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Aim: investigate the product difference of different size boxes and produce an algebraic formula. First I will draw a box around four numbers and find the product of the numbers cross opposite side of the corners of the square. The product is found by multiplying the top left number with the bottom right number in the box. Now do the same thing with the top right and the bottom left as shown in the diagram. 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 98 100 1 2 3 11 12 13 21 22 23 Product 1: 12 x 23 = 276 Product 2: 13 x 22 = 286 Now subtract the two products, to find the difference 286 - 276 = 10 I will use this method to calculate the difference of more 2 by 2 boxes, chosen randomly in the big 10 by 10 grid. 2 by 2 Boxes Subtracting products Difference 1st 2832 - 2842 10 2nd 2530 - 2520 10 3rd 70 - 60 10 4th 682 - 672 10 5th 5986 - 5976 10 Now I will prove that the difference is 10...

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