Ttotal coursework.
Extracts from this document...
Introduction
Ttotal 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 
On the grid on the right, you can see a 9 by 9 grid. On the grid, we see a “T” shape highlighted. The sum of the numbers within the Tshape is 1 + 2 + 3 + 11 + 20 = 37. This is known as the Ttotal.
The Tnumber is the number that is at the bottom of the Tshape. In this example, 20 is the Tnumber.
During this coursework, I will be investigating the relationships between the Tshapes and how they relate to grid size. I will also be looking closely into the significance of the Tnumber and how it could be used to figure out the Ttotal.
9 by 9 Grid
We have already figured out the ttotal for one tshape in the 9 by 9 grid. Here are some more results.
34 + 35 + 36 + 44 + 53 = 202
46 + 47 + 48 + 56 + 65 = 262
5 + 6 + 7 + 15 + 24 = 57
58 + 59 + 60 + 68 + 77 = 322
In this investigation, I’ll be implementing the use of equations. Here is how I started off.



1  2  3  
10  11  12  
19  20  21  

N 
If I bring all these figures together, I should get a correct equation.
T = N – 19 + N – 18 + N – 17 + N – 9 + N
= 5N – 63
Middle
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
As I did with the 9 by 9 grid, I worked out the ttotal for various tshapes in the grid the long way (adding each individual digit in the tshape, one by one). I will the see if the equation for the 9 by 9 grid would work on this grid.
1 + 2 + 3 + 10 + 18 = 34
5 + 6 + 7 + 14 + 22 = 54
33 + 34 + 35 + 42 + 50 = 194
37 + 38 + 39 + 46 + 54 = 214
Then I attempted to use the equation in the previous grid to work out the ttotal of a tshape.
T = 5N  63
N = 22
T = (5x22) – 63
= 110 –63
= 47
As we can see above, the result was wrong. So I decided to do what I did in the previous grid and work out a new equation.


 
1  2  3  
9  10  11  
17  18  19  

N 
Now I bring all the terms together to get an equation.
T = N – 17+N – 16+N – 15+N – 7+N
= 5N – 56
I then check if the equation is correct.
N = 18
T = (5x18) – 56
= 34
We find that this new equation work in this case, but try it with a different tnumber to confirm its validity.
N = 50
T = (5x50) –56
= 194
Again, the equation has produced another correct result. I try it again one more time to make sure.
N = 22
T = (5x22) – 56
= 54
So I have produced another equation that works with in this grid.
7 by 7 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 
Conclusion
T = 5N – 63
63 / 7 = 9
So now what I can say is to figure out the ttotal of a tshape in any size grid, you need the formula “T = 5N – X”. The way you find out the ttotal is as follows.
You firstly choose the tshape you wish to find the ttotal for. You then look at the grid size e.g. 7 by 7, and take the “7” from the grid size and multiply it by 7. This is your “X” value. You then multiply the tnumber of the tshape you are working out the ttotal for and subtract the X value away from it. You should see, if done correctly, that the result would correspond with that of the real ttotal.
What you can also figure out with this method is the ttotal of an upsidedown tshape. To do this, you do as above, but instead of subtracting the X value away from 5N, you add it on. Note that all of the above equations have been based on upright tshapes and don’t work if the tshape is on its side.
This student written piece of work is one of many that can be found in our GCSE TTotal section.
Found what you're looking for?
 Start learning 29% faster today
 150,000+ documents available
 Just £6.99 a month