# maths grid coursework

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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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