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

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Top Drawer Teachers: Splitting arrays into known parts

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- 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