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Maths Coursework Robyn Hoaksey 11Oh - Algebra Number stairs Aim: My aim is to investigate patterns on number stairs. 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 S number Hypothesis 1 S number = 1 S Total = 1+2+3+11+12+21 = 50 I think that there will be a link between the S number and the S total. I am going to use algebra to explore this. S total = S+S+1+S+2+S+10+S+11+S+20 = 6S+44 S Number = 1 S Total = 50 S Total = 6x1+44 = 6+44 = 50 Why is it 6S? There are 6 boxes in the stairs shape. Why is it +44? Not sure yet, I will have to do some more working out. Hypothesis 2. I Will now change the grid size to 9x9 to see if there is a pattern. 73 74 75 76 77 78 79 80 81 64 65 66 67 68 69 70 71 72 55 56 57 58 59 60 61 62 63 46 47 48 49 50 51 52 53 54 37 38 39 40 41 42 43 44 45 28 29 30 31 32 33 34 35 36 19 20 21 22 23 24 25 26 27 10 11 12 13 14 15 16 17 18 1 2 3 4 5 6 7 8 9 S Number = 1 S Total = 46 Does it fit 6L+44? = 6L+44 = 6+44 = 50 - No it does not. T total = S+S+1+S+2S+18+ S+9+ S+10 = 6S+40 Does it work? 6x1+40 = 46 - S Total - Yes it does work. Is there a pattern yet?...

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