# T totals. By drawing 4of these t-shapes I have noticed that the T-total increases by 5. When I moved my T-shape 1 place to the right, my T-number increased by 1.

Extracts from this document...

Introduction

T-Totals

T=3+4+5+13+22=47

T-Total=47

T-number=22

T=4+5+6+14+23=52

T-Total=52

T-number=23

T=5+6+7+15+24=57

T-Total=57

T-number=22

T=6+7+8+16+25=62

T-Total=62

T-number=25

Comment

By drawing 4of these t-shapes I have noticed that the T-total increases by 5. When I moved my T-shape 1 place to the right, my T-number increased by 1.

Comment

T=m+ (m-9) +(m-18)+ (m-17) + (m-19) Comment

=5m-63

CheckT=Total

47=5(22)-63 m=T-number

47=110-63

47=47

8 by 8 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 |

I am now going to do the same method but by using an 8 by 8 grid.

T=17+18+19+26+34=114

T-Total=114

T-number=34

T=18+19+20+27+35=119

T-Total=119

T-number=35

T=19+20+21+28+36+124

T-Total=124

T-number=36

T=6+7+8+16+25=62

T-Total=62

T-number=37

Comment

By drawing 4of these t-shapes I have noticed that the T-total still increases by 5.

Middle

T=m+ (m-7) + (m-14) + (m-15) + (m-13) Comment

=5m-49

CheckT=Total

m=T-number

9 by 9

T=5m-63

8 by 8

T=5m-56

7 by 7

T=5m-49

I have noticed that all multiples of 7. The numbers on top of the T-number increase by 1.

Grid Size

Comment

Check

9 by 9

Comment

T=Total

T-number=21

T=5(21)-7(9)

105-63

Comment

I am now going to do the same method but I will put the T-shape in different positions.

9 by 9

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=3+12+21+11+10=54

T-Total=57

T-number=10

T=4+13+22+12+11=62

T-Total=62

T-number=11

T=5+14+23+13+12=67

T-Total=67

T-number=12

T=6+15+24+14+13=72

T-Total=72

T-number=13

Comment

By drawing 4of these shapes I have noticed that the T-total increases by 5.

Conclusion

T-number=32

Comment

By drawing 4 of these shapes I have noticed that the T-total increases by 5. When I moved my shape 1 place to the right, my T-number increased by 1.

Comment

T=m+ (m+9) +(m+18)+ (m+17) + (m+19) Comment

=5m+63

CheckT=Total

47=5(22)-63 m=T-number

47=110-63

47=47

I am now going to do the same method but put it in another position again.

9 by 9

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=3+12+13+14+21=63

T-Total=63

T-number=14

T=4+13+14+15+22=68

T-Total=

T-number=15

T=5+14+15+16+23=73

T-Total=73

T-number=16

T=6+15+16+17+24=78

T-Total=78

T-number=17

Comment

By drawing 4 of these shapes I have noticed that the T-total increases by 5. When I moved my shape 1 place to the right, my T-number increased by 1.

Comment

T=m+ (m+1) +(m+2)+ (m-7) + (m+11) Comment

=1+2=3

=3+11=14

=14-7=7

=5m+7

CheckT=Total

47=5(22)-63 m=T-number

47=110-63

47=47

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

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