• 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 2x2 cutout anywhere on the 10x10 grid by implementing the use of simple algebra. I can call the top left number in the cutout n, the top right number n + 1, the bottom left number n + 10 and the bottom right n + 11, as this is

  2. Algebra Investigation - Grid Square and Cube Relationships

    n+2(w-1)+2g(h-1) Simplifies to: n n+2w-2 n+2gh-2g n+2w+2gh-2g-2 Stage A: Top left number x Bottom right number = n(n+2w+2gh-2g-2) = n2+2nw+2ghn-2gn-2n Stage B: Bottom left number x Top right number = (n+2gh-2g)(n+2w-2) = n2+2nw-2n+2ghn+4ghw-4gh-2gn-4gw+4g = n2+2nw+2ghn-2gn-2n+4ghw-4gh-4gw+4g Stage B - Stage A: (n2+2nw+2ghn-2gn-2n+4ghw-4gh-4gw+4g)-(n2+2nw+2ghn-2gn-2n)

  1. Maths - number grid

    4 90 10 x 9 10 x 3 5 x 5 160 10 x 16 10 x 4 6 x 6 250 10 x 25 10 x 5 7 x 7 360 10 x 36 10 x 6 8 x 8 490 10 x 49 10 x 7 9 x

  2. Maths-Number Grid

    I will firstly begin, by multiplying together the bottom left number which is 45 by the top right number which is 9, The product comes to 405. I will then work out the next product number by multiplying together the bottom right number by the top left number, which gives me a result of 245.

  1. Investigate The Answer When The Products Of Opposite Corners on Number Grids Are Subtracted.

    - N�(N- N + 1) This is a bit complicated so if I multiply out the brackets and simplify, the formula will be: A = N (1 + N� - N) - N�(1 + N - N) = N + N� - N� - N� = N� - N� + N - N� A =

  2. Maths Grids Totals

    22 31 32 33 11 x 31 = 343 9 x 33 = 299 343 - 299 = 44 4 x 4 squares: 83 84 85 86 94 95 96 97 105 106 107 108 116 117 118 119 86 x 116 = 9976 83 x 119 = 9877 9976

  1. 100 Number Grid

    I will prove this prediction using an algebraic formula: X X + 1 X + 2 X + 10 X + 11 X + 12 X + 20 X + 21 X + 22 Step 1. x (x + 22)

  2. number grid

    2 X 2 Grid I have chosen the top left number of the square randomly. I have done this by using the random number function on my calculator. In my investigation I am going to find the product of the top left number and the bottom right number.

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