• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  10. 10
    10
  11. 11
    11
  12. 12
    12
  13. 13
    13
  14. 14
    14
  15. 15
    15
  16. 16
    16
  17. 17
    17
  • Level: GCSE
  • Subject: Maths
  • Word count: 1987

Number Grids.

Extracts from this document...

Introduction

Number Grids The diagram shows a 10*10 grid, a rectangle has been shaded on the 10*10 grid. I will find the diagonal difference between the products of the numbers in the opposite corners of the rectangle. 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 Opposite numbers in the rectangle are:- 54 and 66 56 and 64 56*64=3584 54*66=3564 .�. The Diagonal Difference = 3584 - 3564 = 20 Study I have studied some more 3*2 rectangles and I have found this:- 12 13 14 22 23 24 12*24=288 14*22=308 Diagonal difference =308 - 288=20 74*86=6364 76*84=6384 Diagonal difference =6384 - 6364=20 74 75 76 84 85 86 27*39=1053 29*37=1073 Diagonal difference =1073 - 1053= 20 27 28 29 37 38 39 So from this I conclude that all 3*2 rectangles have a diagonal difference of 20. ...read more.

Middle

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 I will begin by doing some 3*2 rectangles 21*32= 672 23*30=690 Diagonal difference=690 - 672 =18 21 22 23 30 31 32 57*68= 3876 59*66=3894 Diagonal difference=3894 - 3876 =18 57 58 59 66 67 68 So I conclude that all 3*2 squares on a 9*9 grid have a diagonal difference of 18. I have tested the other way by using a 2*3 rectangle. 1*20=20 2*19=38 Diagonal difference = 38 - 20 = 18 1 2 10 11 19 20 40*59=2360 41*58=2378 Diagonal difference = 2378 - 2360 = 18 40 41 49 50 58 59 So all 3*2 and 2*3 squares have a diagonal difference of 18. I will study more rectangles on a 9*9grid and then draw up a table. ...read more.

Conclusion

3*2 rectangle on an 8*8 grid I use my formula to predict that: - (3-1)*(2-1)*8 =2*1*8 =16 2*12=24 4*10=40 Diagonal difference = 40 - 24=16 2 3 4 10 11 12 My prediction is right. So using my formula I predict that a 3*3 square on an 8*8 grid will be (X-1)*(X-1)*8 (3-1)*(3-1)*8 =2*2*8 =32 46*64=2944 48*62=2976 Diagonal difference = 2976 - 2944 =32 46 47 48 54 55 56 62 63 64 So my prediction and formula are also right. A pattern A pattern has shown up in the formulas so I made this table: - Grid rectangle Formula 10*10 (R-1)*(C-1)*10 9*9 (R-1)*(C-1)*9 8*8 (R-1)*(C-1)*8 7*7 (R-1)*(C-1)*7 6*6 (R-1)*(C-1)*6 5*5 (R-1)*(C-1)*5 Grid Square Formula 10*10 (X-1)*(X-1)*10 9*9 (X-1)*(X-1)*9 8*8 (X-1)*(X-1)*8 7*7 (X-1)*(X-1)*7 6*6 (X-1)*(X-1)*6 So on a 6*6 grid I would expect a 3*2 rectangle to be: - (3-1)*(2-1)*6 =2*1*6 =12 So 8*16=128 10*14=140 Diagonal difference = 140 - 128 =12 8 9 10 14 15 16 Also a 3*3 square on a 6*6 grid would be: - (X-1)*(X-1)*6 => (3-1)*(3-1)*6 =2*2*6 =24 3*17=51 5*15=75 Diagonal difference = 75 - 51 =24 3 4 5 9 10 11 15 16 17 Both predictions and formulas are correct so I conclude that the overall formula is: - R= rows C= columns X= square N� G= grid Rectangle: - (R-1)*(C-1)*G ...AND... Square: - (X-1)*(X-1)*G ...read more.

The above preview is unformatted text

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

Found what you're looking for?

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

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Number Stairs, Grids and Sequences essays

  1. Investigation of diagonal difference.

    a trend for all of the 2x2 cutouts in a 10x10 grid. From this I will be able to calculate the diagonal difference of a cutout anywhere on the grid, as n is independent of where the cutout is on the grid.

  2. Algebra Investigation - Grid Square and Cube Relationships

    Instead, in order to ensure the grid could be used to calculate a cube or cuboid of any height, width and depth, with any step size, the original terms are used. n: The top left number of the front face grid.

  1. Investigate the differences between products in a controlled sized grid.

    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 I am now going to apply the formula I found for squares and see if it worked with rectangles.

  2. Investigate the diagonal difference of a 2 by 2 grid inside a 10 by ...

    know that the diagonal difference of two by two grids is 10, so I assume that if I did another square then I will get the answer of 10 because both grids have gave me an answer of 10, but just in case I will do a final two by two grid to prove that the diagonal difference is 10.

  1. Investigate the difference between the products of the numbers in the opposite corners of ...

    75 76 85 86 75 x 86 = 6450 76 x 85 = 6460 6460 - 6450 = 10 This has confirmed my results. I can now prove that no matter where a 2x2 square is on a 10x10 grid the difference remains at 10.

  2. Number Grids

    This leaves a gap of 2 x 73, which equals 142. This is, of course, with the top right hand corner number taken away from this total, but because the difference between 71 and 73 is 2 (and not 1), the number in the top hand corner that is taken away is doubled, to be '2 x 53' (106).

  1. Maths - number grid

    Again I am going to use algebra to prove that the defined difference of my 3x3 squares is correct. r (r+2) (r+20)(r+22) (r+2)(r+20)-(r+22)r =r (r+20)+2(r+20) - r -22r =r +20r+2r+40-r -22r =40 I have now calculated a trend for my 2x2 squares and came to a difference of 10 and

  2. Maths Grids Totals

    All of the differences are multiples of 9. The formula for the 10 x 10 grid was 10(n-1)2. Is it possible that the formula for a 9 x 9 grid is 9(n-1)2? A 2 x 2 square would be 9(n-1)2 = 9(2-1)2 = 9 x 1 = 9.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work