• 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

    Where a = 16, p = 6, q = 7, and z = 23: I predict z x [p - 1][q - 1] = 23 x 5 x 6 = 690 Difference = (a + [p - 1])(a + z[q - 1])

  2. Investigation of diagonal difference.

    7 x 8 grid 7 x 7 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

  1. Algebra Investigation - Grid Square and Cube Relationships

    The bottom right number in the rectangle is directly linked to the top right and bottom left numbers. It is the sum of these that equal the bottom right, or: Formula 1: Bottom Right (BR) = Top Right (TR) + Bottom Left (BL)

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

    In a square the number of rows and columns is the same. However it a rectangle they are different so two different letters will need to be allocated to the number of Rows and the number of Columns. I am now going to investigate further.

  1. Number Grid Investigation

    I will now investigate 3 x 3 squares on an 8 x 8 grid. 22 23 24 30 31 32 38 39 40 22 x 40 = 880 Difference= 32 24 x 38 = 912 I know that will be same for all the 3 x 3 squares on the number grid so I will now prove this using algebra.

  2. Number Grid Investigation.

    Question ?? Will this still be the same if I changed the depth? Maybe if I did say, 3 X 4 or 3 X 6 for example. Let's see... 3 X 4 square inside 10 wide grid. Here is a 3 X 4 square taken from a 10 wide grid.

  1. What the 'L' - L shape investigation.

    As part of my investigation is to find the relationship between the L-Sum and the L-Number I am going to times the difference of the L-Sum with the L-Number.

  2. Maths - number grid

    Chapter Two My initial investigation was looking at various squares randomly selected from the provided 10x10 grid. To make my investigation more interesting I am going to repeat my previous process except this time I will be using rectangles. I predict with rectangles that I will get a different result

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