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  • Level: GCSE
  • Subject: Maths
  • Word count: 1463

Number grids

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Introduction

Number grids On a grid number 1 to 100 I have a drawn a rectangle on the grid around the numbers 29, 30, 39 and 40. Then I have multiplied diagonally the opposite numbers in each corner of the rectangle. 1-100 number 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 30 31 32 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 29 30 39 40 On the grid I have located a 2 by 2 rectangle in a different area and I will see if there is any kind of pattern in the answers. I will place ma rectangle around the following numbers 45, 46, 55 and 56. 45 46 55 56 I have noticed a pattern between both of the answers as when I place the 2 by 2 rectangle on the number grid. ...read more.

Middle

22 23 24 25 32 33 34 35 800-770=30 As I predicted the difference would be 30, which it has turned out to be, as before I will check it using algebra. n n+1 n+2 n+3 n+10 n+11 n+12 n+13 I know that the difference will be 30 for any 2 by 4 rectangle drawn anywhere on the number grid. Now I am going to look at a 2 by 5 grid and see if the pattern carries as I increase the rectangle. If I'm correct the difference will be 40. 61 62 63 64 65 71 72 73 74 75 n n+1 n+2 n+3 n+4 n+10 n+11 n+12 n+13 n+14 As before I'm correct the pattern dose continue to carry on as it goes up n 10's each time. If I was to change the shape of the rectangle would it make a difference? I am going to look at the following grid sizes and see what happens: 3 by 2, 4 by 2 and 5 by 2 rectangles. 45 46 55 56 65 66 So far I have noticed that the difference is the same as the 2 by 3 rectangle. I will use algebra to check. n n+1 n+10 n+11 n+20 n+21 The difference between the 2 values is 20 again. ...read more.

Conclusion

55 56 57 58 59 65 66 67 68 69 75 76 77 78 79 85 86 87 88 89 n n+1 n+2 n+3 n+4 n+10 n+11 n+12 n+13 n+14 n+20 n+21 n+22 n+23 n+24 n+30 n+31 n+32 n+33 n+34 We have got a difference of 120 between the two values so I now have rule I will clearly show in how this rule works in a table by bring all my data together as I have looked at the different kinds of rectangles and worked out a pattern for each sequence. Size of Rectangle 1st differences 2nd differences (differences of differences ) Solution 2 x 2 10 +10 1x1x10=10 2 x 3 20 +10 1x2x10=20 2 x 4 30 +10 1x3x10=30 2 x 5 40 +10 1x4x10=40 +10 3 x 3 40 +20 2x2x10=40 3 x 4 60 +20 2x3x10=60 3 x 5 80 +20 2x4x10=80 +10 4 x 4 90 +30 3x3x10=90 4 x 5 120 +30 3x4x10=120 4 x 6 150 +30 3x5x10=150 I have showed how, the pattern seems to build up as we increase the rectangle by 1 row. I have added an extra column on the end which is the solution of the value of each difference found using a different multiplication as I have worked out in the solution column. The way I have worked out this is by taking away 1 less from each number of the size of each rectangle Sandeep Patel ...read more.

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