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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

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

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.

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

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