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Top Drawer Teachers: Possible Arrays

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

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

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Top Drawer Teachers: Possible 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 • 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