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# Top Drawer Teachers: Possible Arrays

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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: Possible Arrays

1. 1. I wonder how many differentarrays you can make for 24?• Record all your thinking and thedifferent arrays on paper.• What are some interesting thingsyou notice?• How do you know if you havethem all?Possible arrays
2. 2. Noticing• What is the same about allthe arrays?• What is different about them?• What do you notice about thenumber of rows and number oftiles in each row?Possible arrays
3. 3. Teaching tips• Focusing their attention to thestructure and possibly to noticingthe commutative facts in eachinstance, e.g., 6 × 4 and 4 × 6.• This might prompt a discussionof 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 noticingrelationships in factor pairs, e.g.,6 × 4 = 3 × 8 (doubling and halving).Possible arrays
4. 4. • If such connections are not forthcomingfrom students, list all the facts for 24vertically 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 connectionsbetween them.• Having the visual of each array will alsoassist them to see the doubling and halvingrelationship.Teaching tipsPossible arrays
5. 5. 4 rows of 6Possible arraysDifferent arrays for 24
6. 6. Possible arraysDifferent arrays for 246 rows of 4
7. 7. Possible arraysDifferent arrays for 242 rows of 12
8. 8. Possible arraysDifferent arrays for 2412 rows of 2
9. 9. Different arrays for 241 row of 24Possible arrays
10. 10. Different arrays for 2424 rows of 1Possible arrays
11. 11. Different arrays for 243 rows of 8Possible arraysPossible arrays
12. 12. Different arrays for 248 rows of 3Possible arraysPossible arrays
13. 13. Different arrays for 246 rows of 4Possible arrays
14. 14. Different arrays for 244 rows of 6Possible arrays
15. 15. Different arrays for 248 rows of 3Possible arrays
16. 16. Different arrays for 243 rows of 8Possible arrays
17. 17. Different arrays for 241 row of 24Possible arrays
18. 18. Different arrays for 242 rows of 12Possible arrays