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Investigative Maths Coursework We looked at a T-shape drawn on a nine width grid like this: 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 The total of the numbers inside the T-shape is called the T-total. 1 2 3 11 20 (1+2+3+11+20=37) The number at the end of the stem of the T-shape is the T-number. This remains the same even if you rotate the T-shape. Our first task was to translate the T-shape into different positions on the same sized grid and investigate the relationship between the T-total and T-number. n = T-number t = T-total (By 'difference between' I mean the amount added or subtracted to get to the next number in the second column) n t Difference between 5n 5n - t Therefore 5n - 63 20 37 100 63 t 21 42 5 105 63 t 22 47 5 110 63 t 23 52 5 115 63 t 24 57 5 120 63 t So the equation for finding the T-total anywhere on a nine width grid if you only know the T-number is 5n - 63 = t. You can prove his by using algebra: n-19 n-18 n-17 n-9 n n + (n - 9) + (n - 18) + (n - 17) + (n - 19) = 5n...

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