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Investigating how the numbers worked on a number grid.

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Introduction

Maths GCSE Coursework

Kaleigh Mills

Investigation

 I was given the task of investigating how the numbers worked on a number grid. This is what I did to find out:

I chose a grid of four numbers and I multiplied the Top Left (TL) by the Bottom Right (BR) then I did the same with the Top Right (TR) and the Bottom Left (BL). I then found out the difference between the two outcomes.

n

n+1  

n+10

n+

11

E.g.

12

13

22

23

44

45

54

55

After trying a few 2 x 2 grids I then went on to do some 3 x 3 grids.

n

n + 2

n + 20

n + 22

E.g.

61

62

63

71

72

73

81

82

83

5

6

7

15

16

17

25

26

27

n

n+3

n+ 30

n+

33

n(n + 33) = n2 + 33n

(n + 3)

...read more.

Middle

n+40
n+44

53

54

55

56

57

63

64

65

66

67

73

74

75

76

77

83

84

85

86

87

93

94

95

96

97

5

6

7

8

9

15

16

17

18

19

25

26

27

28

29

35

36

37

38

39

45

46

47

48

49

       After testing a lot of grids I have discovered that the rule for a square of any size is  

       (n-1)2x10. To prove this I am going to test it for a 6 x 6 grid.

Prediction

I predict that for a 6 x 6 grid the difference will always be 250.

For a 6 x 6 grid the algebraic formula is:

n(n + 55) = n2 + 55n

(n + 5)(n + 50) = n2 + 55n + 250

Difference = 250

Testing

2

3

4

5

6

7

12

13

14

15

16

17

22

23

24

25

26

27

32

33

34

35

36

37

42

43

44

45

46

47

52

53

54

55

56

57

By predicting what the outcome would be with

...read more.

Conclusion

6 x 6 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

7

8

13

14

22

23

24

28

29

30

34

35

36

After testing a few square grids from a 6 x 6 grid I found the differences to be 6 and 24, these are both multiples of 6. Therefore I have now proved that my prediction is correct.

...read more.

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