Possible arrays I wonder how many different arrays

Possible arrays 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 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 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 Teaching tips 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.

Possible arrays Different arrays for 24 4 rows of 6

Possible arrays Different arrays for 24 6 rows of 4

Possible arrays Different arrays for 24 2 rows of 12

Possible arrays Different arrays for 24 12 rows of 2

Possible arrays Different arrays for 24 1 row of 24

Possible arrays Different arrays for 24 24 rows of 1

Possible arrays Different arrays for 24 3 rows of 8

Possible arrays Different arrays for 24 8 rows of 3

Possible arrays Different arrays for 24 6 rows of 4

Possible arrays Different arrays for 24 4 rows of 6

Possible arrays Different arrays for 24 8 rows of 3

Possible arrays Different arrays for 24 3 rows of 8

Possible arrays Different arrays for 24 1 row of 24

Possible arrays Different arrays for 24 2 rows of 12