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Opposite Corners Maths Coursework Investigation The aim of this investigation is to find out the difference between the products of numbers in the opposite corners of any rectangle that can be drawn on a 100 square. I shall start off researching the 2x3 rectangle and then working onto bigger ones. 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 2x3 Rectangle 7 8 9 17 18 19 1 2 3 11 12 13 88 89 90 98 99 100 1x13=13 88x100=8800 7x19=133 11x3=33 98x90=8820 17x9=153 20 20 20 Prediction I predict that when I multiply a 2x3 rectangle the opposite corners will have a difference of 20. 2x2 Rectangle (square) 72 73 82 83 4 5 14 15 33 34 43 44 4x15=60 33x44=1452 72x83=5976 14x5=70 43x34=1462 82x73=5986 10 10 10 Prediction I predict that when I multiply a 2x2 rectangle (square) the opposite corners will have a difference of 10. 2x4 Rectangle 1 2 3 4 11 12 13 14 67 68 69 70 77 78 79 80 24 25 26 27 34 45 36 37 24x37=888 1x14=14 67x80=5360 34x27=918 11x4=44 77x70=5390 30 30 30 I have noticed a pattern occurring each time the width increases, the difference increases by 10, by 1. Prediction Using the theory I predict that when I multiply a 2x4 rectangle the opposite corners will...

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