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Aim: To find any relationships and patterns in the total of all the numbers in 'Number Stairs', that might occur if this stair was in a different place on the grid. The 10 by 10 grid below is where I am to get all the information I need from to enable me to carry out this investigation. 91 92 93 94 95 96 97 98 99 100 81 82 83 84 85 86 87 88 89 90 71 72 73 74 75 76 77 78 79 80 61 62 63 64 65 66 67 68 69 70 51 52 53 54 55 56 57 58 59 60 41 42 43 44 45 46 47 48 49 50 31 32 33 34 35 36 37 38 39 40 21 22 23 24 25 26 27 28 29 30 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 Part One For other 3-stepped stairs, investigate the relationship between the stair total and the position of the stair shape on the grid. 91 92 93 94 95 96 97 98 99 100 81 82 83 84 85 86 87 88 89 90 71 72 73 74 75 76 77 78 79 80 61 62 63 64 65 66 67 68 69 70 51 52 53 54 55 56 57 58 59 60 41 42 43 44 45 46 47 48 49 50 31 32 33 34 35 36 37 38 39 40 21 22 23 24 25 26 27 28 29 30 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 By looking at this grid, the stair total is: 25 + (25+1) + (25+2) + (25+3) + (25+10) + (25+11) + (25+20) If we call 25, the number in the corner of the stair, 'x' then we get: X + (x + 1) + (x + 2) + (x + 3) + (x + 10) + (x + 11) + (x + 20) = 6x + 1 + 2 + 3 + 10 + 11 + 20...

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