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Maths Grid Investigation

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Introduction

GCSE Maths Coursework Task B The Task After looking at the table of numbers: 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 I will then investigate the diagonal difference of a 4x4 grid, 3x3 grid and 2x2 grid the numbers for these grids will be taken from the 8x8 grid above. The way to investigate diagonal difference is shown in the example: 'Sarah writes down a 3x3 grid from the above table.' 10 11 12 18 19 20 26 27 28 'She notices that when you multiply the opposite corners the difference between the products is 32' For example: 10 x 28 = 280 12 x 26 = 312 The diagonal difference is 312 - 280 = 32. ...read more.

Middle

52 = 2340 2340 - 2332 = 8 33 34 41 42 33 x 42 = 1386 34 x 41 = 1394 1394 - 1386 = 8 What I will Measure/Observe I will measure the diagonal difference from a 4x4 grid, a 3x3 grid and a 2x2 grid. I will take these grids from a table of 8x8 numbers ranging from 1-64. I will find the diagonal difference by taking the four numbers from each corner multiply them by the number in the apposite corner and then I will take away the two numbers found as a result of multiplying the four opposite diagonals. This will then leave me with my diagonal difference. Examples of the type of measurements I will be gathering are found in my preliminary investigations. How I will Carry out any Measurements I will measure the times value of the corners of the 4x4 grid, 3x3 grid, and a 2x2 grid then I will minus the two answers given for each grid and find the diagonal difference. ...read more.

Conclusion

I will collect four sets of results for all of the three grid sizes. I will then compare the diagonal difference values. I will then analyse these four sets of results by putting them into tables and formatting them in charts, this ill then enable me to make comparison between the diagonal differences of each grid size. What I will keep the same to make it a Fair Test I will keep the initial 8x8 grid the same; this is where I will gather my numbers from for the other smaller grid sizes. The 8x8 grid will range from 1-64 in numerical order I will always keep this the same. What Safety Precautions will need to be taken? I will not have to take any safety precautions for this investigation as no safety hazards will occur as a result of this investigation. What graphs and calculations do I intend to do? ? Insert later? My Results Grid (2x2) Calculations Difference 47 48 47x56 = 2632 2640-2632 = 8 55 56 48x55= 2640 49 50 49x58= 2842 2850-2842 = 8 57 58 50x57= 2850 15 16 15x24 = 360 368-360 = 8 23 24 16x23 = 368 9 10 9x18 = 162 170-162 = 8 17 18 10x17 = 170 ...read more.

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