T-Totals. I am going to investigate the relationship between the T-total and the Tnumber. I will use a 9 x 9 grid. I will draw different Tshapes onto the grid.

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                                       MATHS COURSEWORK

                                     

                                  T-TOTALS

           BY EMMET MURPHY 11K

Aim:   I am going to investigate the relationship between the     T-total and the T–number.  I will use a 9 x 9 grid.  I will draw different T–shapes onto the grid.  Then I will find the T–total and the T–number.  I will put the answers into a table of results. I will try to find the relationship between these numbers.

Method:   To find the T-total I had to add up all the numbers in the T- shape.  For example:

1+2+3+11+20 = 37

2+3+4+12+21 = 42

3+4+5+13+22 = 47

4+5+6+14+23 = 52

5+6+7+15+24 = 57

6+7+8+16+25 = 62

7+8+9+17+26 = 67

10+11+12+20+29 = 82

11+12+13+21+30 = 87

12+13+14+22+31 = 92

13+14+15+23+32 = 97

14+15+16+24+33 = 102

15+16+17+25+34 = 107

16+17+18+26+35 = 112

17+18+19+27+36 = 117

18+19+20+28+37 = 122

   

                   

                                  Table of Results  

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The relationship between the T-number and the T-total is:

Whenever the T-number increases by 1, the T-total increases by 5.  Therefore the difference is five, which means that the      T-total has a constant difference of 5.

Analysis of Results:  To find the formula for the 9x9 grid I took the first T-number, 20 and multiplied it by the difference which is 5.  This totalled 100.  To get the first T-total, I subtracted 37 from 100 to give me 63.  When put into a formula it will look like this:

5n – 63.

I will substitute ...

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