The document discusses possible arrays for the number 24 and teaching tips related to noticing patterns in the arrays. It suggests having students list all possible arrays for 24 on paper and notice what is the same and different about the arrays. The arrays include combinations such as 4 rows of 6, 6 rows of 4, 2 rows of 12, and others. It also recommends listing the factor pairs of 24 vertically to help students see connections like doubling and halving between arrays.

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
Focus the students’ attention to the structure and
(possibly) to notice 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 and 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 show 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:
1× 24, 2 × 12, 3 × 8, 4 × 6, 6 × 4, 8 × 3, 12 × 2, 24 × 1
Ask students to look for connections between them.
Showing the visual of each array will also assist
students 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