grids

... Mariela Mezquita 10ª Math, Mr Bhoja 30 April 2008 COURSEWORK Aim: To find out a formula for rectangles on different grid sizes. That is done by multiplying the corners of the rectangle and then we subtract them. Hypothesis: Eg. (on a 10x10 grid size with a 2x3 rectangle) 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 72 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 3 x 11= 33 1 x 13=13 33-13 = 20 Then, move on the rectangle. A 2 x 3 cube... 1 2 3 11 12 13 2 3 4 12 13 14 3 4 5 13 14 15 As we can see, when we have a 2 x 3 rectangle, the final result will always be 20. Explanation: If we substitute the numbers by x we could find out the answer. x= 1 x x+2 x+10 x+12 x+2(x+10) x(x +12) Then we expand x+2(x+10) = x²+10x+2x+ 20 x(x +12) = x²+12x x²+10x+2x+ 20 x²+12x =20 The x² and the 12x cancel each other out leaving us with a result of 20. To find out more patterns, change the size of the rectangle. 1 2 3 4 11 12 13 14 21 22 23 24 2 3 4 5 12 13 14 15 22 23 24 25 It will always be 60.. Explanation: x x+3 x+20 x+23

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