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# Number Grid Coursework.

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Introduction

Number Grid Coursework 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 99 100 Use the following rule: Find the product of the top left number and the bottom right number in the square. Do the same thing with the bottom left and the top right numbers in the square. Calculate the following difference between these numbers. INVESTIGATE! The first thing I'm going to do is work out the rule for a 10 x 10 grid. To do this I'm going to work out what the difference is between each row using 2 x 2, 3 x 3, 4 x 4, and 5 x 5 grids inside the main 10 x 10 one. 10 x 10 grid 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 99 100 2 x 2 3 x 3 23 x 14 = 322 33 x 15 = 495 13 x 24 = 312 difference = 10 13 x 35 ...read more.

Middle

627 30 x 39 = 1170 difference = 8 17 x 35 = 595 difference = 32 50 x 43 = 2150 62 x 48 = 2976 42 x 51 = 2142 difference = 8 46 x 64 = 2944 difference = 32 4 x 4 5 x 5 29 x 8 = 232 34 x 6 = 204 5 x 32 = 160 difference = 72 2 x 38 = 76 difference = 128 43 x 22 = 946 60 x 32 = 1920 19 x 46 = 874 difference = 72 28 x 64 = 1792 difference = 128 49 x 28 = 1372 41 x 13 = 533 25 x 52 = 1300 difference = 72 9 x 45 = 405 difference = 128 I can also work out these differences using algebra. 2 x 2 x x + 1 x + 8 x + 9 (x + 8)(x + 1) => x� + 9x + 8 (x)(x + 9) => x� + 9x difference = 8 3 x 3 x x + 1 x + 2 x + 8 x + 9 x + 10 x + 16 x + 17 x + 18 (x + 16)(x + 2) => x� + 18x + 32 (x)(x + 18) => x� + 18x difference = 32 4 x 4 x x + 1 x + 2 x + 3 x + 8 x + 9 x + 10 x + 11 x + 16 x + 17 x + 18 x + 19 x + 24 x + 25 x + 26 x + 27 (x + 24)(x + 3) => x� + 27x +72 (x)(x + 27) => x� + 27x difference = 72 5 x 5 x x + 1 x + 2 x + 3 x + 4 x + 8 x + 9 x + 10 x + 11 x + 12 x + 16 x + 17 x + 18 x + 19 x + 20 ...read more.

Conclusion

91 95 1 x 95 = 95 difference = 360 3 7 93 x 7 = 651 93 97 3 x 97 = 291 difference = 360 Rectangle: 2 x 5 3 x 5 4 x 5 6 x 5 7 x 5 8 x 5 9 x 5 10 x 5 40 80 120 200 240 280 320 360 * 4 8 12 20 24 28 32 36 /\ /\ /\ /\ /\ /\ /\ /\ Multiples: 1 4 2 4 3 4 5 4 6 4 7 4 8 4 9 4 *Here I can remove a factor of 10 from each difference. I can now use these to work out a general rule for rectangle grids on a 10 x 10 grid. 2 x 5 2 = width 5 = length 2 - 1 = 1 5 - 1 = 4 1 and 4 are multiples of 4 which is the difference of a 2 x 5 rectangle with a factor of 10 removed. 3 x 5 3 = width 5 = length 3 - 1 = 2 5 - 1 = 4 2 and 4 are multiples of 8 which is the difference of a 3 x 5 rectangle with a factor of 10 removed. 4 x 5 4 = width 5 = length 4 - 1 = 3 5 - 1 = 4 3 and 4 are multiples of 12 which is the difference of a 4 x 5 rectangle with a factor of 10 removed. Using these I can assume a general rule for finding the difference: (w-1)(l-1) but because I took a factor of 10 out all this would have to be multiplied by 10 10(w-1)(l-1) To show that this works I am going to use rectangles 6 x 5, 7 x 5 and 8 x 5. 6 x 5 10 x 5 x 4 = 200 7 x 5 10 x 6 x 4 = 240 8 x 5 10 x 7 x 4 = 280 ...read more.

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