# Investigating how the numbers worked on a number grid.

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Introduction

Maths GCSE Coursework

Kaleigh Mills

Investigation

I was given the task of investigating how the numbers worked on a number grid. This is what I did to find out:

I chose a grid of four numbers and I multiplied the Top Left (TL) by the Bottom Right (BR) then I did the same with the Top Right (TR) and the Bottom Left (BL). I then found out the difference between the two outcomes.

n | n+1 |

n+10 | n+ 11 |

E.g.

12 | 13 |

22 | 23 |

44 | 45 |

54 | 55 |

After trying a few 2 x 2 grids I then went on to do some 3 x 3 grids.

n | n + 2 | |

n + 20 | n + 22 |

E.g.

61 | 62 | 63 |

71 | 72 | 73 |

81 | 82 | 83 |

5 | 6 | 7 |

15 | 16 | 17 |

25 | 26 | 27 |

## n | n+3 | ||

n+ 30 | ## n+33 |

n(n + 33) = n2 + 33n

(n + 3)

Middle

##### n+40

##### n+44

53 | 54 | 55 | 56 | ## 57 |

63 | 64 | 65 | 66 | 67 |

73 | 74 | 75 | 76 | 77 |

83 | 84 | 85 | 86 | 87 |

## 93 | 94 | 95 | 96 | ## 97 |

5 | 6 | 7 | 8 | ## 9 |

15 | 16 | 17 | 18 | 19 |

25 | 26 | 27 | 28 | 29 |

35 | 36 | 37 | 38 | 39 |

## 45 | 46 | 47 | 48 | ## 49 |

After testing a lot of grids I have discovered that the rule for a square of any size is

(n-1)2x10. To prove this I am going to test it for a 6 x 6 grid.

Prediction

I predict that for a 6 x 6 grid the difference will always be 250.

For a 6 x 6 grid the algebraic formula is:

n(n + 55) = n2 + 55n

(n + 5)(n + 50) = n2 + 55n + 250

Difference = 250

Testing

2 | 3 | 4 | 5 | 6 | 7 |

12 | 13 | 14 | 15 | 16 | 17 |

22 | 23 | 24 | 25 | 26 | 27 |

32 | 33 | 34 | 35 | 36 | 37 |

42 | 43 | 44 | 45 | 46 | 47 |

52 | 53 | 54 | 55 | 56 | 57 |

By predicting what the outcome would be with

Conclusion

6 x 6 grid

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 |

7 | 8 |

13 | 14 |

22 | 23 | 24 |

28 | 29 | 30 |

34 | 35 | 36 |

After testing a few square grids from a 6 x 6 grid I found the differences to be 6 and 24, these are both multiples of 6. Therefore I have now proved that my prediction is correct.

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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