?

3. Which sentence matches this picture?

4. Which picture shows equal groups of 3?

Phase 2 – Groups, repeated addition and multiplication

5. 3 groups of 5 is equal to…

6. Which expression matches 4 + 4 + 4?

7. Which repeated addition matches 2 Ă— 6?

8. Which multiplication means 5 groups of 2?

Phase 3 – Arrays and structure

9. An array has 3 rows with 4 in each row. Which multiplication does it show?

10. Which array shows 4 rows with 2 in each row?

11. What is true about 3 Ă— 4 and 4 Ă— 3?

12. An array has 2 rows with 5 counters in each row. How many counters are there altogether?

Phase 4 – Derived facts and relationships

13. If 3 Ă— 4 = 12, then 6 Ă— 4 = 24 because:

14. If 2 Ă— 7 = 14, then 4 Ă— 7 = 28 because:

15. If 5 Ă— 6 = 30, then 10 Ă— 6 = 60 because:

16. If 3 Ă— 8 = 24, then 9 Ă— 8 = 72 because:

Phase 5 – Choosing efficient methods

17. Which is the best way to think about 7 Ă— 6 = 42?

18. Which is the best way to think about 9 Ă— 4 = 36?

19. Which is the best way to think about 8 Ă— 3 = 24?

20. Which is the best way to think about 7 Ă— 8 = 56?

Phase 6 – Inverse and fact families

21. If 6 × 4 = 24, then…

22. If 3 × 4 = 12, then…

23. If 8 × 5 = 40, then…

24. If 7 × 3 = 21, then…

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