# Number grids. In this investigation I have been attempting to work out a formula that will find the difference between the products of the top left and bottom right of a number grid and the top right and bottom left of a number grid.

Extracts from this document...

Introduction

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 | 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 | 79 | 80 |

81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 |

91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |

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 |

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 | 79 | 80 | 81 |

In this investigation I have been attempting to work out a formula that will find the difference between the products of the top left and

Middle

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A 10x10 number grid

If you choose any 2x2 box on a 10x10 number grid then the difference should equal 10…

35x46=1610

Difference=10

36x45=1620

The difference equals 10. So what would happen if you tried the same thing with a 3x3 box?

37x19=703

Difference=40

17x39=663

The difference equals 40. So if you try it with a 4x4 box…

61x94=5734

Difference=90

91x64=5824

The difference equals 90. Lets just try one more:

55x99=5445

Difference=160

95x59=5605

We now have enough results.

Conclusion

[N+(L-1)+10(W-1)] [N+(L-1)]

N2+10(W-1)N+(L-1)N+

Difference=10(L-1)(W-1)

Rectangular grid= LxW

Difference =G(L-1)(W-1)

Finally we can work out how the change of multiples in the grid would affect the formula.

In this formula L=Length, W=width, M=multiple and G=grid size.

N[N+M(L-1)+MG(W-1)]

=N2+N(l-1)M+NMG(w-1)N

[N+M(L-1)][N+GM(W-1)]

N2+NGM(W-1)+NM(L-1)+

This formula is the final part of this investigation. I cannot think of another way to extend my investigation. This investigation has enlightened me to the real-life ways in which math’s can be applied. Previously I was not aware of how complicated and interesting number grids can be!

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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## Here's what a teacher thought of this essay

A well written piece of work with only a couple of minor errors. This piece of work shows an excellent application of multiplying double brackets. 4 stars ****

Marked by teacher Mick Macve 18/03/2012