Maths Grid Investigation

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GCSE Maths Coursework

Task B

The Task

After looking at the table of numbers:

2

3

4

5

6

7

8

9

0

1

2

3

4

5

6

7

8

9

20

21

22

23

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25

26

27

28

29

30

31

32

33

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36

37

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45

46

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51

52

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54

55

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61

62

63

64

I will then investigate the diagonal difference of a 4x4 grid, 3x3 grid and 2x2 grid the numbers for these grids will be taken from the 8x8 grid above.

The way to investigate diagonal difference is shown in the example:

'Sarah writes down a 3x3 grid from the above table.'

0

1

2

8

9

20

26

27

28

'She notices that when you multiply the opposite corners the difference between the products is 32'

For example:

0 x 28 = 280

2 x 26 = 312

The diagonal difference is 312 - 280 = 32.

What I think will happen

I think that the diagonal difference will always be 32 with a 3x3 grid.

I think that the diagonal difference for a 2x2 grid will be 8 each time.
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I am also going to investigate the diagonal difference of a grid sized 4x4; I think the difference will be 72 each time.

I came to these conclusions by doing a series of preliminary investigations.

Preliminary Investigations

For a 3x3 grid:

2

3

9

0

1

7

8

9

x 19 = 19

3 x 17 = 51

51 - 19 = 32

46

47

48

54

55

56

62

63

64

...

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