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Top Drawer Teachers: Facts within Facts

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

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If I know 2 × 4 = 8
what else do I know?
Facts within facts
2 × 4 = 8 double it gives 4 × 4 = 16
Double 4 × 4 = 16 gives 8 × 4 = 32
If I know 8 × 4 = 32
I know 4 × 8 =32
2 fours
are 8
4 fours
are 16 8 fours
are 32
Facts within facts
If I know 2 × 4 = 8
what else do I know?
What other facts can you see in 8 × 4 ?
Facts within facts
What can I see in 8 × 4 ?
Within 8 × 4 = 32 I can see:
5 × 4 and 3 × 4
6 × 4 and 2 × 4
7 × 4 and 1 × 4
5 fours
is 20
3
fours
is 12
6 fours
is 24
2
fours
is 8
Facts within facts
What can I see in 8 × 4 ?
Within 8 × 4 = 32 I can see:
5 × 4 and 3 × 4
6 × 4 and 2 × 4
7 × 4 and 1 × 4
This can help work out:
10 × 4 (double 5 × 4)
5 fours
is 20
3
fours
is 12
6 fours
is 24
2
fours
is 8
Facts within facts
What can I see in 8 × 4 ?
If I double 8 × 4 = 32
I get 8 × 8 = 64
What can this help me
to work out?
5 fours
is 20
3
fours
is 12
6 fours
is 24
2
fours
is 8
Facts within facts

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Top Drawer Teachers: Facts within Facts

  • 1. If I know 2 × 4 = 8 what else do I know? Facts within facts
  • 2. 2 × 4 = 8 double it gives 4 × 4 = 16 Double 4 × 4 = 16 gives 8 × 4 = 32 If I know 8 × 4 = 32 I know 4 × 8 =32 2 fours are 8 4 fours are 16 8 fours are 32 Facts within facts If I know 2 × 4 = 8 what else do I know?
  • 3. What other facts can you see in 8 × 4 ? Facts within facts
  • 4. What can I see in 8 × 4 ? Within 8 × 4 = 32 I can see: 5 × 4 and 3 × 4 6 × 4 and 2 × 4 7 × 4 and 1 × 4 5 fours is 20 3 fours is 12 6 fours is 24 2 fours is 8 Facts within facts
  • 5. What can I see in 8 × 4 ? Within 8 × 4 = 32 I can see: 5 × 4 and 3 × 4 6 × 4 and 2 × 4 7 × 4 and 1 × 4 This can help work out: 10 × 4 (double 5 × 4) 5 fours is 20 3 fours is 12 6 fours is 24 2 fours is 8 Facts within facts
  • 6. What can I see in 8 × 4 ? If I double 8 × 4 = 32 I get 8 × 8 = 64 What can this help me to work out? 5 fours is 20 3 fours is 12 6 fours is 24 2 fours is 8 Facts within facts
  • 7. What else can I see? Within 8 × 4 = 32 I can see: 5 × 4 and 3 × 4 Facts within facts
  • 8. What else can I see? Within 8 × 4 = 32 I can see: 5 × 4 and 3 × 4 4 × 5 = 20 20 ÷ 5 = 4 4 × 3 = 12 12 ÷ 3 = 4 Facts within facts
  • 9. What else can I see? Within 8 × 4 = 32 I can see: 6 × 4 and 2 × 4 Facts within facts
  • 10. What else can I see? Within 8 × 4 = 32 I can see: 6 × 4 and 2 × 4 Facts within facts 4 × 6 = 24 24 ÷ 6 = 4 4 × 2 = 8 8 ÷ 2 = 4
  • 11. What else can I see? Within 8 × 4 = 32 I can see: 7 × 4 and 1 × 4 Facts within facts
  • 12. What else can I see? Within 8 × 4 = 32 I can see: 7 × 4 and 1 × 4 Facts within facts 4 × 7 = 28 28 ÷ 7 = 4 4 × 1 = 4 4 ÷ 1 = 4
  • 13. What else can I see? If I double 8 and halve 4 what do I get? Facts within facts
  • 14. What else can I see? If I double 8 and halve 4 what do I get? Facts within facts 16 × 2 = 32
  • 15. What else can I see? If I double 8 and halve 4 what do I get? Facts within facts 16 × 2 = 32 Knowing this I also know: 2 × 16 = 32 32 ÷ 16 = 2 32 ÷ 2 = 16
  • 16. × 1 2 3 4 5 6 7 8 9 10 1 4 2 8 3 12 4 4 8 12 16 20 24 28 32 40 5 20 6 24 7 28 8 32 64 9 10 40 Facts within facts
  • 17. × 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Facts within facts
  • 18. Going further ideas and tips • In pairs, students choose a known fact and use doubles and partitioning to record some related facts. For example, given 3 × 4, doubling one factor (3 in this case) to get 6 × 4, doubling and halving both factors to get 3 × 8. Teaching tips Drawing the arrays on the grid provides a visual image of how the dimensions when one factor is doubled. It can also show ways to partition the array. Recording the product on the multiplication grid provides the link between the visual and the symbolic representation. Facts within facts
  • 19. Going further ideas and tips • Build up a class list of multiplication facts on the multiplication grid generated by doubling and partitioning. • Students may also explore use of halving and doubling to work out tricky facts such as 7 eights and related division facts. For example, if I know 7 fours is 28 then I double the fours get 7 eights. Double the product of 28 to get 56 (i.e. 7× 8). Facts within facts