This Piece of course work is to investigate the relationship between the T Total and the T Number . The T shapes will be 3 squares across and 3 squares down and they will be on a 9*9 grid.

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This Piece of course work is to investigate the relationship between the T Total and the T Number . The T shapes will be 3 squares across and 3 squares down and they will be on a 9*9 grid.

Firstly I will draw some T shapes onto the grid and see if I can  spot a relationship.

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11


20

T Number=20      T Total=1+2+3+11+20=37

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33

T Number=33       T Total=14+15+16+24+33=102

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71

T Number=71      T Total=52+53+54+62+71=292

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T Number=71          T Total+55+56+57+65+74=307

Although those results could give me enough information to find a formula to find the T Total from the T Number, Now I will draw up some more T Shapes but this time all adjacent so that when I draw a table it will be easier to spot the relationship.

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T Number=20       T Total=1+2+3+11+20=37

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T Number=21       T Total=2+3+4+12+21=42

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T Number=22      T Total=3+4+5+13=22=47

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T Number=23       T Total=4+5+6+14+23=52

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T Number=24      T Total=5+6+7+15+24=57

If I now put the these results into a table I will be able to see a pattern more clearly

T Number :  20  21  22  23  24

…………..……………………………..  

T Total      :  37  42  47  52  57          

The T Total goes up in 5’s because there are 5 squares in each T and each Square in The T goes up 1 adding up to 5.

Join now!

If I substitute my T Numbers for N and the other numbers in the squares in relation to N I should be able to find the formula.

E.g.

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20

Change this Blue square to this red Square:

N-19
N-18
N-17

N-9


N

Then if you add up all the N’s and the numbers our formula for the T total would be

T=5N-63

To make sure the Formula is correct I will test it:

1+2+3+11+20=37

T=37       T also=5n-63

5n=100    100-63=37       This proves that the formula is correct

 Key

T= T Total        

N=T ...

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