T-Total and T-Number - page 2
Keywords: T-Total and T-Number
By Grant867 on 07/12/2008
Level: GCSE Key Stage 4 (Years 10-11)
Page Number: 2 of 6 pages: 1 2 3 4 5 6
the number turns out to be 63. This is where the 63 came from in this equation. There is also another place this 63 comes from. This is 9*7=63. The nine in this comes from the size of the grid this one been nine. If the grid size were 10 by 10 then it would be 10*7. At the end of this piece of coursework when we but all the formulas together we realise that the number we minus or plus by is divisible b y seven. This is where we get the seven from. The seven works with all the same sizes. The other method will also work with a different size grid.
If we add these two together we have our formula.
5tn-63=t-total
Here is an example of using the formula
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
5*57-63=t-total
5*57-63= 222
Check
T-total = 38+39+40+48+57=222
This formula has proven to work.
PART 2
This next section involves using grids of different sizes and then translating the t-shape to different positions. Then investigation of the relationship between the t-total, the t-number and the grid size. Here we are doing what we did in the last section but finding out more about the grid size and what it is capable of doing.
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
T-total = 1+2+3+13+24 = 43
T-number = 24
The t-total and the t-number have risen even though the t-shape looks to be in the same place. The t-number has risen by four and the t-total has risen by six. If we use the same rules we made in the last section it works. Here is the longer method
Difference
24-1= 23
24-2 = 22
24-3 =21
24-13 =11
TOTAL =77
Or the shorter way
7* 11 (grid size) = 77
Try out the new formula
5tn – 77= t-total
5*24-77=43
The same formula works with only changing the last number in the formula. This will be tried on a smaller grid size to make sure it is not if the grid size is bigger.
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
T-number = 10
T-total = 1+2+3+6+10= 22
7 * 4 (grid size) = 28
5tn- 28= t-total
5*10-28=22
This has proven to work on a smaller scale. We can see that by changing the grid size we have had to change the formula but still managing to keep to the rule of how you get the number to minus in the formula.
PART 3
In this next section there is change in the size of grid. Also there is transformations and combinations of transformations. The investigation of the relationship between the t-total, the t-numbers, the grid size and the transformations.
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