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

2. 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 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 ? 5 × 4 and 3 × 4 6 × 4 and 2 × 4 7 × 4 and 1 × 4 5 fours are 20 3 fours are 12 6 fours are 24 2 fours are 8 Facts within facts

5. 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 3 fours are 12 6 fours are 24 2 fours are 8 Facts within facts This can help work out 10 × 4 (which is double 5 × 4)

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 are 20 3 fours are 12 6 fours are 24 2 fours are 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 = 2828 ÷ 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. × 12345678910 14 28 312 448 162024283240 520 624 728 83264 9 1040 Facts within facts

17. × 12345678910 1 2 3 4 5 6 7 8 9 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, 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. Facts within facts

19. Going further: ideas and tips 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. Facts within facts

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

21. Going further: ideas and tips 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. Facts within facts