Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  • Level: GCSE
  • Subject: Maths
  • Essay length: 941 words

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 essay...

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

Middle

99 100 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. A 9x9 number grid If you choose any 2x2 box on a 9x9 number grid then the difference should equal 9... 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

Conclusion

For a 3x3 box N(N+20)=N2+20N (N+2)(N+18)=N2+20N+36 As before the difference equals 20. From these results we can work out that, if S is the size of the square, then these are the results. For a SxS box N[N+10(S-1)]=N2+10(S-1)N [N+(S-1)][N+9(S-1)] The difference as an expression would be: =N2+9(S-1)N+(S-1)N+9(S-1)2 =N2+10(S-1)+9(S-1)2 Difference=9(S-1)2 N[N+(G+1)x(S-1)=N2+(G+1)x(S-1)N [N+(S-1)][N+G(S-1)] =N2+(S-1)G(S-1)+NG(S-1)+N(S-1) =N2+ (S-1)2 +N(S-1)(9+1) When G = the grid size and S = square size The formula is G(S-1)2 Rectangle This rectangle is of length L and of width W. For a grid of 10x10. N[N+(L-1)+10(W-1)]=N2+(L-1)N+10(W-1)N [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!

The above preview is unformatted text

Found what you're looking for?

  • Start learning 29% faster today
  • Over 150,000 essays available
  • Just £6.99 a month

Here's what a teacher thought of this essay

4 star(s)

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

Not the one? Search for your essay title...
  • Over 180,000 student essays
  • Every subject and level covered
  • Thousands of essays marked by teachers
  • Over 180,000 essays
    written by students
  • Annotated by
    experienced teachers
  • Ideas and feedback to write
    your own great essays

Marked by a teacher

This essay has been marked by one of our great teachers. You can read the full teachers notes when you download the essay.

Peer reviewed

This essay has been reviewed by one of our specialist student essay reviewing squad. Read the full review on the essay page.

Peer reviewed

This essay has been reviewed by one of our specialist student essay reviewing squad. Read the full review under the essay preview on this page.