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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

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

 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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