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Facts within facts

Facts within facts. If I know 2 × 4 = 8 what else do I know?. Facts within facts. If I know 2 × 4 = 8 what else do I know?. 2 × 4 = 8. Double 2 × 4 = 8 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.

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Facts within facts

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  1. Facts within facts If I know 2 × 4 = 8 what else do I know?

  2. Facts within facts If I know 2 × 4 = 8 what else do I know? 2 × 4 = 8. Double 2 × 4 = 8 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

  3. Facts within facts What other facts can you see in 8 × 4 ?

  4. Facts within facts What can I see in 8 × 4 ? 5 × 4 and 3 × 4 6 × 4 and 2 × 4 7 × 4 and 1 × 4 5 fours are 20 6 foursare 24 3 fours are 12 2 fours are 8

  5. Facts within facts What can I see in 8 × 4 ? 5 × 4 and 3 × 4 6 × 4 and 2 × 4 7 × 4 and 1 × 4 5 fours are 20 6 foursare 24 This can help work out 10 × 4 (which is double 5 × 4) 3 fours are 12 2 fours are 8

  6. 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 are 20 6 foursare 24 3 fours are 12 2 fours are 8

  7. Facts within facts Within 8 × 4 = 32 I can see: 5 × 4 and 3 × 4 What else can I see?

  8. Facts within facts 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

  9. Facts within facts Within 8 × 4 = 32 I can see: 6 × 4 and 2 × 4 What else can I see?

  10. Facts within facts What else can I see? Within 8 × 4 = 32 I can see: 6 × 4 and 2 × 4 4 × 6 = 24 24 ÷ 6 = 4 4 × 2 = 8 8 ÷ 2 = 4

  11. Facts within facts Within 8 × 4 = 32 I can see: 7 × 4 and 1 × 4 What else can I see?

  12. Facts within facts What else can I see? Within 8 × 4 = 32 I can see: 7 × 4 and 1 × 4 4 × 7 = 28 28 ÷ 7 = 4 4 × 1 = 4 4 ÷ 1 = 4

  13. Facts within facts If I double 8 and halve 4 what do I get? What else can I see?

  14. Facts within facts What else can I see? If I double 8 and halve 4 what do I get? 16 × 2 = 32

  15. Facts within facts What else can I see? If I double 8 and halve 4 what do I get? 16 × 2 = 32 Knowing this I also know: 2 × 16 = 32 32 ÷ 16 = 2 32 ÷ 2 = 16

  16. Facts within facts

  17. Facts within facts

  18. Facts within facts In pairs, students choose a known fact and use doubles and partitioning to record some related facts. For example, given 3 × 4, students could double one factor (3 in this case) to get 6 × 4. They could double the other factor to get 3 × 8.For some facts, they could halve one and double the other. Going further: ideas and tips

  19. Facts within facts Teaching tips Drawing the arrays on the grid provides a visual image of how the dimensions change 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. Going further: ideas and tips

  20. Facts within facts Build up a class list of multiplication facts on the multiplication grid generated by doubling and partitioning. Going further: ideas and tips

  21. Facts within facts Students may also explore the use of halving and doubling to work out tricky facts such as 7 lots of 8 and related division facts. For example, if I know 7 fours is 28, then I can double the fours to get 7 eights. Double the product of 28 gives 56, which is the product of 7 and 8. Going further: ideas and tips

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