# From the table I have noticed that when that when you move a T shape across each time all the numbers go up by one, as they are five numbers the total goes up by five.

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Introduction

T Shape Coursework

9 Grid

My teacher gave me a candidatesheet if I add up the total in the T shape I get:

1 | 2 | 3 |

11 | ||

20 |

T Total=1+2+3+11+20=37

20x5-63=37

I am now going to draw 3 more T shape moving to the right across one on a 9 grid

2 | 3 | 4 |

12 | ||

21 |

T Total= 2+3+4+12+21=42

21x5-63=42

3 | 4 | 5 |

13 | ||

22 |

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

22x5-63=47

4 | 5 | 6 |

14 | ||

23 |

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

23x5-63=52

Sum | Total | Increase |

1+2+3+11+20 | 37 | |

2+3+4+12+21 | 42 | 5 |

3+4+5+13+22 | 47 | 5 |

4+5+6+14+23 | 52 | 5 |

From the table I have noticed that when that when you move a T shape across each time all the numbers go up by one, as they are five numbers the total goes up by five.

I am now to investigate the total by moving the T shape down the grid

1 | 2 | 3 |

11 | ||

20 |

T Total= 1+2+3+11+20=37

20x5-63=37

10 | 11 | 12 |

20 | ||

29 |

T Total= 10+11+12+20+29=82

29x5-63=82

19 | 20 | 21 |

29 | ||

38 |

T Total= 19+20+21+29+38=127

38x5-63=127

28 | 29 | 30 |

38 | ||

47 |

T Total=28+29+30+38+47=172

47x5-63=172

I have noticed that each time I move the T shape down the grid each number increases by nine, as they are five numbers the total increase by 45.

Sum | Total | Increase |

1+2+3+11+20 | 37 | |

10+11+12+20+29 | 82 | 45 |

19+20+21+29+38 | 127 | 45 |

28+29+30+38+47 | 172 | 45 |

Middle

21

T total=4+5+6+13+21=49

21x5=105-56=49

Sum | Total | Increase |

1+2+3+10+18 | 34 | |

2+3+4+11+19 | 39 | 5 |

3+4+5+12+20 | 44 | 5 |

4+5+6+13+21 | 49 | 5 |

From the table I have noticed that when that when you move a T shape across each time all the numbers go up by one, as they are five numbers the total goes up by five.

I am now to investigate the total by moving the T shape down the grid

9 | 10 | 11 |

18 | ||

26 |

T total=9+10+11+18+26=74

26x5=130-56=74

17 | 18 | 19 |

26 | ||

34 |

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

34x5=170-56=114

25 | 26 | 27 |

34 | ||

42 |

T total=25+26+27+34+42=154

42x5=210-56=154

Sum | Total | Increase |

1+2+3+10+18 | 34 | |

9+10+11+18+26 | 74 | 40 |

17+18+19+26+34 | 114 | 40 |

25+26+27+34+42 | 154 | 40 |

I have noticed that each time I move the T shape down the grid each number increases by eight, as they are five numbers the total increase by 40.

10 Grid

t-21 | t-20 | t-19 |

t-10 | ||

T |

T total= (t) + (t-21) + (t-20) + (t-19) + (t-10)

=5t-70

1 | 2 | 3 |

12 | ||

22 |

T Total= 1+2+3+12+22=40

22x5=110-70=40

I am now going to draw 3 more T shape moving to the right across one on the grid

2 | 3 | 4 |

13 | ||

23 |

T Total= 2+3+4+13+23=45

23x5=115-70=45

3 | 4 | 5 |

14 | ||

24 |

T Total=3+4+5+14+24=50

24x5=120-70=50

4 | 5 | 6 |

15 | ||

25 |

T Total=4+5+6+15+25=55

25x5=125-70=55

Sum | Total | Increase |

1+2+3+12+22 | 40 | |

2+3+4+13+23 | 45 | 5 |

3+4+5+14+24 | 50 | 5 |

4+5+6+15+25 | 55 | 5 |

I am now to investigate the total by moving the T shape down the grid

11 | 12 | 13 |

22 | ||

32 |

T Total= 11+12+13+22+32=90

32x5=160-70=90

21 | 22 | 23 |

32 | ||

42 |

T Total=21+22+23+32+42=140

42x5=210-70=140

31 | 32 | 33 |

42 | ||

52 |

Conclusion

t-20

t-19

t-10

T

T total= (t) + (t-10) + (t-20) + (t-19) + (t-21)

=5t-70

(This only works on a 10 grid)

9 Grid

t-19 | t-18 | t-19 |

t-9 | ||

T |

T total= (t) + (t-9) + (t-18) + (t-17) + (t-19)

=5t-63

(This only works on a 9 grid)

8 Grid

t-17 | t-16 | t-15 |

t-8 | ||

T |

T total= (t) + (t-8) + (t-16) + (t-15) + (t-17)

=5t-56

(This only works on a 8 grid)

7 Grid

t-15 | t-14 | t-13 |

t-7 | ||

T |

T total= (t) + (t-7) + (t-14) + (t-13) + (t-15)

=5t-49

(This only works on a 7 grid)

I have noticed that the algebra changes because the grid size is different each time.

I call the size ‘g’ I can work out some algebra for each box.

t-2g-1 | t-2g | t-2g+1 |

t-g | ||

T |

(This is now a ‘g’ grid)

T total= (t) + (t-g) + (t-2g) + (t-2g-1) + (t-2g+1)

=5t-7g

So to work out the total of a t shape anywhere on a grid I can multiply the t number by 5 and subtract 7 lots of the grid size.

I will now check this on this T shape a 10 grid with 26 as the T number.

5 | 6 | 7 |

16 | ||

26 |

T total= 5+6+7+16+26 = 60 T number= 26

T total= 5x26=130-70=60 Grid size= 10

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

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