# T-Total Maths coursework

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Introduction

Name: Farhana Akther

Candidate Number:0000

Date: 04/12/2007

In this coursework I am going to investigate the relationship between T-numbers and T-totals. I will find the relationship between T-number and T-totals by looking at the pattern of the sequence, which goes up by 5 each times when you add the T-total with 5.

I will use grids of different size and will translate the T-shape into different positions in order to examine the correlation between them. The T-total and T-number will be translated onto different positions such as 900 clockwise. After the translation of T-total and T-number, I will find the formula that will be devised by putting a careful scrutiny on the pattern of my T-numbers.

Aim: The aim of this investigation is to find a relationship between the T-total and T-numbers, but in this case the T-shape can be positioned in different ways, for example upside down or side ways. As the T-shape can also be changed a relationship between the transformations also has to be found.

Method: I will first draw out a 9 by 9 grid and put T-shape within it first placing them upside down, then side ways on the right and then also on the left. I will place my results into a table and attempt to find a relationship between the T-total and T-number as I did before. I will incorporate this relationship into a rule using letters and numbers only. I will then do a similar thing for 8 by 8 grids and 7 by 7 grids.

In this investigation I am going to investigated relationships between the T-total, T-numbers and grid size by translating the T-shape to different positions on the grid and changing the grid size.

T- Total (9 by 9)

Look at this T-shape drawn on a 9 by 9 number grid.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |

19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 |

28 | 39 | 30 | 31 | 32 | 33 | 34 | 35 | 36 |

37 | 38 | 49 | 40 | 41 | 42 | 43 | 44 | 45 |

46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 |

55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 |

64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 |

73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 |

What is the T-total?

Middle

T-number

T = (5x10) +7

= 50+7

T = 57

T-total

This equation has produced its first correct answer. I will carry on and test T-shape I know the T-total for

N = 11

T = (5 x 11) + 7

= 55+7

= 62

As expected, the equation has produced yet another correct answer. Another example is below,

N= 12

T= (5x 12) + 7

= 60+7

= 67

Here is the last equation I will show from the 9 by 9 grid to show that the equation

N=13

T= (5x13) +7

= 65+7

= 72

Rotation of 2700

9 by 9

T-number and T-total table

T-number | T-total |

12 | 53 |

13 | 58 |

14 | 63 |

15 | 68 |

Here I have added a prediction of mine when I realized the pattern of the sequence, which goes up by 5 each time.

Formula: T=5N-7

I tested that when: T-number=72

T-total=337

Below is a T-shape, and in each cell how number is connected with T-number on a 9 by 9 number grid.

To prove the formula: T= N+N-1+N+11+N+2+N+7

T= 5N-7

How the formula works there are some example shown in following are:

Formula: T=5N-7

I tested that when: T-number=62

T-total=353

N = 12 13 14 15

T = 53 58 63 68

T-number

T = (5x12) -7

= 60-7

T = 53

T-total

This equation has produced its first correct answer. I will carry on and test T-shape I know the T-total for

N = 13

T = (5 x 13) - 7

= 65-7

= 58

As expected, the equation has produced yet another correct answer. Another example is below,

N= 14

T= (5 x 14) - 7

= 70 - 7

= 63

Here is the last equation I will show from the 9 by 9 grid to show that the equation

N= 15

T= (5 x 15) - 7

= 75-7

= 68

T- Total (8 by 8)

Look at this T-shape drawn on an 8 by 8 number grid.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |

25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 |

33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |

41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 |

49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 |

57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 |

T-number and T-Total table

T-number | T-total |

18 | 34 |

19 | 39 |

37 | 129 |

38 | 134 |

62 | 254 |

63 | 259 |

Here I have added a prediction of mine when I realized the pattern of the sequence, which goes up by 5 each time.

Formula: T=5N-56

I tested that when: T-number= 63

T-total= 191

Below is a T-shape, and in each cell how number is connected with T-number on an 8 by 8 number grid.

To prove the formula: T= N+N-9+N-17+N-16+N-15

Conclusion

I enjoy doing this investigation and the things I have found most interesting is finding out the formula for the any gird size. In following there is an example of a formula which can be solving for any grid size.

The Formula for any grid size is N=5n-7g

9x9 Gird size °

N = 20

5N

= 5x20

= 100

G = 9

= 7x9

= 63

I now have enough data to prove that my formula works

5N - 7G

= 100 - 63

= 37

So my Formula works because T = 37. The formula also works for 9x9 grids.

I found exciting to found out the formula for any grid size. I found this coursework is ok.

The things I am strongest in this coursework is finding out the relationship between T-number and the T-totals because, the things you have to look at the pattern of the sequence.

In this coursework I am weakest to prove to formula because you have explained what you are doing on there.

The things I think it was wasting time is doing same things over and over again but it improve my explanation and it helps me to memories the method by doing over again.

Overall I like it because it helps me to think with the formula going to be for next grid and the relationship between T-number and T-totals.

When I rotated the T-shape around I found the formula are connected with each other and they reflected with each other as well.

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