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

As part of my coursework I have chosen number grid.

Extracts from this document...

Introduction

As part of my coursework I have chosen number grid.

According to the task, I followed four steps in 10   10 grid

  1. A box is drawn round four numbers.
  2. Find the product of the top left number and the bottom right number.
  3. Do the same with the top right and bottom left number.
  4. Calculate the difference between these numbers.

The results are noted in the table below.

BOX

MULTIPLIED NUMBER

PRODUCT

DIFFERENCE

4          5

4       15

60

10

14       15

5      14

70

26       27

26     37

962

10

36       37

27     36

972

81       82

81     92

7452

10

91      92

91     82

7462

From the worked examples I find that the difference between the product found for the diagnol square in the 10      10  is 10.

From these results I predict that the difference between the next products in a diagnol square of 2    2 will be 10in 10    10 grid.

BOX

MULTIPLIED NUMBER

PRODUCT

DIFFERENCE

31     32

31     42

1302

10

41     42

32     41

1312

66     67

66     77

5082

10

76     77

67     76

5092

89     90

89     100

8900

10

99     100

90     99

8910

...read more.

Middle

4     37

148

90

24    25    25    26

7     34

238

34    35    36    37

21    22    23    24

31    32    33    34

21     54

1134

90

41    42    43    44

24     51

1224

51    52    53    54

56    57    58    59

66    67    68    69

56     89

4984

90

76    77    78    79

59     86

5074

86    87    88     89

The results show that the difference between the products in 4    4 square is 90.It is five times to the difference in 3    3 square.I predict that it will be true for next squares in 4    4 square in 10    10 grid.

BOX

MULTIPLIED NUMBER

PRODUCT

DIFFERENCE

7      8       9     10

17    18    19    20

7     40

280

27    28    29    30

10     37

370

90

37    38    39    40

33    34    35    36

43    44    45    46

33     66

2178

53    54    55    56

36     63

2268

90

63    64    65    66

46    47    48    49

56    57    58    59

46     79

3634

90

66    67    68    69

49     76

3724

76    77    78    79

The results show that the prediction was right.

What would be the difference in 5    5 square in this grid ?

BOX

MULTIPLIED NUMBER

PRODUCT

DIFFERENCE

4      5      6      7      8

14     15   16    17    18

24    25    26    27    28

4    48

192

160

34    35    36    37    38

8     44

352

44    45    46    47    48

11   12    13     14    15

21    22    23    24    25

31    32    33    34    35

11     55

605

160

41    42    43    44    45

15     51

765

51    52    53    54    55

26    27    28    29    30

36    37    38    39    40

46    47    48    49    50

26     70

1820

56    57    58    59    60

30     66

1980

160

66    67    68    69    70

The difference between the products is 160.

...read more.

Conclusion

THE SEQUENCE OF NUMBERS:  10, 40, 90, 160,

Position Number

1

2

3

4

Term

10

40

90

160

Difference

30

50

70

2nd Difference

20

20

The 2nd difference between the succesive terms is (+)20.So the nth term will be

DINO

Nth term = 20n – 10

               =10

4th term  = 20     4 – 10

              = 80 –10

             = 70

5th term = 20    5 – 10

                = 100 – 10

                = 90

10th term =  20    10 – 10

               = 200 – 10

                = 190

BOX

MULTIPLIED NO

PRODUCT

DIFFERENCE

x              x + 1

x(x + 11)

x + 11

10

x + 10       x + 11

(x + 1) (x + 10)

x + 10x + x +10

3    3 SQUARE

x            x + 1       x + 2

x(x + 22)

x + 22x

x + 10    x +11      x + 12

(x + 2) (x + 20)

x +22x +2x + 40

40

x +20    x + 21     x + 22

4    4  SQUARE

x           x + 1      x + 2   x + 3  

x + 10   x + 11    x + 12  x + 13

x(x + 33)

x + 33x

x + 20   x + 21    x + 22  x + 23

(x + 3) (x + 30)

x +30x + 3x + 90

90

x + 30   x +31     x + 32   x + 33

x         x + 1      x + 2     x + 3     x + 4

x +10  x + 11    x + 12    x + 13   x + 14

x(x + 44)

x + 44x

x +20   x +21   x + 22     x + 23  x + 24

(x + 4) (x +40)

x + 40x +4x + 160

160

x + 30   x + 31   x + 32   x + 33   x + 34

x +40   x + 41   x + 42    x + 43   x + 44

...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. Staircase Coursework

    57 58 59 60 41 42 43 44 45 46 47 48 49 50 31 32 33 34 35 36 37 38 39 40 21 22 23 24 25 26 27 28 29 30 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6

  2. Maths Coursework: Number Stairs

    = 15n + (229.1666667 + 0 + -9.166666674) = 15n + (229.1666667 + -9.166666674) = 15n + 220 15n + 220 = 15 * 1 + 220 = 15 + 220 = 235 The answer establishes the formula to be correct.

  1. Mathematics Layers Coursework

    of the grid when the number of empty squares on the first layer is greater than one. Method: I am going to use grids that are relatively small grid so that it is possible to draw a;; the combinations, then I am going to formulate a formula that works and test it.

  2. Number Grid Coursework

    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

  1. algebra coursework

    12+ (2-1) = 13 Z + 10(X-1) = 22 (bottom left number) 12 +10(2-1) = 22 Z+11(X-1) = 23 (bottom right number) 12+11(2-1) = 23 Z + 11 (X-1) = Z + 11X - 11 (bottom right number) Z (Z +11X -11) = Z� + 11XZ - 11Z Z + 10(X-1)

  2. Maths - number grid

    67x89 - 65x91 5963 - 5915 Difference = 48 17x39 - 15x41 663 - 615 Difference = 48 My prediction was correct. When investigating a 3x3 square from the 12x12 number grid the defined difference is 48.

  1. number grid

    The Difference for any 2 X 3 grid is always 20 within a 10 X 10 grid. 2 X 4 Grid Here is an algebraic grid for a 2 X 4 grid within a 10 X 10 grid. a a+3 a+10 a+13 Therefore: a(a + 13)

  2. Mathematical Coursework: 3-step stairs

    3+4+5+13+14+23= 62 91 92 93 94 95 96 97 98 99 100 81 82 83 84 85 86 87 88 89 90 71 72 73 74 75 76 77 78 79 80 61 62 63 64 65 66 67 68 69 70 51 52 53 54 55 56 57 58

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