# For my investigation I will be finding out patterns and differences in a number grid.

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Introduction

Introduction For my investigation I will be finding out patterns and differences in a number grid. An example of a number grid that I am going to use for my investigation is shown below. Columns 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 28 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 Rows As you can see I will draw a box on the number grid and multiply the top left number with the bottom right number in the box. I will then do the same for the top right and the bottom left number. Once I have the sum for each multiplication I will then find the difference between the two calculations. I will different size of boxes e.g. 2x2 and 3x3; these numbers represent the number of numbers there are across the side of box and on top of the box. An example of this would be 4x4 means there is 4 numbers on the side and 4 numbers on the top as shown below. 1 2 3 4 11 12 13 14 21 22 23 24 31 32 33 34 Multiply the top left number with the bottom right number then do the same, multiply the bottom left number with the top right number. After this take both calculations and minus them both from each other. Plan For my plan I will firstly find out calculations for 2x2, 3x3, 4x4 and 5x5 squares and find out the differences for each set of boxes. ...read more.

Middle

I am predicting that the difference would be 240. 3 4 5 6 7 13 14 15 16 17 23 24 25 26 27 33 34 35 36 37 43 44 45 46 47 53 54 55 56 57 63 64 65 66 67 3 x 67 = 201 63 x 7 = 441 441 - 201 - 240 31 32 33 34 35 41 42 43 44 45 51 52 53 54 55 61 62 63 64 65 71 72 73 74 75 81 82 83 84 85 91 92 93 94 95 31 x 95 = 2945 91 x 35 = 3185 3185 - 2945 = 240 26 27 28 29 30 36 37 38 39 40 46 47 48 49 50 56 57 58 59 60 66 67 68 69 70 76 77 78 79 80 86 87 88 89 90 26 x 90 = 2340 86 x 30 = 2580 2580 - 2340 = 240 my prediction for my 6x7 and 7x6 will both be 300. I predict this because I just added 60 to the 6x5 and 5x6. 34 35 36 37 38 39 44 45 46 47 48 49 54 55 56 57 58 59 64 65 66 67 68 69 74 75 76 77 78 79 84 85 86 87 88 89 94 95 96 97 98 99 34 x 99 = 3366 94 x 39 = 3666 3666 - 3366 = 300 11 12 13 14 15 16 17 21 22 23 24 25 26 27 31 32 33 34 35 36 37 41 42 43 44 45 46 47 51 52 53 54 55 56 57 61 62 63 64 65 66 67 11 x 67 = 737 61 x 17 = 1037 1037 - 737 = 300 2 3 4 5 6 7 2 10 20 30 40 50 60 3 20 40 60 80 100 120 4 30 60 90 120 150 180 5 40 80 120 160 200 240 6 50 100 ...read more.

Conclusion

Also I would have found more differences and formulas in different size number grids such as 20x5 or 30x10 etc. This would have made my view and points clearer and proved my opinion more. I would also like to see if my investigation were to change if I were to instead of multiply but add the top left number with the bottom right, perhaps this method might have changed my entire investigation. This piece of coursework was different from our last data handling coursework because the last coursework included using standard deviation and graphs. For this investigation on number grids I had to use a lot of tables and a lot of calculator calculations were needed. Not much equipment was used to do this investigation because I did do most of it on the computer. As you can see I filled out a difference table for both number grids shown on pages 23(10x10 number grid) and page 40(15x15 number grid). This gave me a clear look at what patterns I could notice in each table. I noticed that in my 10x10 number grid all the differences were a multiple of 10 and in my 15x15 number grid all my differences were multiples of 15. I think I have done quiet well for the presentation of my investigation but I do feel that it could have been extended more with further methods of investigation. I found this investigation very challenging and it did teach me a great deal on number girds and their differences. I never expected my investigation to be a great amount of pages but looking at some other pieces of coursework I found it to be normal, This just shows that I did a lot of calculations and methods of investigating formulas and patterns. In conclusion, this investigation has been very challenging and useful to my class work because it has taught me a lot on formulas and differences in number grids also it taught me a lot on how to investigate problem solving. 4141 Page 1 Sharish Rughoo 11L Candidate number 8146 Centre number 13428 ...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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