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Number Grid Maths Coursework Introduction In this investigation I will look at different number grids and different sized rectangles within these grids and try to explain the patterns and give algebraic equations for the results that are found during this investigation. In a grid a rectangle is drawn and then the product of the opposite corners is found and the difference is calculated. From this, and further investigation I will find these patterns and work out equations which can then be proven by numerical examples. Squares in a 10 x 10 grid In this first section of the investigation I will investigate what patterns can be found with 2x2, 3x3, 4x4 etc. squares in a 10x10 grid. Numerical Examples 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 Square Difference 12,13,22,23 (2x2) 10 84,85,94,95 (2x2) 10 41,43,61,63 (3x3) 40 78,80,98,100 (3x3) 40 44,47,74,77 (4x4) 90 7,10,37,40 (4x4) 90 Results From the number grid and table above I can therefore say that with every 2x2 square in a 10x10 grid that the difference is 10. I can also say that...

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