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  • 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.

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