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Introduction

Planning What is your task about? What do you have to do? My task is to take a number grid, draw a square around four numbers, and work out the product of the top left corner and bottom right corner. I am to do the same for the top right and bottom left corner. I must then work out the formula for my calculations so it can apply to any four numbers in a square on that size grid. Have you got any questions you would like to add to the original tasks? After each section of results I will do an Analysis of my results to look for any kind of relationship forming. What will you do first? To begin with I will plan my results table and then begin work on my task analysis. What information or data will you need to collect in order to complete the task? The information I need to collect is the product of the top right and bottom left numbers in a two-by-two square on a ten-by-ten number grid. I will also need to find the product of the top right and bottom left numbers. I will then use these numbers to calculate an nth term. How much information do you think you will need to collect? I will need to take 3, 4 or 5 readings (depending on grid size) ...read more.

Middle

99 100 Numbers Top Left x Bottom Right Top Right x Bottom Left Difference 1, 2, 11, 12 1 x 12 = 12 2 x 11 = 22 10 26, 27, 36, 37 26 x 37 = 962 27 x 36 = 972 10 58, 59, 68, 69 58 x 69 = 4002 59 x 68 = 4012 10 73, 74, 83, 84 73 x 84 = 6132 74 x 83 = 6142 10 89, 90, 99, 100 89 x 100 = 8900 90 x 99 = 8910 10 n, n + 1, n + 10, n + 11 n(n + 11) = n2 + 11n (n + 1)(n + 10) = n2 + 11n + 10 10 1.2 - Seven-by-Seven Grid, Two-by-Two Square 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 Numbers Top Left x Bottom Right Top Right x Bottom Left Difference 1, 2, 8, 9 1 x 9 = 9 2 x 8 = 16 7 12, 13, 19, 20 12 x 20 = 240 13 x 19 = 247 7 25, 26, 32, 33 25 x 33 = 825 26 x 32 = 832 7 30, 31, 37, 38 30 x 38 = 1140 31 x 37 ...read more.

Conclusion

1, 3, 15, 17 1 x 17 = 17 3 x 15 = 45 28 4, 6, 18, 20 4 x 20 = 80 6 x 18 = 108 28 23, 25, 37, 39 23 x 39 = 897 25 x 37 = 925 28 33, 35, 47, 49 33 x 49 = 1617 35 x 47 = 1645 28 n, n + 2, n + 14, n + 16 n(n + 16) = n2 + 16n (n + 2)(n + 14) = n2 + 16n + 28 28 2.3 - Five-by-Five Grid, Three-by-Three Square 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 Numbers Top Left x Bottom Right Top Right x Bottom Left Difference 1, 3, 11, 13 1 x 13 = 13 3 x 11 = 33 20 13, 15, 23, 25 13 x 25 = 325 15 x 23 = 345 20 n, n + 2, n + 10, n + 12 n(n + 12) = n2 + 12n (n + 2)(n + 10) = n2 + 12n + 20 20 Results Analysis Two In this set of results I have realised that the difference between the two products is 4 times the grid size, i.e. on a 7x7 grid, with a 3x3 square, the difference will be 4x7. On a 5x5 grid with a 3x3 square, the difference will be 4x5. ...read more.

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