T-Total Maths coursework

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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.

What is the T-total?

The total of the numbers inside the T-shape is 1+2+3+11+20 = 37. The T-total for this T-shape is 37.

What is the T-number?

The number at the bottom of the T-shape is called T-Number. The T-number for this is 20

T-number and T-total table

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-63

I tested that when: T-number=80

                               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-9+N-19+N-18+N-17

                                    T= 5N-63

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

Formula:  T = 5N-63

N =  20         21         22          23

T =  37         42         47           52

                             

                                                               T-number

T = (5x20)-63

   = 100-63

T = 37

                                                             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 = 20

T = (5 x 20)-63

   = 100-63 =37

   

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

N = 21

T = (5 x 21)-63

   = 105-63

   = 42

N = 39

T = (5 x 39)-63

   = 195-63

   = 132

N = 40

T = (5 x 40)-63

   = 200-63

   = 137

N = 79

T = (5 x 79)-63

   = 495-63

   = 332

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

N = 80

T = (5 x 80)-63

   = 400-63

   = 337

Rotation of 1800

9 by 9

T-number and T-total table

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+63

I tested that when: T-number=80

                               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-9+N-17+N-18+N-19

                                    T= 5N+63

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

Formula: T=5N+63

I tested that when: T-number=62

                               T-total=373

N = 2         3              4            5

T = 73      78            83           88

        T-number

T = (5x2) +63

   = 10+63

T = 73

        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 = 3

T = (5 x 3) +63

   = 15+63

   = 78

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

N= 4

T= (5x 4) +63

  = 20+63

  = 83

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

N=5

T= (5x5) +63

  = 25+63

  = 88

Rotation of 900

9 by 9

T-number and T-total table


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=70

                               T-total=357

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 below are:

Formula: T=5N+7

I tested that when: T-number=62

                               T-total=373

N = 10      11            12           13

T = 57      62            67           72

        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

Join now!

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

Here ...

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