• 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
  • Level: GCSE
  • Subject: Maths
  • Word count: 2399

Number Grid.

Extracts from this document...

Introduction

Maths coursework. Number Grid. Introduction I have a number grid that ranges from 1 to 100 in rows and columns of ten. I have been given a box of four numbers, I was told to multiply the top left and then the bottom right then the bottom left and the top right. Below are the numbers that I choose. 12 13 22 23 I have been asked to find the products of: 12 23 13 22 . Then calculate the difference between the two results I have then been asked to investigate further. Plan 1. I plan to try some more boxes of 4 numbers to see how the results compare. 2. I am then going to try some bigger squares, rectangles, and different size number grids to see if I can find any number patterns emerging. 3. I will then put my answers and try to find the formulas for the boxes. 4. When I find the formulas I intend to test them out to see if they are correct. 5. I will then the formulas into algebraic form. 12 x 23 = 276 13 x 22 = 286 The difference between the products is 10. I will now try some more: 55 56 65 66 55 x 66 = 3630 56 x 65 = 3640 The difference is 10 again. ...read more.

Middle

28 X 53 = 1484 The difference is 150. I am now going to tabulate my answers so I can look for a pattern. Rows & Columns Difference 2 x 3 20 2 x 4 30 3 x 4 60 4 x 5 - 4 x 6 150 When I found that the column and row numbers squared times 10 wouldn't work on rectangles I searched for other numbers times 10. I started by looking at the differences to try and find patterns. After looking for ages I noticed that: Rows minus one and Columns minus one multiplied, then times by ten gives me the same answers as in table. This will imply that if I use the formula: (R-1) (C-1) x10 I should get the right answer; I am going to try with a 4 x 5 rectangle so I can complete my table. (R-1) (C-1) x10 (4 -1) (5-1) x10 (3 x 4) x10 12 x 10 = 120 I am going to check the answer with a number box. 4 5 6 7 8 14 15 16 17 18 24 25 26 27 28 34 35 36 37 38 4 x 38 = 152 8 x 34 = 272 The difference is 120 I am going to try again on an 8 x 5 box. ...read more.

Conclusion

(R-1) (C-1) x G (6-1) (3-1) x 13 (5 x 2) x 13 10 x 13 =130 This is the correct formula CONCLUSION Whilst doing the number grid I discovered the patterns as my coursework progressed. I discovered first that all my first set of answers with the squares were square numbers x 10, but when I put them into a table they were in the column above the square size which would be there square root. I made a formula up for squares which worked, but when I tried rectangles I could see it would not. After sitting there for ages looking at the results table I made for rectangles, I noticed that if you subtract 1 from the row size and 1 from the column size multiply the answer, and then multiply by 10; I got the same answers as in my table. I tried this out, it worked then I made a formula from it: (R-1) (C-1) x10. This worked until I changed the Grid size. I then discovered that the number of columns in the Grid changed the answer. To make my formula work for any square or rectangular box in any size Grid I had to change the end. My formula is: R = Rows in box C = Columns in box G = grid size (R -1) (C-1) x G. Row minus 1 times column minus 1 times the grid size (columns in the grid) Jack Jackson page 1 04/05/2007 Mathematics module 4 Jack Jackson ...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

    is the bottom-left number in the box, because it is always "z multiplied by [q - 1]" more than a; (a + z[q - 1] + [p - 1]) is the bottom-right number in the box, because it is "z multiplied by [q - 1]" plus "[p - 1]" more than a.

  2. Investigation of diagonal difference.

    calculating square cutouts on square grids as the cutouts of a rectangular grid have identical corner values to that of square grids when looking at grids with the same length. To check that my assumptions are correct I will calculate the diagonal difference of a 3 x 3 cutout from

  1. Maths - number grid

    going to again increase my rectangles to 6x4 as I did in chapter two. Furthering my investigation As can be seen the only trend I have found so far in this part of my investigation is that my defined differences are all multiples of 12, the reason I would say

  2. number grid

    Therefore: a(a + 33) = a� + 33a (a + 3)(a + 30) = a� + 33a + 90 (a� + 33a + 90) - (a� + 33a) = 90 According to this, the difference between the product of the top left number and the bottom right number, and the

  1. Mathematical Coursework: 3-step stairs

    49 50 51 52 53 54 55 56 41 42 43 44 45 46 47 48 33 34 35 36 37 38 39 40 25 26 27 28 29 30 31 32 17 18 19 20 21 22 23 24 9 10 11 12 13 14 15 16 1 2

  2. 100 Number Grid

    14 x 47 = 658 17 x 44 = 748 Product difference = 90 C. 53 x 86 = 4558 56 x 83 = 4648 Product difference = 90 D. 67 x 100 = 6700 70 x 97 = 6790 Product difference = 90 Based on this investigation, I predict

  1. The patterns

    (S-1)�x10=D (5-1)�x10=D 4�x10=D 16x10=D 160=D 1 2 3 4 5 6 7 8 9 10 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 32 33 34 35 36 37 38 39 40 1 42 43 44 45

  2. number grid investigation]

    Formula 1 Calculating a General Formula Using the Term 'n' The formulas stated above can also be used to calculate the general terms that would appear in a box with any selected top left number (n). To obtain the top right number, it is necessary to implement formula number 2

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