• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Investigating how the numbers worked on a number grid.

Extracts from this document...

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.

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

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Number Stairs, Grids and Sequences essays

  1. Number Grids Investigation Coursework

    = a2 + amw - aw + an + mnw - nw - mw - a + w - a2 - amw + aw - an + a = mnw - nw - mw + w = w (mn - n - m + 1) = w (m - 1)

  2. What the 'L' - L shape investigation.

    To do this I am going to look at the change in the L-Shape when it is rotated. I will start by doing a diagram of the four rotations that are possible using a standard L-Shape. 1 2 3 4 5 6 7 8 9 10 11 12 13 14

  1. Number Grid Coursework

    to the difference of the two products if I varied the length of the box, the width of the box and the grid width. Section 5: "p x q" Box on Width z Grid 1) Introduction Throughout this section, the variable q will be continue to be used to represent

  2. Investigation of diagonal difference.

    n n + 1 n + 4G n + 4G + 1 40 6 2 n n + 1 n + 5G n + 5G + 1 50 From analysing my table of results for vertically aligned cutouts I have noticed a relationship between the height of the cutout and

  1. Algebra Investigation - Grid Square and Cube Relationships

    = 30 When finding the general formula for any number (n), both answers begin with the equation n2+31n, which signifies that they can be manipulated easily. Because the second answer has +30 at the end, it demonstrates that no matter what number is chosen to begin with (n), a difference of 30 will always be present.

  2. Maths Grid Investigation

    =b x b + 8(a - 1) + (a - 1) = b + a - 1 x b + 8(a - 1) =b x b +8a - 8 + a - 1 = b + a - 1 x b + 8a

  1. GCSE Maths coursework - Cross Numbers

    =2g - 2 If I replace X, I get the following results. If X = 33 then [(33+10) - (33-10)] - [(33+1) - (33-1)] = [33+10 - 33+10] - [33+1 - 33+1] = 2x10-2 =18 If X=83 then [(83+10) - (83-10)] - [(83+1)

  2. Maths - number grid

    I will again increase the size of my rectangles and aim to come up with a major pattern. I will increase the size of my rectangles to 7x4, and with any luck this will help me reach my aim. 8x32 - 2x38 f 256 -76 Difference = 180 58x82 -

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work