Top Drawer Teachers The Australian Association of Mathematics Teachers (AAMT) Inc. http://topdrawer.aamt.edu.au

1. I wonder how many different
arrays you can make for 24?
• Record all your thinking and the
different arrays on paper.
• What are some interesting things
you notice?
• How do you know if you have
them all?
Possible arrays

2. Noticing
• What is the same about all
the arrays?
• What is different about them?
• What do you notice about the
number of rows and number of
tiles in each row?
Possible arrays

3. Teaching tips
• Focusing their attention to the
structure and possibly to noticing
the commutative facts in each
instance, e.g., 6 × 4 and 4 × 6.
• This might prompt a discussion
of the pairs of factors for each
(e.g., 3, 4) and the factors for 24
(i.e., 1, 2, 3, 4, 6, 8, 12, 24).
• It could also lead to noticing
relationships in factor pairs, e.g.,
6 × 4 = 3 × 8 (doubling and halving).
Possible arrays

4. • If such connections are not forthcoming
from students, list all the facts for 24
vertically on the board in sequential order
(e.g., 1× 24, 2 × 12, 3 × 8, 4 × 6, 6 × 4, 8 × 3,
12 × 2, 24 × 1)
• Ask students to look for connections
between them.
• Having the visual of each array will also
assist them to see the doubling and halving
relationship.
Teaching tips
Possible arrays

5. 4 rows of 6
Possible arrays
Different arrays for 24

6. Possible arrays
Different arrays for 24
6 rows of 4

7. Possible arrays
Different arrays for 24
2 rows of 12

8. Possible arrays
Different arrays for 24
12 rows of 2

9. Different arrays for 24
1 row of 24
Possible arrays

10. Different arrays for 24
24 rows of 1
Possible arrays

11. Different arrays for 24
3 rows of 8
Possible arraysPossible arrays

12. Different arrays for 24
8 rows of 3
Possible arraysPossible arrays

13. Different arrays for 24
6 rows of 4
Possible arrays

14. Different arrays for 24
4 rows of 6
Possible arrays

15. Different arrays for 24
8 rows of 3
Possible arrays

16. Different arrays for 24
3 rows of 8
Possible arrays

17. Different arrays for 24
1 row of 24
Possible arrays

18. Different arrays for 24
2 rows of 12
Possible arrays