# The T-Total Mathematics Coursework Task.

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Introduction

The T-Total Mathematics Coursework Task The Task Looking at the T-shape drawn on a 9 by 9 number grid below. The total of the numbers inside the T-shape is 1+2+3+11+20=37 This is called the T-Total. The number at the bottom of the T-shape is called the T-Number. The T-number for this T-shape is 20. 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 What I have been asked to do Translate the T-shape to different positions of the grid. * Investigate the relationship between the T-number and the T-total * Use grids of different sizes. Translate the T-shape to different positions. Investigate relationships between T-total, the T-numbers and the grid size. * Use grids of different sizes again. Try other transformations and combinations of transformations. Investigate relationships between the T-total, the T-numbers, the grid size and the transformations. The Method I have chosen I will follow my plan below while following the task and customizing it to achieve maximum marks. * I will first draw out one or two 9 by 9 number grids. Then I will fill in T-shapes until I see a pattern, each shape will be in a different colour to make the shapes stand out, on separate piece of paper I will work out the T-total and the T-number while showing how I came to these results. The other T-shapes will be written with the others on the separate page as there is no need for the to be drawn on the grid. ...read more.

Middle

+ 56 T = 180 + 56 T = 236 Which is the same answer as before proving this formula works. Analysis of T-shapes Rotated 270 degrees to the right on an 8 by 8 number grid Again using the above formula and method we are able to find the equation for the T-shape that has been rotated 270 degrees clockwise. When: T=T-total t=T-number This formula is used to find the T-total from any possible T-number for a T-shape that has been rotated 270 degrees clockwise on an 8 by 8 number grid. T = 5t - 7 Sub Conclusion for The T-shapes including rotations on an 8 by 8 Grid In conclusion for the T-shapes that have been rotated through 360 degrees on an 8 by 8 number grid I am now able to put together a basic table that can outline the relationships. T-Shape Rotation Formula used to find T-Total Difference between T-Totals T = 5t - 56 5 T = 5t + 7 5 T = 5t + 56 5 T = 5t - 7 5 From this table we can see that the Formulas are reversed when the T-shape is flipped, e.g. when the Normal T-shape is flipped to an upside down position the - sign changes to a + sign, this implies the same rules as an equation, whatever you do to one side is done to the other side. The differences between the T-totals is 5, this shows a relationship between all the T-totals and T-numbers. The T-totals increase in proportion to the T-numbers, this is visible on the tables as we can see the numbers increase steadily. Normal T-shapes on a 10 by 10 number grid T-number Bottom of T-shape T-total All numbers in T-shape added T-number Bottom of T-shape T-total All numbers in T-shape added 22 40 62 240 23 45 63 245 24 50 64 250 25 55 65 255 26 60 66 260 27 65 67 265 28 70 68 270 29 75 69 ...read more.

Conclusion

I have worked out some other shapes to prove that the method works. The examples are all on a 9 by 9 number grid, although the method works on all shaped grids as shown in my coursework. Bearing in mind that these shapes are drawn to the specific way I have constructed them. Shape Formula I 7i E 8e + 5 P 9p - 210 O 12o - 228 F 8f - 40 A 14a - 267 G 14g + 1 H 12h + 198 Evaluation I have found this coursework enjoyable and yet challenging. I have learnt many new ways to tackle and succeed more advanced algebraic equations and formulas, as well as compiling evidence and investigation against problems set. During this coursework I have particularly found the formulas and equations tricky to work on as they are obtained by using different methods and calculations. The area of the coursework where I fell I have used the least effort due to the pure simplicity of the work has have to have been the table of T and L numbers and Totals. This is because when a pattern emerges I was able to pick it up immediately and successfully complete the table with minimum effort. I think that I will be able to achieve a relatively high mark with this piece of coursework as I have met the demands of the task set and gone beyond them by setting myself personnel targets and errands such as trying irregular grid sizes, plotting graphs and trying new shapes. If I were to do this project again I would probably change the layout of the coursework as I think it is too complicated and repetitive. I would also cut down on some lengthy areas such as the sub-conclusions and tables of T and L numbers. If I were to set myself another similar project on this based around the same topic as this coursework I would attempt the triangle grid and hexagonal grid as they are more complicated and may involve more algebra and methods, which I could endeavour. Neel Joshi Maths Coursework - T-Total 1 ...read more.

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