T-Total and the T-Number.

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Maths Investigation

CODE  –  tn = T-Number. tt = T-Total

Aim:  I) Investigate the relationship between the T-Total and the T-Number

           II) Investigate the relationship between the T-Total, the T-Numbers and the grid size, using translation

          III) Investigate the relationship between the T-Total, the T-Numbers, the grid size and the transformations.

Part I

We were working with a 9x9 grid, and we had to construct a t-shape like this

 And so on…

 

 To make the T-TOTAL, we had to add all the numbers inside the T together, and the T-NUMBER was the number at the bottom of the T (as highlighted inside the T).

  To start with I added all the numbers together inside the T, and for 20 the T-Total was 37 – (1+2+3+11+20 = 37). I then did 21,22, 23 and so on up to 26. My results were as follows:

20 = 37

21 = 42

22 = 47

23 = 52

24 = 57

25 = 62

  Just from these results I can see that the T-Total rises by 5 every time the T-Number rises by 1. This means that there is a 1:5 ratio in terms of the T-Total and T-Number.

  After this I had to work out a formula showing the relationship between the T-Total and the T-Number. To start with I knew it would be 5 x the T-Number, as the tt goes up 5 every time the tn goes up 1.  Also, if I added the amounts that the numbers inside the T are subtracted from the tn, then it could finish the formula.

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 Therefore I did the following sum, 19 + 18 + 17 + 9 = 63.                                                                

As they were subtracted from the tn, it means that they      

are all minus,   my final formula is 5n – 63. As far as ...

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