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  • Level: GCSE
  • Subject: Maths
  • Word count: 1373

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.

Extracts from this document...

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

37image00.png

2+3+4+12+21

42image01.png

5

3+4+5+13+22

47image02.png

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

37image00.png

10+11+12+20+29

82image01.png

45

19+20+21+29+38

127image02.png

45

28+29+30+38+47

172

45

...read more.

Middle

21

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

            21x5=105-56=49

Sum

Total

Increase

1+2+3+10+18

34image00.png

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

34image00.png

9+10+11+18+26

                     74image01.png

40

17+18+19+26+34

114image02.png

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

40image00.png

2+3+4+13+23

45image01.png

5

3+4+5+14+24

50image02.png

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

...read more.

Conclusion

t-20

t-19

t-10

  T

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

          =5t-70

image05.png

             (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

image06.png

                (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

image07.png

                (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

image08.png

(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

...read more.

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