• 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.

    similar pattern as 2 x 2 cutouts on a 10 x 10 grid when using n. The top two numbers can still be represented as n and n + 1, because the top right number is always 1 more than the top left number.

  2. Algebra Investigation - Grid Square and Cube Relationships

    on any size grid, by implementing the formulae below to find a general calculation and grid rectangle. It is additionally possible to see that the numbers that are added to n (mainly in the corners of the grids) follow certain, and constant sets of rules, which demonstrates confirmation of a pattern.

  1. Maths - number grid

    28x91 - 21x98 2548 - 2058 Difference = 490 I will again use algebra to prove my defined difference of 490 for any given 8x8 square is correct. (r+7)(r+70)- r(r+77) r(r+70) +7 (r+70)- r -77r r +70r+7r+490-r -77r =490 I now feel that I have identified and proven a

  2. Maths-Number Grid

    I will begin this by multiplying 46 by 19 to give me a product of 874. I will continue to multiply the next 2 multiples which are 49 by 16 to give me a product of 784. Finally, I will subtract 874 away from 784 to give me a product difference of 90.

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

    (4 x 13) - (16 x 1) 52 - 16 = 36: Which is correct. Therefore the formula for number grids with equal side, with numbers increasing by one is: A = N (N�- N + 1) - N�(N- N + 1)

  2. Maths Grids Totals

    - 9877 = 99 37 38 39 40 48 49 50 51 59 60 61 62 70 71 72 73 40 x 70 = 2800 37 x 73 = 2701 2800 - 2701 = 99 5 x 5 squares: 4 5 6 7 8 15 16 17 18 19 26

  1. 100 Number Grid

    54 x 76 = 4104 56 x 74 = 4144 Product difference = 40 The results indicate that for every 3 x 3 square, the product difference is 40. Using these examples, I predict that for any 3 x 3 square on the number grid, the product difference will be 40.

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

    This method would be good because it will show me the diagonal difference of any square of any size, because I would just have to insert the value of n in the formula to find out the diagonal difference of that square, therefore I will not have to write out all the squares and work out the diagonal difference.

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