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maths grid coursework

Extracts from this document...

Introduction

Maths coursework

i am going to investigate a pattern by taking a squares and rectangles and multiplying the top corners.

For squares 2x2, 3x3, 4x4, 5x5

for rectangles 2x3,24,2x5,3x2,3x4,3x5,4x2,4x3,4x5

 i will be doing this in a nine squared grid and a ten squared grid  

after my results if there is a pattern i will make a formula to describe the pattern

2x2 squares on 10 squared grid.

16

26        

15

25

16x25=400    400-390=10  

15x26=390

59

60

49

50

59x50=2950  2950-2940=10

49x60=2940

3x3

22

23

24

32

33

34

42

43

44

22x44=968   1008-268=40

24x42=1008

27

28

29

37

38

39

47

48

49

27x49=1323  1363-1323=40

47x29=1363

Algerbraic

equation.

Key

G= grid size

N= number

w= number of squares.

2x2 sqaure on a 10 size grid

n

n+(w-1)

n+g

n+(w-1)+g

3x3 sqaure on a 10 size grid

n

n+(w-2)

n+(w-1)

n+g

n+(w-2)+g

n+(w-1)+g

n+2g

n+(w-2) +2g

n+(w-1)+ 2g

...read more.

Middle

25

21x15=315 315-275=40

11x25=275

3x4

36

37

38

39

46

47

48

49

56

57

58

59

36x59=2124 2184-2124=60

56x39=2184

7

8

9

10

17        

18

19

20

27    

28

29

30

7x30=210   270-210=60

10x27=270

3x5

4

5

6

7

8

14

15

16

17

18

24

25

26

27

28

 4X28=112 192-112=80

8x24=192

61

62

63

64

65

71

72

73

74

75

81

82

83

84

85

61x85=5185 5265-5185=80

81x65=5265

4x2

8

9

18

19

28

29

38

39

8x39=312 342-312=30

9x38=342

4x3

6

8

7

16

17

18

26

27

28

36

37

38

6x38=228   288-228=60

8x36=288

4x5

65

66

67

68

69

75

76

77

78

79

85

86

87

88

89

95

96

97

98

99

99x65=6435  6555-6435=120

95x69=6555

RESULTS

Sides in squares

...read more.

Conclusion

9x24=216

216-162= 54

33x54=1782

36x51=1836

1836-1782=54

3x5

59 x 81=4779

77x63=4851

4851-4779=72

10x32=320

14x28=392

392-320=72

4x2

37x65=2405

38x64=2435

2435-2405=27

39x67=2613

40x66=2640

2640-2613=27

4x3

6x35=210

33x8=264

264-210=54

61x90=5490

63x88=5544

5490-5544=54

4x5

1x32=32

5x28=140

140-32=108

55x86=4730

59x82=4838

4838-4730=108

results

Side in squares

Difference between answers 9 squared

Difference between answers 10 squared

difference

2x3

18

20

2

2x4

27

30

3

2x5

36

40

4

3x2

18

20

2

3x4

54

60

6

3x5

72

80

8

4x2

27

30

3

4x3

54

60

6

4x5

108

120

12

With these results we can say that the formula is when m is the shortest side and n is the  longest side  (m-1)(n-1)x 9

 example 4x5

4= m 5=n   4-1x5-1=3x4=12  12x9=108

if a rectangle had a side of   14x45  14=m 45=n 14-1x45-1=13x44= 572

572 x 9=5148 would be the difference of the corners timed together  

evaluation

i believe i could have improved this experiment by using more resources and different shaped grids such as triangles to test my formula also i should have tested  each grid number  at least 4 times and used different sized grids.

...read more.

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