T-Total and T-Number - page 3
Keywords: T-Total and T-Number
By Grant867 on 07/12/2008
Level: GCSE Key Stage 4 (Years 10-11)
Page Number: 3 of 6 pages: 1 2 3 4 5 6
If we turned the t- shape around 180 degrees it would look like this. When we have done this we should realise if we reverse the t-shape we should have to reverse something in the formula.
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It is obvious that we will have to change the minus sign to a different sign. We should try the opposite of minus which is plus
5tn + 63=t-total
5 * 2 + 63 = 73
Check to see if the formula has worked
T-number = 2
T-total = 2+11+19+20+21 =73
The reverse in the minus sign has worked.
The next step is to move the shape on its side. Again we nearly keep the same formula as we had at the beginning. Again we change the minus number. We can work out the number to minus by working out the difference in the t-number to each number in the t-shape.
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Difference
12-1 =11
12-10= 2
12-19= -7
12-11 = 1
TOTAL = 7
Formula
5tn - 7 =t-total
5*12 - 7= 53
Check to see if the formula is right
T-number = 12
T-total = 1 +10 +19 +11 +12 = 53
This formula has worked. If we rotated the t-shape 180 degrees, The same will happen, as what happened when the t-shape was turned 180 degrees from it is first original position. This is proven below.
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5tn + 7 = t-total
5* 70 + 7 = 357
Check
T-number = 70
T-total = 70+71+72+63+81 = 357
If we were to put the t-shape diagonally on the grid we find that the same rule applies again apart from you can not use the 2nd rule were you times the grid size by seven.
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The red t-shape has t-number of 33 and the t-total = 7+17+27+25+33 = 109
The difference between the t-number and the rest of the numbers in the t-shape.
33-25= 8
33-7= 26
33-17= 16
33- 27 = 6
TOTAL= 56
5tn+56= t-total
5 * 33 - 56 =109
The reverse triangle the sign should be reversed to a plus. The t-shape used here is the one in blue.
T-number is 13
T-total = 19+29+39+21+13 = 121
5tn+56= t-total
5*13+ 56= 121
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The t-shapes above holds more formulas as the rest they all work the same.
The red t-shape has a t-number of 32 and a t-total of 32+42+52+60+44= 230
This t-shape has a formula the formula is 5tn + 70 = t-total
To see if this formula works
First we work out the difference in between the t-number and the rest of the numbers in the t-shape.
Difference
42-32= 10
52-32= 20
60-32= 28
44-32= 12
TOTAL= 70
5*32 + 70 = 230
The blue shape
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