# Investigate the relationship between the T-Total and the T-Number. Use grids of different sizes. Translate the T-Shapes to the different positions. Investigate

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Introduction

09th January 2006

GCSE Mathematics Coursework

T-Totals

- Investigate the relationship between the T-Total and the T-Number.
- Use grids of different sizes. Translate the T-Shapes to the different positions. Investigate relationships between the T-Total, the T-Number and the grid sizes.
- Use grids of different sizes again. Try other transformations and combinations of transformations. Investigate the relationships between the T-Total, the T-Number, the grid size and the transformations.

T-Total 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 | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 |

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

T-Numbers (T) | 20 | 21 | 22 | 23 | 24 |

T-Total | 37 | 42 | 47 | 52 | 57 |

+5 +5 +5 +5

5 x 20 = 100

∴ 100 – 37 = 63

The difference between the T-Totals is 5 this makes the first part of the formula: 5T

To work out the second part takes the T-Number and multiplies by the difference.

#### 5T - 63

The 50th Term is:

Middle

5 x 16 = 80

∴ 80 – 31 = 49

## 5T – 49

The 50th Term is:

5 x 50 = 250

∴ 250 - 49 = 201

To Test:

## T Number 40

5 x 40 = 200

∴200 – 49 = 151

T-Total 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 |

T-Number | 14 | 15 | 16 | 17 | 18 |

T-Total | 28 | 33 | 38 | 43 | 48 |

+5 +5 +5 +5

5 x 14 = 70

∴ 70 – 28 = 42

## 5T – 42

The 50th Term is:

5 x 50 = 250

∴ 250 - 42 = 208

To Test:

## T Number 30

5 x 30 = 150

∴150 – 42 = 108

### Relationships and Master Formula Working Out

Formulae’s

9 x 9 Grids: 5T - 63

8 x 8 Grids: 5T - 56

7 x 7 Grids: 5T – 49

6 x 6 Grids: 5T – 42

- Smaller the Grid Size the less you have to take away from the T-Total
- The Larger the grid size the more you have to take away from the T-Total
- All The Formulas have gaps of 7

(Ex. 63 – 56 = 7. 56 – 49 = 7. 49 – 42 = 7.)

I found out that the master formula is 5T-(7xG)

I got the 5 by looking at the differences of the number.

The T stands for the T-Number (which is always 5; as there are 5 squares in the T; and it is current throughout.)

Conclusion

## T-Number 30

5 x 30 = 150

∴150 – -63 = 213

8 x 8 Grids: Transformation

T-Number | 11 | 12 | 13 | 14 | 15 |

T-Total | 48 | 53 | 58 | 63 | 68 |

5 x 11 = 55

∴ 55 – 48 = 7

5T - 7

The 50th Term is:

5 x 50 = 250

∴ 250 – 7 = 243

To Test:

## T-Number 30

5 x 30 = 150

∴150 – 7 = 143

7 x 7 Grids: Transformation

T-Number | 8 | 9 | 10 | 11 | 12 |

T-Total | 47 | 52 | 57 | 62 | 67 |

5 x 8 = 40

∴ 40 - 47 = -7

5T - -7

The 50th Term is:

5 x 50 = 250

∴ 250 – -7 = 257

To Test:

## T-Number 30

5 x 30 = 150

∴150 – -7 = 157

7 x 7 Grids: Transformation

T-Number | 2 | 3 | 4 | 5 | 6 |

T-Total | 59 | 64 | 69 | 74 | 79 |

5 x 2 = 10

∴ 10 - 59 = -49

5T - -49

The 50th Term is:

5 x 50 = 250

∴ 250 – -49 = 299

To Test:

## T-Number 30

5 x 30 = 150

∴150 – -49 = 199

7 x 7 Grids: Transformation

T-Number | 2 | 3 | 4 | 5 | 6 |

T-Total | 59 | 64 | 69 | 74 | 79 |

5 x 2 = 10

∴ 10 - 59 = -49

5T - -49

The 50th Term is:

5 x 50 = 250

∴ 250 – -49 = 299

To Test:

## T-Number 30

5 x 30 = 150

∴150 – -49 = 199

6 x 6 Grids: Transformation

T-Number | 7 | 8 | 9 | 10 | 11 |

T-Total | 42 | 47 | 52 | 57 | 62 |

5 x 7 = 35

∴ 35 - 42 = -7

5T - -7

The 50th Term is:

5 x 50 = 250

∴ 250 – -7 = 257

To Test:

## T-Number 30

5 x 30 = 150

∴150 – -7 = 157

6 x 6 Grids: Transformation

T-Number | 2 | 3 | 4 | 5 | 6 |

T-Total | 52 | 57 | 62 | 67 | 72 |

5 x 2 = 10

∴ 10 - 52 = -42

5T - -42

The 50th Term is:

5 x 50 = 250

∴ 250 – -42 = 292

To Test:

## T-Number 30

5 x 30 = 150

∴150 – -42 = 192

6 x 6 Grids: Transformation

T-Number | 9 | 10 | 11 | 12 | 13 |

T-Total | 38 | 43 | 48 | 53 | 58 |

5 x 9 = 45

∴ 45 - 38 = 7

5T - 7

The 50th Term is:

5 x 50 = 250

∴ 250 – 7 = 243

To Test:

## T-Number 30

5 x 30 = 150

∴150 – 7 = 143

##### Relationships

This student written piece of work is one of many that can be found in our GCSE T-Total section.

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