# T-total.I have taken the T-shape template from the example and moved it along the row from the T-number 20 to 26. I will then work out the T-total of each T-number by adding all the numbers in the T-shape.

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Introduction

T-total Coursework

Part 1 – Investigate the relationship between the T-total and the T-number

T-shape

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

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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-number

I have taken the T-shape template from the example and moved it along the row from the T-number 20 to 26. I will then work out the T-total of each T-number by adding all the numbers in the T-shape. The results were as follows:

T-number | T-total |

20 | 27 |

21 | 42 |

22 | 47 |

23 | 52 |

24 | 57 |

25 | 52 |

26 | 67 |

I have found a pattern emerging, which is, as the T-number increases by 1 the T-total increases by 5. I will try and find out the relationship between the T-total and the other numbers in the T-shape.

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 |

I have chosen a random T-number of 60 and will try and find a relationship between all of the other numbers in the T-shape.

First I will try and take away all the other numbers from the T-number:

60-41 = 19

60-42 = 18

60-43 = 17

60-51 = 9

I will now try the same thing again but using a different T-number to see if the same pattern occurs:

12 | 13 | 14 |

21 | 22 | 23 |

30 | 31 | 32 |

I will use the T-number

of 31

Middle

I have substituted the T-number into the equation

My formulae is correct as if I were to do the sum manually without using the formulae by adding 61+62+63+71+80 (all the numbers in the T-shape) it will equal 337 the same answer I got using my formulae. This proves that my formulae Is correct.

## Part 2 – Use grids of different sizes. Translate the T-shape to different positions. Investigate relationships between the T-total, the T-numbers and the grid size.

To investigate the relationship between the T-total, T-number and the grid size I will need to put the template into algebraic form.

I have changed the template into algebraic form. When I added the equations in the T-shape (Tn + Tn-g + Tn-2g-1 + Tn-2g + Tn-2g+1) and got the answer 5Tn – 7g, where Tn is the T-number and g is the grid size.

I will now try and see if the formulae are correct for different grid sizes.

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In my grid I have chosen a random T-number of 40 and will find a formulae for rotation

21 | 22 | 23 |

31 | ||

40 |

Tn-19 + Tn-18 + Tn-17 + Tn-

= 9 + Tn

= 5Tn-63

33 | ||

40 | 41 | 42 |

51 |

Tn + Tn+1 + Tn+2 + Tn-7 +

= Tn+11 = 5Tn+7

40 | ||

49 | ||

57 | 58 | 59 |

Tn + Tn+9 + Tn+17 +

= Tn+18 + Tn+19

= 5Tn+63

29 | ||

38 | 39 | 40 |

47 |

= Tn-11 + Tn-2 +Tn+7 + Tn-1

+ Tn

= 5Tn-7

I can see from this that:

When the T is at 0° the formulae will be 5T-7g

When the T is at 90° the formulae will be 5Tn+7

When the T is at 180° the formulae will be 5Tn+7g

When the T is at 240° the formulae will be 5Tn-7

I will now test my formulae to see if they are correct by using the formulae I found and seeing if I get the same results as I would doing it manually.

0°90°

5Tn-7g 5Tn+7

5x40 – 7x9 =137 5x40+7 =207

180°240°

5Tn+7g 5Tn-7

5x40 + 7x9 =263 5x40-7 = 193

Now I will do the calculations manually:

0°90°

Tn=40 Tn=40

Tn+21+22+23+31 = 137 Tn+41+42+33+51 =207

180°240°

Tn=40 Tn=40

Tn+49+57+58+59 =263 Tn+39+38+47+29 =193

I got the same results as I did by using my formulae this proves that my formulae is correct for rotation.

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

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