# Number Grid.

Extracts from this document...

Introduction

Mathematics Coursework 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 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 Using 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 top right numbers in the square. Calculate the difference between these numbers. I N V E S T I G A T E!!!! I am going to work out a formula to work out the difference between the top right and bottom left numbers, and top left and bottom right numbers. I will work out the difference to many different sized number squares with in the grid. I will change the shape of the number pattern and I will also change the size of the number grid itself. 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 This is the original number grid. ...read more.

Middle

N N+2 N+10 N+12 N(N+12) = N�+12N (N+10)(N+2) = N�+10N+2N+20 N�+12N - N�+12N+20 20 I have again come to the difference of 20. I will now try a 3 by 4 rectangle. 16 17 18 19 26 27 28 29 36 37 38 39 16 x 39 = 624 > 60 19 x 36 = 684 I have found the difference of 60. I will try a couple more to check this. 72 73 74 75 82 83 84 85 92 93 94 95 72 x 95 = 6840 > 60 92 x 75 = 6900 56 57 58 59 66 67 68 69 76 77 78 79 56 x 79 = 4424 >60 59 x 76 = 4484 I have come up with the difference of 60 for my rectangle 3 by 4 pattern. n n+3 n+20 n+23 N(N+23) = N�+23N (N+20)(N+3) = N�+3N+20N+60 N�+23n - N�+23N+60 60 The difference for a 3 by 4 number pattern is 60. I am now going to try out this formula to predict the difference for a 4 by 5 pattern. N N+4 N+30 N+34 N(N+34) = N�+34N (N+30)(N+4) = N�+4N+30N+120 N�+34N - N�+34N+120 120 I have found the difference of 120 for a 4 by 5 grid. I am going to check this. 35 36 37 38 39 45 46 47 48 49 55 56 57 58 59 65 66 67 68 69 35 x 69 = 2415 > 120 39 x 65 = 2535 1 2 3 4 5 11 12 13 14 15 21 22 23 24 25 31 32 33 34 35 1 x 35 = 35 > 120 5 x 31 = 155 I have checked my prediction and the difference is 120. I am now going to try a 5 by 6 grid. 1 2 3 4 5 6 11 12 13 14 15 16 21 22 23 24 25 26 31 32 33 34 35 36 41 42 43 44 45 46 1 x 46 = 46 > 200 6 x 41 = 246 I have come to the difference of 200. ...read more.

Conclusion

90 91 92 93 94 95 96 97 98 99 100 And this rule, Using 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 top right numbers in the square. Calculate the difference between these numbers. I need to find a general formula. The width of the number pattern subtract 1, multiply by the grid size, multiplied by the length subtract 1. (W-1)grid size(L-1) W = the width of the number pattern L = the length of the number pattern The grid size = the size of the number grid I am now going to use this formula and make a prediction and then test it to see if I am correct. I am going to use a number grid which is 10 by 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 (6-1)10(6-1) (5x10)5 50 x 5 = 250 I predict that the difference for a 6 by 6 pattern is 250. 23 24 25 26 27 28 33 34 35 36 37 38 43 44 45 46 47 48 53 54 55 56 57 58 63 64 65 66 67 68 73 74 75 76 77 78 23 x 78 = 1794 > 250 28 x 73 = 2044 I can see that my prediction was correct, I can see that my general formula is justified. 1 Simon Bedwell 11Q ...read more.

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

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