• 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
  18. 18
    18
  19. 19
    19
  20. 20
    20
  • Level: GCSE
  • Subject: Maths
  • Word count: 3243

Number Grid.

Extracts from this document...

Introduction

Mathematics Coursework Number Grid 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 Using the following rule: Find the product of the top left number and the bottom right number in the square. Do the same thing with the bottom left and top right numbers in the square. Calculate the difference between these numbers. I N V E S T I G A T E!!!! I am going to work out a formula to work out the difference between the top right and bottom left numbers, and top left and bottom right numbers. I will work out the difference to many different sized number squares with in the grid. I will change the shape of the number pattern and I will also change the size of the number grid itself. 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 This is the original number grid. ...read more.

Middle

N N+2 N+10 N+12 N(N+12) = N�+12N (N+10)(N+2) = N�+10N+2N+20 N�+12N - N�+12N+20 20 I have again come to the difference of 20. I will now try a 3 by 4 rectangle. 16 17 18 19 26 27 28 29 36 37 38 39 16 x 39 = 624 > 60 19 x 36 = 684 I have found the difference of 60. I will try a couple more to check this. 72 73 74 75 82 83 84 85 92 93 94 95 72 x 95 = 6840 > 60 92 x 75 = 6900 56 57 58 59 66 67 68 69 76 77 78 79 56 x 79 = 4424 >60 59 x 76 = 4484 I have come up with the difference of 60 for my rectangle 3 by 4 pattern. n n+3 n+20 n+23 N(N+23) = N�+23N (N+20)(N+3) = N�+3N+20N+60 N�+23n - N�+23N+60 60 The difference for a 3 by 4 number pattern is 60. I am now going to try out this formula to predict the difference for a 4 by 5 pattern. N N+4 N+30 N+34 N(N+34) = N�+34N (N+30)(N+4) = N�+4N+30N+120 N�+34N - N�+34N+120 120 I have found the difference of 120 for a 4 by 5 grid. I am going to check this. 35 36 37 38 39 45 46 47 48 49 55 56 57 58 59 65 66 67 68 69 35 x 69 = 2415 > 120 39 x 65 = 2535 1 2 3 4 5 11 12 13 14 15 21 22 23 24 25 31 32 33 34 35 1 x 35 = 35 > 120 5 x 31 = 155 I have checked my prediction and the difference is 120. I am now going to try a 5 by 6 grid. 1 2 3 4 5 6 11 12 13 14 15 16 21 22 23 24 25 26 31 32 33 34 35 36 41 42 43 44 45 46 1 x 46 = 46 > 200 6 x 41 = 246 I have come to the difference of 200. ...read more.

Conclusion

90 91 92 93 94 95 96 97 98 99 100 And this rule, Using the following rule: Find the product of the top left number and the bottom right number in the square. Do the same thing with the bottom left and top right numbers in the square. Calculate the difference between these numbers. I need to find a general formula. The width of the number pattern subtract 1, multiply by the grid size, multiplied by the length subtract 1. (W-1)grid size(L-1) W = the width of the number pattern L = the length of the number pattern The grid size = the size of the number grid I am now going to use this formula and make a prediction and then test it to see if I am correct. I am going to use a number grid which is 10 by 10 grid. 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 (6-1)10(6-1) (5x10)5 50 x 5 = 250 I predict that the difference for a 6 by 6 pattern is 250. 23 24 25 26 27 28 33 34 35 36 37 38 43 44 45 46 47 48 53 54 55 56 57 58 63 64 65 66 67 68 73 74 75 76 77 78 23 x 78 = 1794 > 250 28 x 73 = 2044 I can see that my prediction was correct, I can see that my general formula is justified. 1 Simon Bedwell 11Q ...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. Number Grid Coursework

    Product 2 (TR x BL) Difference (P'duct 2 - P'duct 1) 5 195 228 33 17 867 900 33 24 1392 1425 33 36 2520 2553 33 43 3311 3344 33 b) Here are the results of the 5 calculations for 3x6 Box on Width 13 Grid: Top-Left Number Product 1 (TL x BR)

  2. Investigation of diagonal difference.

    n + (X - 1)G n + (X - 1)G + (X - 1) 1 1 + (2 - 1) = 2 1 + ((2 - 1) 10) = 11 1 + ((2 - 1)10) + (2-1) = 12 => The solutions give the correct final products and the corner

  1. Algebra Investigation - Grid Square and Cube Relationships

    = n+ (Height (h) - 1) x 10 n ~ n+w-1 ~ ~ ~ n+20 ~ n+20+w-1 The above grid simplifies to form: n ~ n+w-1 ~ ~ ~ n+20 ~ n+19+w Stage A: Top left number x Bottom right number = n(n+19+w)

  2. Maths Grid Investigation

    14 6 x 11 = 66 14 - 8 = 6 66 - 60 = 6 The diagonal Difference for a 2 x 2 grid inside a 6 x 6 grid = 6 1 2 3 4 5 7 8 9 10 11 13 14 15 16 17 19 20

  1. Maths - number grid

    This has happened because I have jumped in sizes of rectangles and have not kept to a pattern. I have shown my answers and difference between each below: 60 70 30 20 80 150 180 Furthering my investigation Still with the results I have I am unable to see any

  2. Mathematics - Number Stairs

    24 25 26 27 24 + 25 + 26 + 27 + 33 + 34 + 35 + 42 + 43 + 51 = 340 Algebraic Proof: n+27 n+18 n+19 n+9 n+10 n+11 n n+1 n+2 n+3 n + (n+1) + (n+2) + (n+3) + (n+9) + (n+10) + (n+11)

  1. 100 Number Grid

    X X + 1 X + 2 X + 3 X + 4 X + 10 X + 11 X + 12 X + 13 X + 14 X + 20 X + 21 X + 22 X + 23 X + 24 X + 30 X + 31 X

  2. number grid

    After looking at my table I have found out that the difference between, the product of the top left number and the bottom right number, and the product of the top right number and the bottom left number is always 10 in a 2 X 2 grid.

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