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

Number grids. In this investigation I have been attempting to work out a formula that will find the difference between the products of the top left and bottom right of a number grid and the top right and bottom left of a number grid.

Extracts from this document...

Introduction

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

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

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

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

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

image00.png

In this investigation I have been attempting to work out a formula that will find the difference between the products of the top left and

...read more.

Middle

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

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

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

A 10x10 number grid

If you choose any 2x2 box on a 10x10 number grid then the difference should equal 10…

35x46=1610image10.png

                        Difference=10

36x45=1620

The difference equals 10. So what would happen if you tried the same thing with a 3x3 box?

  37x19=703image01.png

                            Difference=40

  17x39=663

The difference equals 40. So if you try it with a 4x4 box…

61x94=5734image02.png

             Difference=90

91x64=5824

The difference equals 90. Lets just try one more:

55x99=5445image03.png

            Difference=160

95x59=5605image28.pngimage27.pngimage04.png

We now have enough results.

...read more.

Conclusion

2+(L-1)N+10(W-1)N

[N+(L-1)+10(W-1)] [N+(L-1)]

N2+10(W-1)N+(L-1)N+

Difference=10(L-1)(W-1)

Rectangular grid= LxW

Difference =G(L-1)(W-1)

Finally we can work out how the change of multiples in the grid would affect the formula.

In this formula L=Length, W=width, M=multiple and G=grid size.

image23.pngimage22.png

image24.png

image25.png

N[N+M(L-1)+MG(W-1)]

=N2+N(l-1)M+NMG(w-1)N

[N+M(L-1)][N+GM(W-1)]

N2+NGM(W-1)+NM(L-1)+

image26.png

This formula is the final part of this investigation. I cannot think of another way to extend my investigation. This investigation has enlightened me to the real-life ways in which math’s can be applied. Previously I was not aware of how complicated and interesting number grids can be!

...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

Here's what a teacher thought of this essay

4 star(s)

A well written piece of work with only a couple of minor errors. This piece of work shows an excellent application of multiplying double brackets. 4 stars ****

Marked by teacher Mick Macve 18/03/2012

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. GCSE Maths Sequences Coursework

    Then in the 3rd stage in the sequence, if you pair off the shaded squares into sets of 3 you are left with 4 sets of 3 squares. This tells us that if you multiply the stage number (N) by 4, you are given the amount of shaded squares in the shape.

  2. Number Grids Investigation Coursework

    + (11a - 11a) + 10 = 10 So I have proved that, in a 2 x 2 square, the difference between the products of the opposite corners will always equal 10 because the expression will cancel down to 10.

  1. Investigate the number of winning lines in the game Connect 4.

    Height (h) Width (w) No. of winning lines 1 4 1 1 5 2 1 6 3 1 7 4 1 w w-3 Therefore on a 1 x (w) board, the number of winning lines = w - 3 I then decided to alter the height of the grid, instead of constantly

  2. Number Grid Investigation.

    This proves algebraically that the difference in a 2 X 2 square is 10. What can be done now? Brainstorm * Vary the shape of box (square, rectangle) * Vary size of grid (width, shape) * Try different calculations. * Use a different pattern of numbers.

  1. Investigation of diagonal difference.

    common in all 2 x 2 cutouts on a 10 x 10 grid, I will calculate the diagonal difference of a further 2x2 cutout. What have I noticed? From these cutouts I have noticed that the diagonal difference of a 2 x 2 cutout is 10 and that the grid length is 10.

  2. Number stairs

    I am going to add the value inside the 3-step stair above so: Total= X +(x+20) + (x+10) + (x+11) + (x+1) + (x+2) = 44 As a result we can find the total value of 3-step stairs in a 10 by 10 Number Grid by using the algebra equation:

  1. Opposite Corners Investigation

    = 6 x 1 x 2 = 12. 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 8 10 14 16 10 x 14 = 140 8 x 16 = 128 Difference = 12 My equation is correct.

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

    the L-Sum and the L-Number I am going to times the difference of the L-Sum with the L-Number. Thus giving me 5L.The results show that the 1st difference is constant and therefore, the formula must consist of 5L. My results shown in table format are as follows: Number in sequence 5L Difference Sum of L-Shape (L-Sum)

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