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If I know 2 × 4 = 8what else do I know?Facts within facts
2 × 4 = 8 double it gives 4 × 4 = 16Double 4 × 4 = 16 gives 8 × 4 = 32If I know 8 × 4 = 32I know 4 × 8 =322 foursare 84 fo...
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 × 46 × 4 and 2 × 47 × 4 and 1 × 45 foursis 203foursis 126...
What can I see in 8 × 4 ?Within 8 × 4 = 32 I can see:5 × 4 and 3 × 46 × 4 and 2 × 47 × 4 and 1 × 4This can help work out:1...
What can I see in 8 × 4 ?If I double 8 × 4 = 32I get 8 × 8 = 64What can this help meto work out?5 foursis 203foursis 126 f...
What else can I see?Within 8 × 4 = 32 I can see:5 × 4 and 3 × 4Facts within facts
What else can I see?Within 8 × 4 = 32 I can see:5 × 4 and 3 × 44 × 5 = 20 20 ÷ 5 = 44 × 3 = 12 12 ÷ 3 = 4Facts within facts
What else can I see?Within 8 × 4 = 32 I can see:6 × 4 and 2 × 4Facts within facts
What else can I see?Within 8 × 4 = 32 I can see:6 × 4 and 2 × 4Facts within facts4 × 6 = 24 24 ÷ 6 = 44 × 2 = 8 8 ÷ 2 = 4
What else can I see?Within 8 × 4 = 32 I can see:7 × 4 and 1 × 4Facts within facts
What else can I see?Within 8 × 4 = 32 I can see:7 × 4 and 1 × 4Facts within facts4 × 7 = 28 28 ÷ 7 = 44 × 1 = 4 4 ÷ 1 = 4
What else can I see?If I double 8 and halve 4 what do I get?Facts within facts
What else can I see?If I double 8 and halve 4 what do I get?Facts within facts16 × 2 = 32
What else can I see?If I double 8 and halve 4 what do I get?Facts within facts16 × 2 = 32Knowing this I also know:2 × 16 =...
× 1 2 3 4 5 6 7 8 9 101 42 83 124 4 8 12 16 20 24 28 32 405 206 247 288 32 64910 40Facts within facts
× 1 2 3 4 5 6 7 8 9 1012345678910Facts within facts
Going further ideas and tips• In pairs, students choose a known fact and usedoubles and partitioning to record some relate...
Going further ideas and tips• Build up a class list of multiplication factson the multiplication grid generated bydoubling...
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Top Drawer Teachers: Facts within Facts

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

Published in: Education, Technology
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Top Drawer Teachers: Facts within Facts

  1. 1. If I know 2 × 4 = 8what else do I know?Facts within facts
  2. 2. 2 × 4 = 8 double it gives 4 × 4 = 16Double 4 × 4 = 16 gives 8 × 4 = 32If I know 8 × 4 = 32I know 4 × 8 =322 foursare 84 foursare 16 8 foursare 32Facts within factsIf I know 2 × 4 = 8what else do I know?
  3. 3. What other facts can you see in 8 × 4 ?Facts within facts
  4. 4. What can I see in 8 × 4 ?Within 8 × 4 = 32 I can see:5 × 4 and 3 × 46 × 4 and 2 × 47 × 4 and 1 × 45 foursis 203foursis 126 foursis 242foursis 8Facts within facts
  5. 5. What can I see in 8 × 4 ?Within 8 × 4 = 32 I can see:5 × 4 and 3 × 46 × 4 and 2 × 47 × 4 and 1 × 4This can help work out:10 × 4 (double 5 × 4)5 foursis 203foursis 126 foursis 242foursis 8Facts within facts
  6. 6. What can I see in 8 × 4 ?If I double 8 × 4 = 32I get 8 × 8 = 64What can this help meto work out?5 foursis 203foursis 126 foursis 242foursis 8Facts within facts
  7. 7. What else can I see?Within 8 × 4 = 32 I can see:5 × 4 and 3 × 4Facts within facts
  8. 8. What else can I see?Within 8 × 4 = 32 I can see:5 × 4 and 3 × 44 × 5 = 20 20 ÷ 5 = 44 × 3 = 12 12 ÷ 3 = 4Facts within facts
  9. 9. What else can I see?Within 8 × 4 = 32 I can see:6 × 4 and 2 × 4Facts within facts
  10. 10. What else can I see?Within 8 × 4 = 32 I can see:6 × 4 and 2 × 4Facts within facts4 × 6 = 24 24 ÷ 6 = 44 × 2 = 8 8 ÷ 2 = 4
  11. 11. What else can I see?Within 8 × 4 = 32 I can see:7 × 4 and 1 × 4Facts within facts
  12. 12. What else can I see?Within 8 × 4 = 32 I can see:7 × 4 and 1 × 4Facts within facts4 × 7 = 28 28 ÷ 7 = 44 × 1 = 4 4 ÷ 1 = 4
  13. 13. What else can I see?If I double 8 and halve 4 what do I get?Facts within facts
  14. 14. What else can I see?If I double 8 and halve 4 what do I get?Facts within facts16 × 2 = 32
  15. 15. What else can I see?If I double 8 and halve 4 what do I get?Facts within facts16 × 2 = 32Knowing this I also know:2 × 16 = 3232 ÷ 16 = 232 ÷ 2 = 16
  16. 16. × 1 2 3 4 5 6 7 8 9 101 42 83 124 4 8 12 16 20 24 28 32 405 206 247 288 32 64910 40Facts within facts
  17. 17. × 1 2 3 4 5 6 7 8 9 1012345678910Facts within facts
  18. 18. Going further ideas and tips• In pairs, students choose a known fact and usedoubles and partitioning to record some relatedfacts.For example, given 3 × 4, doubling one factor(3 in this case) to get 6 × 4, doubling andhalving both factors to get 3 × 8.Teaching tipsDrawing the arrays on the grid provides a visualimage of how the dimensions when one factoris doubled.It can also show ways to partition the array.Recording the product on the multiplication gridprovides the link between the visual and thesymbolic representation.Facts within facts
  19. 19. Going further ideas and tips• Build up a class list of multiplication factson the multiplication grid generated bydoubling and partitioning.• Students may also explore use of halving anddoubling to work out tricky facts such as 7eights and related division facts.For example, if I know 7 fours is 28 then Idouble the fours get 7 eights. Double theproduct of 28 to get 56 (i.e. 7× 8).Facts within facts

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