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# Top Drawer Teachers: Splitting arrays into known parts

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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

1. 1. How might you split the array?
2. 2. How might you split the array?
3. 3. How might you split the array?I know 6rows of 5 is30.
4. 4. How might you split the array?I know 6rows of2 is 12.I know 6rows of5 is 30.
5. 5. How might you split the array?So 6 rows of 7 is 42. 6 × 7 = 42I know 6rows of5 is 30.I know 6rows of2 is 12.
6. 6. How might you split the array?Is there another way?
7. 7. How might you split the array?I know!6 rowsof 5 is 30
8. 8. How might you split the array?I know 5rows of7 is 35I know 5rows of7 is 35.
9. 9. How might you split the array?I know 5rows of7 is 35I know 5rows of7 is 35.I know 1row of 7is 7.
10. 10. How might you split the array?I know 5rows of7 is 35I know 5rows of7 is 35.I know 1rows of7 is 7. So 6 rows of 7 is 42. 6 × 7 = 42
11. 11. How might you split the array?Is there another way?
12. 12. How might you split the array?
13. 13. How might you split the array?I know 6rows of6 is 36.
14. 14. How might you split the array?I know 6rows of6 is 36.I know 6 rowsof 1 is 6.
15. 15. How might you split the array?I know 6rows of6 is 36.I know 6 rowsof 1 is 6.So 6 rows of 7 is 42.6 × 7 = 42
16. 16. How might you split the array?How could you split this array?
17. 17. 4 rows of 54 × 5 = 204 rows of 34 × 3 = 12How might you split the array?
18. 18. 4 rows of 54 × 5 = 204 rows of 34 × 3 = 12How might you split the array?4 rows of 84 × 8 = 32
19. 19. How might you split the array?Is there another way?
20. 20. How might you split the array?
21. 21. How might you split the array?4 rows of 44 × 4 = 164 rows of 44 × 4 = 16
22. 22. How might you split the array?4 rows of 44 × 4 = 164 rows of 44 × 4 = 164 rows of 84 × 8 = 32
23. 23. How might you split the array?4 rows of 44 × 4 = 164 rows of 44 × 4 = 164 rows of 84 × 8 = 32Splitting arrays into known parts provides anopportunity for square numbers to be identifiedand explored in relation to the original fact andlead to generalisations.
24. 24. Straws are useful to show theway an array has been split.8 × 4 = (4 × 4) + (4 × 4)How might you split the array?
25. 25. Use colour to show the differentways to split an array in to therelated known facts.This enables students to seeconnections such as doubling andhalving, and square numbers.How might you split the array?
26. 26. 3 × 10 + 3 × 23 rows of 12 3 × 12Splitting arrays into known facts
27. 27. (3 × 10) + (3 × 2)3 × 12(3 × 6) + (3 × 6)6 × 6Splitting arrays into known facts
28. 28. 3 × 12(3 × 4) + ( 3 × 4) + (3 × 4)6 × 6 (6 × 4) + (3 × 4)(5 × 4) + (4 × 4)Splitting arrays into known facts(3 × 10) + (3 × 2)(3 × 6) + (3 × 6)