# Grid coursework - This 2 by 2 grid was taken from a 10 by 10 grid.

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Introduction

Maths Coursework

By Mohammad Arsalan 11eah Date 4/7/03

This 2by2 grid was taken from a 10by10 grid.

12 13 2by2 Grid

22 23

12 13 I am going to multiply the number diagonally……

22 23

So….

12 x 23 = 276 (answer)

13 x 22 = 286 (answer)

Now I am going to subtract the answers like so.

286-276=10 now I am going to do another 2by2 grid.

32 33

42 43

32 x 43 = 1376

33 x 42 = 1386

1386-1376=10

Both 2by2 grids have produced the same answer, but I will do more 2by2 grids to be sure.

46 47

56 57

46 x 57 = 2622

47 x 56 = 2632

2622- 2632 = 10

On my third attempt my answer for the 2by2 grid hasn’t changed. This means that every 2by 2 grid will produce the same answer.

3by3 Grids

Now I am going to do a 3by3 grid taken from the main 10by10 grid and do exactly the same as I did with the 2by2 grid. Remember all the grids are chosen at random.

Middle

3by3 40

4by4 90 n x n=

5by5 160

Now I am going to make a 9by9 grid and randomly select grids from it

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 From this 9by9 grid I am going to take a

19 20 21 22 23 24 25 26 27 2by2 grid like I did with the 10by10 grid.

28 29 30 31 32 33 34 35 36

37 38 39 40 41 42 43 44 45

46 47 48 49 50 51 52 53 54

55 56 57 58 59 60 61 62 63

64 65 66 67 68 69 70 71 72

73 74 75 76 77 78 79 80 81

This 2by2 grid was taken from the 9by9 grid above. We do exactly the same we did before. We are trying to find out if the answers match or if thee is a pattern.

Last time the answer was 10 lets see what the answer is now.

12 13

21 22

13 x 21 = 273

12 x 22 = 264

273-264 = 9 The answer is 9! The answer has changed because the last time I did a 2by2 grid the answer was 10. I will do some more 2by2 grids to be sure.

2by2 grid

30 31

39 40

31 x 39 = 1209

30 x 40 = 1200

1209-1200 = 9

1 2

10 11

2 x 10 = 20

1x 11 = 11

20-11= 9 The answer is again 9.

3by3 Grids

23 24 25

32 33 34

41 42 43

25 x 41 =1025

23 x 43 = 989

Conclusion

Now I am going to do a 4by4.

38 39 40 41

46 47 48 49

54 55 56 57

62 63 64 65

38 x 65= 2470

41 x 62= 2542

2470-2542= 72

35 36 67 38

43 44 45 46

51 52 53 54

59 60 61 62

35 x 62 =2170

38 x 59 =2242

2170-2242 = 72 the answer is the same as before.

5by5 grid

11 12 13 14 15

20 21 22 23 24

28 29 30 31 32

36 37 38 39 40

44 45 46 47 48

11 x 48 =528

15 x 44 =660

528-660= 132

1 2 3 4 5

9 10 11 12 13

18 19 20 21 22

26 27 28 29 30

34 35 36 37 38

1 x 38= 38

5 x 34= 170

38-170= 132

Grid difference

2by2 8

3by3 32

4by4 72

5by5 132 n x n=

I will continue to investigate by making a 7by7 grid

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 16 17 18 19 20 21

22 23 24 25 26 27 28

29 30 31 32 33 34 35

36 37 38 39 40 41 42

43 44 45 46 47 48 49

Now I am going to do a 2by2 grid using this 7by7 grid.

29 30

36 37

29x37 =1073

30x36 =1080

1073-1080=7 the answer is 7.

15 16

22 23

15 x 23= 345

16 x 22= 352

345-352= 7 The answer is again 7 which means the all the 2by2 grids in the 7by7 grid will give the same answer.

3by3 grids

31 32 33

38 39 40

45 46 47

31 x 47=1457

33 x 45=1485

1457-1485= 28

29 30 31

36 37 38

43 44 45

29 x 45=1305

31 x 43=1333

1305-1333=28 The answer is the same as before 28.

Now I am going to do a 4by4 grid.

11 12 13 14

18 19 20 21

25 22 23 24

32 33 34 35

11 x 35 = 385

14 x 32 = 448

297-448= 63

22 23 24 25

29 30 31 32

36 37 38 39

43 44 45 46

22 x 46 =1012

25 x 43 =1075

1012-1075=63

Now I am going to o a 5by5 grid.

15 16 17 18 19

22 23 24 25 26

39 30 31 32 33

36 37 38 39 40

43 44 45 46 47

15 x 47= 705

19 x 43= 817

705-817= 112

17 18 19 20 21

24 25 26 27 28

31 32 33 34 35

38 39 40 41 42

45 46 47 48 49

17 x 49= 833

21 x 45=945

833-945= 112 The answer remains the same.

Grid difference

2by2 7

3by3 28

4by4 63

5by5 112 n x n=

How did I get my rule?

1 2 3 4 5 6

7 8 9 10 11 12

13 14 15 16 17 18

19 20 21 22 23 24

25 26 27 28 29 30

31 32 33 34 35 36

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

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