Chapter practice examination

Show your thinking; use diagrams when they help. Do not open solutions during your first attempt.

Check your work: Finish the problems first, then ask a parent or instructor to review them with the separate answer-key copy.

1. A1

   A student answers the following question with “9”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: 56 counters are shared equally into 7 groups. How many counters are in each group? (3 points)

2. A2

   Find 6 groups of 4. Can you use 5 groups plus one more? (2 points)

3. A3

   Find 8 groups of 9. Can you use 7 groups plus one more? (2 points)

4. A4

   Explain how splitting 6 equal groups of 7 helps you find their total. (2 points)

5. A5

   A student answers the following question with “49”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: Compute 6 × 8. Explain a strategy using a known fact. (3 points)

6. A6

   Each tray holds 6 counters. How many full trays are required to arrange 42 counters? (2 points)

7. A7

   Compute 9 × 8. Explain a strategy using a known fact. (2 points)

8. A8

   Compute 8 × 8. Explain a strategy using a known fact. (2 points)

9. A9

   A student answers the following question with “57”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: There are 7 equal trays with 8 counters on each tray. How many counters are there? (3 points)

10. A10

    Each tray holds 8 counters. How many full trays are required to arrange 40 counters? (2 points)

11. A11

    There are 9 equal trays with 10 counters on each tray. How many counters are there? (2 points)

12. A12

    There are 8 equal trays with 5 counters on each tray. How many counters are there? (2 points)

13. A13

    A student answers the following question with “64”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: An array has 9 rows, with 7 objects in each row. Split it into smaller arrays and find the total. (3 points)

14. A14

    Find 7 groups of 8. Can you use 6 groups plus one more? (2 points)

15. A15

    81 counters are shared equally into 9 groups. How many counters are in each group? (2 points)

16. A16

    Find 9 groups of 7. Can you use 8 groups plus one more? (2 points)

17. A17

    A student answers the following question with “36”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: An array has 7 rows, with 5 objects in each row. Split it into smaller arrays and find the total. (3 points)

18. A18

    Use two useful multiplication facts to work out 8 × 8. What is the product? (2 points)

19. A19

    Explain how splitting 9 equal groups of 8 helps you find their total. (2 points)

20. A20

    Use two useful multiplication facts to work out 7 × 8. What is the product? (2 points)

21. A21

    A student answers the following question with “11”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: Each tray holds 8 counters. How many full trays are required to arrange 80 counters? (3 points)

22. A22

    Find 6 groups of 9. Can you use 5 groups plus one more? (2 points)

23. A23

    An array has 7 rows of 3 dots. A student says turning it creates 3 more dots. Explain the error and find the total. (3 points)

24. A24

    Without counting individual counters, show two different decompositions for 6 × 4, and explain why both work. (3 points)