• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  • Level: GCSE
  • Subject: Maths
  • Word count: 1769

Investigate the diagonal difference of a 2 by 2 grid inside a 10 by 10 grid

Extracts from this document...

Introduction

Naila Parveen        Maths Coursework        year 11

 Maths Coursework-Diagonal Difference

Introduction

I am given a 10 by 10 grid. I am going to find the diagonal difference of different size grids (For e.g. 3 by 3, 4 by 4) within the 10 by 10 grid, by multiplying the opposite corners which results in two answers, we then deduct these two to get a final answer for that size.

This is the grid that I will use to help me investigate.

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

Aim

I am going to investigate the diagonal difference of a 2 by 2 grid inside a 10 by 10 grid.  I will then try to find a formula which relates to the diagonal difference of each square, I will then further this investigation by trying to find the diagonal difference of an 11 by 11 grid and a 12 by 12 grid and find the formula and see if it is the same. I will also do an extension by doing a rectangle and a square and then find the diagonal difference and the formula for this.

I am going to find the formula by finding

...read more.

Middle

32

33

34

41

42

43

44

11 x 44 = 484

14 x 41 = 574

Diagonal difference: 90

Now I am going to try a 5 by 5 grid.

51

52

53

54

55

61

62

63

64

65

71

72

73

74

75

81

82

83

84

85

91

92

93

94

95

51 x 95 = 4845

55 x 91 = 5005

Diagonal difference: 160

Now I am going to try out work out the algebraic formula for working out the diagonal differences for all squares.

So for a 6 by 6 grid I predict that the diagonal difference would be; 250.

To show this I will do a number grid and also in algebra.

The general difference formula that I predict is (n-1)2 x 10.

Now to show that it works!

45

46

47

48

49

50

55

56

57

58

59

60

65

66

67

68

69

70

75

76

77

78

79

80

85

86

87

88

89

90

95

96

97

98

99

100

45 x 100 = 4500

50 x 95 = 4750

Diagonal difference: 250

Now to show this in an algebraic form.

x

x+1

x+2

x+3

x+4

x+5

x+10

x+11

x+12

x+13

x+14

x+15

x+20

x+21

x+22

x+23

x+24

x+25

x+30

x+31

x+32

x+33

x+34

x+35

x+40

x+41

x+42

x+43

x+44

x+45

x+50

x+51

x+52

x+53

x+54

x+55

(x+50) (x+5)-x(x+55)

          = x2+50x+5x+250-(x2+55x)image01.pngimage02.pngimage00.pngimage00.png

          = x2+55x+250-x2-55x

          = 250

My formula works. So if I were to do a 7 by 7 I would do 62x10.

Now I am going to put my results in a table.

Size of square

Differences

2 x 2

10

12x10

3 x 3

40

22x10

4 x 4

90

32x10

5 x 5

160

42x10

6 x 6

250

52x10

I have shown that for a 5 by 5 square grid you will have to 42x10 to get the answer, so if I wanted to do a 7 by 7 grid I would have to do; 62x10

7 x 7 it would be (7-1)2x10

                = 62 x 10

                =36 x 10

                =360

As I have said before that the general formula is:

(n-1)2x10

So the grid would look like this:image03.png

image04.png

Now I a going to try out the rectangular grids. For this I will try to use an algebraic formula for each grid.

I am going to start of with a 2 by 3 rectangular grid.  

35

36

37

45

46

47

35 x 47 = 1645

45 x 37 = 1665

Diagonal difference: 20

Now in algebra:

x

x+1

x+2

x+10

x+11

x+12

...read more.

Conclusion

Now I am going to try a 2 by 5 rectangular grid.

32

33

34

35

36

42

43

44

45

46

32 x 46= 1472

36 x 42= 1512

Diagonal difference: 40

x

x+1

x+2

x+3

X+4

x+10

x+11

x+12

x+13

x+14

(x+4) (x+10)-x(x+14)

                      = x2+14x+10x+40-(x2+14x)

                  = x2+14x+40-x2-14x

                  = 40

Now I am going to put my results in a table, for the working out that is shown above.

Sizes of rectangles

Width (w)

Length (L)

Differences

2

2

10

1 x 10

2

3

20

2 x 10

2

4

30

3 x 10

2

5

40

4 x 10

2 x L

10 (L-1)

(L-1)x10

During the investigation I have discovered that my research is correct and when I observed my results using algebra the outcomes were the same as to when I used numbers.

Now I am going to change the width to 3 and keep the length the same.

Now I am going to try a 3 by 4 rectangular grid.

65

66

67

68

75

76

77

78

85

86

87

88

65 x 88 = 5720

85 x 68 = 5780

5780-5730 = 60

Now I am going to try a 3 by 5 rectangular grid

63

64

65

66

67

73

74

75

76

77

83

84

85

86

87

63 x 87=5481

83 x 67=5561

Diagonal difference: 80

Now I am going to try a 3 by 6 rectangular grid.

63

64

65

66

67

68

73

74

75

76

77

78

83

84

85

86

87

88

68 x 83 = 5644

63 x 88 = 5544

Diagonal difference: 100

Now I am going to do a 3 by 7 rectangular grid.

22

23

24

25

26

27

28

32

33

34

35

36

37

38

42

43

44

45

46

47

48

22 x 48 = 1056

42 x 28 = 1176

Diagonal difference: 120

Now I am going to do a table to show my results.

Sizes of rectangles

Width (w)

Length (L)

Differences

3

4

60

6 x 10

3

5

80

8 x 10

3

6

100

10 x 10

3

7

120

12 x 10

3 x L

10 (L-1)

(L)x10

...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. Marked by a teacher

    I am going to investigate by taking a square shape of numbers from a ...

    4 star(s)

    72, 128, +24 +40 +56 +16 +16 nth term= 8n� The n is not the box size because for example if I put the 3x3 square in an 8x8 grid I will get 72. Unfortunately, this formula does not work but if I minus the box size by one I will then get 32 which is the right answer.

  2. Number Grid Investigation.

    * The formula for the nth term is 8n�. 9x 9 Grid: * The smallest square selection size 2x2 gives the result 9, which is the grid size. * The product difference an `difference between each difference` are all multiples of 9. * The increase between product difference and p.d.

  1. Number Grid Coursework

    9) Extension Having done this, I saw that my formula would only work for 2x2 boxes on a Width z grid. To improve the usefulness of my formula, I wondered what would happen to the difference of the two products if I varied the length of the box i.e.

  2. Number Grids Investigation Coursework

    = (a + 3) (a + 10) - a (a + 13) = a2 + 3a + 10a + 30 - a2 - 13a = a2 + 13a + 30 - a2 - 13a = (a2 - a2) + (13a - 13a) + 30 = 30 As I have proved the difference between the

  1. "Multiply the figures in opposite corners of the square and find the difference between ...

    31 32 33 34 35 41 42 43 44 45 1 x 45 = 45 5 x 41 = 205 205 - 45 = 160 x x + 1 x + 2 x + 3 x + 4 x + 10 x + 11 x + 12 x + 13

  2. Number Grid Investigation

    any affect on the overall difference that I am trying to calculate. In this case, the Number Gap (L) is 2 as it is an alternative number to the previous number gap that I have used in all of my experiments, 1, to calculate the various factors that I had been trying to find.

  1. Number Grid Investigation.

    = 20. Product difference = 20. My results in a 3 X 3 box showed a product difference of 40. In a 3 X 2 it is 20. I will now try this another two times to see if it is the same on any square taken from the grid.

  2. 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.

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