Maths- T-Totals

Authors Avatar

Contents

  • Aim and Method
  • Grid 1: 9 by 9
  • Across the Grid
  • Gown the grid Diagonally
  • Down the grid
  • Across the Grid:
  • Grid 2: 5 by 5
  • Grid 3: 6 by 6
  • Grid 4: 7 by 7
  • Grid 5: 10 by 10
  • Grid 6: 11 by 11
  • Extension: Transformations Grid 7: 9 by 9 (Going across)
  • T at 180 degrees
  • T at 90 degrees
  • T at 270 degrees
  • Conclusion

Aim:

I will investigate the relationship between the T-total (all the numbers in the T added up) and T-number (the number at the end of the T), using grids of different sizes to translate the t-shape to different positions within the grid. I will try different combinations of transformations later within the coursework.

Method:

Part 1

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

Part 2  

Use grids of different sizes. Translate the T-shape to different positions. Again investigate the relationship within the different sizes of the grids.

Part 3

Use grids of different sizes again. Try other transformations and combinations of transformations. Investigate relationships between the T-Total, and T-Numbers on the grid of different sizes.          

Grid 1: 9 by 9 – Across (      )

In the T below, I noticed that the number at the end of the T (the T-Number) was 20. I will now go across this grid writing down the T-Number on one side and the T-Total in the other aswell showing my working by putting all the numbers within that T.I will also write the trend of the T-Number and T-Total in the table and express I in the nth term after I have acquired results from various points in the grid.

Formula Expressed in the nth term

As the tables show every time the T-Number increases by 1 the T-Total increases by 5. I will express in the nth term by using these common differences and start on the basis of ‘if n=1’ but change accordingly if appropriate.

At the T-Number the common difference is 1.

For example take 20 and 21 subtract them (21 -20) and you get 1.

Therefore the formula of this is 1n ± C = T-Number/ n ± C = 20, 20 -1=19.

Therefore nth term= n+19=20

At the T-Total, the common difference is 5.

 

For example take 37 and 42 subtract them (42-37) and you get 5. Therefore the formula of this is 5n ± C = T-Total/ 5n ± C = 37, (if n=20 (T-Number) ) 20 x 5= 100,  100 -37= 63.

Therefore nth term= 5n-63=37

Grid 1: 9 by 9 – Diagonally (      )

Formula Expressed in the nth term

As the tables show every time the T-Number increases by 10 the T-Total increases by 50. I will express in the nth term by using these common differences and start on the basis of ‘if n=1’ but change accordingly if appropriate.

Join now!

At the T-Number the common difference is 10.

For example take 20 and 30 subtract them (30 -20) and you get 10.

Therefore the formula of this is 10n ± C = T-Number/ n ± C = 20, 20 - 10=10.

Therefore nth term= 10n+10=20

At the T-Total, the common difference is 50.

 

For example take 37 and 87 subtract them (87-37) and you get 50. Therefore the formula of this is 50n ± C = T-Total/ 5n ± C = 37, 50 - 37= 13.

Therefore nth term= 50n -13=37

...

This is a preview of the whole essay