TShapes Coursework
Extracts from this document...
Introduction
TShapes Coursework
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 
In this coursework I am going to look at a series of grids and within the grids look at certain Tshapes. The first thing I am going to do in this investigation is pick three TShapes from the grid below.
Above is my 9x9 Grid the numbers ranging from 181. I have chosen my first Tshape to be located in the top left of the grid, and my Tnumber will be 20 The Tshape above has been highlighted in red. Because my choice was the number at the bottom of the Tshape I am going to be consistent with future Tshapes chosen. I have highlighted the Tnumber with a light blue colour.
I have chosen my three Tshapes and have labelled the TNumbers in them appropriately. I am now going to work out the TTotals for each of my Tshape.
Tnumber20=20+11+1+2+3=37
Tnumber21=21+12+2+3+4=42
Tnumber22=22+13+3+4+5=47
TNumber  TTotal 
Tnumber20  20+11+1+2+3=37 
Tnumber21  21+12+2+3+4=42 
Tnumber22  22+13+3+4+5=47 
Middle
= 47
The above calculations show that the formula is correct.
I am now going to test this formula on a different sized grid. The size grid I have chosen to do next is an 11x11 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  101  102  103  104  105  106  107  108  109  110 
111  112  113  114  115  116  117  118  119  120  121 
Ttotal = 1+2+3+13+24 = 43
Tnumber = 24
The TTotal and the TNumber have risen even though the TShape looks to be in the same place. The TNumber has risen by four and the TTotal has risen by six.
Conclusion
Ttotal = 5 x 69 – 63
= 345 – 63
= 282
I will now check my calculations by drawing the appropriate Tshape.
TTotal= 50+51+52+60+69=282
My formula has been proved to work and my calculations correct.
By looking at my previous results, I have now decided that I am going to try and generalise for a G x G grid.
TTotal = T2g1 + T2g + T2g+1 + TG + T
= 5T7G
I will now use my general formula to predict the TTotal of TNumber 24 on a 7 x 7 grid.
T= 24 G=7
TTotal = 5 x 24 – 7 x 7
= 120 – 49
= 71
I will check this by drawing the appropriate Tshape and adding up the numbers within.
I am now going to increase the size of my Tshape and also choose a different size grid for this larger TShape.
The grid size I have chosen to do is a 10 x 10 grid. I am going to enlarge my Tshape to see if my formula will still work on a larger Tshape.

Oliver Mason year 11
This student written piece of work is one of many that can be found in our GCSE TTotal section.
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