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

Top Drawer Teachers: Facts within Facts

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Page 1: Top Drawer Teachers: Facts within Facts

If I know 2 × 4 = 8 what else do I know?

Facts within facts

Page 2: Top Drawer Teachers: 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?

Page 3: Top Drawer Teachers: Facts within Facts

What other facts can you see in 8 × 4 ?

Facts within facts

Page 4: Top Drawer Teachers: 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 × 4

5 fours is 20

3 fours is 12

6 foursis 24

2 fours is 8

Facts within facts

Page 5: Top Drawer Teachers: 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 × 4

This can help work out: 10 × 4 (double 5 × 4)

5 fours is 20

3 fours is 12

6 foursis 24

2 fours is 8

Facts within facts

Page 6: Top Drawer Teachers: 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 foursis 24

2 fours is 8

Facts within facts

Page 7: Top Drawer Teachers: Facts within Facts

What else can I see?

Within 8 × 4 = 32 I can see:5 × 4 and 3 × 4

Facts within facts

Page 8: Top Drawer Teachers: 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 = 44 × 3 = 12 12 ÷ 3 = 4

Facts within facts

Page 9: Top Drawer Teachers: Facts within Facts

What else can I see?

Within 8 × 4 = 32 I can see:6 × 4 and 2 × 4

Facts within facts

Page 10: Top Drawer Teachers: Facts within Facts

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 = 44 × 2 = 8 8 ÷ 2 = 4

Page 11: Top Drawer Teachers: Facts within Facts

What else can I see?

Within 8 × 4 = 32 I can see:7 × 4 and 1 × 4

Facts within facts

Page 12: Top Drawer Teachers: Facts within Facts

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 = 44 × 1 = 4 4 ÷ 1 = 4

Page 13: Top Drawer Teachers: Facts within Facts

What else can I see?

If I double 8 and halve 4 what do I get?

Facts within facts

Page 14: Top Drawer Teachers: Facts within Facts

What else can I see?

If I double 8 and halve 4 what do I get?

Facts within facts

16 × 2 = 32

Page 15: Top Drawer Teachers: Facts within Facts

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 = 3232 ÷ 16 = 2 32 ÷ 2 = 16

Page 16: Top Drawer Teachers: Facts within Facts

× 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

Page 17: Top Drawer Teachers: Facts within Facts

× 1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

Facts within facts

Page 18: Top Drawer Teachers: Facts within Facts

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

Page 19: Top Drawer Teachers: Facts within Facts

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