Investigate the relationship between the T-total and the T-number

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Maths Coursework

Aim: Investigate the relationship between the T-total and the T-number. Use grids of different sizes and translate the T-shape to different positions. Investigate relationships between the T-total and the T-number and the grid size.

Method: In order to find this rule we will have to go through a trial and error process. To secure an algebraic rule expressed in the nth term we will have to test it in many variables. These variables consist of random placement of the T-shapes; another is the shape being placed at different degrees. This will provide us with numerous results, which will help us, gain a conclusive overall algebraic term.

     

9x9 Number grid (Across)

                                                   

As the T-Shape translates across by 1, the T-Number increases by 1. The difference in T-Total is 5 each time so far. Therefore the T-Total for the T-Number 24 should be 57 if the pattern follows. The T-Total for the T-Number 25 should be 62.

The results show the predictions made earlier are correct proving that the pattern follows.

9x9 Square Grid Patterns down

I have noticed patterns within my table of results. One of the patterns I have noticed is, as the T-Shape translates down by 1, the T-Number increases by 9. Another noticeable pattern is the T-Total difference is 45 each time.

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To prove that the patterns work anywhere within the grid I am testing it at a different point within the grid. The T-numbers I will test it with is 56 and 65. If my patterns are work at any point in the grid, than the difference between both results should be 45. Therefore I predict the T-Total for the T-Number 56 should be 217, and the T-total for the T-number 65 should be 262 if the pattern follows.

The results above of the predictions made earlier as to what the T-Total should be if the

T-Number was 56 ...

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