• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Relationships with the T-shapes, the T-total and the position of the stair shape on the grid.

Extracts from this document...

Introduction

T- Total

By Gary Holmes

Introduction:

                In this investigation in which I am presenting, I am going to look at the relationships with the T-shapes, the T-total and the position of the stair shape on the grid. I will be observing patterns and I will look at the other stairs to see if I can notice other formulas for these. Finally, I hope to be able to find the formula for any size grids and any T-total

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

Look at the T-shape drawn on the 9 by 9     number grid.

The total of the numbers inside the T-shape is 1+2+3+11+20=37

This is called the T-total.

The number at the bottom of the T-shape is called theT-number.

The T-number for this T-shape is 20.

T

If you take the other numbers in the T-Shape away from the T-Number you get a T-Shape like this.

T-17

T-18

T-19

T-9

T

You will notice that the centre column of the T-Shape is going up in 9's because of the table size.

...read more.

Middle

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

X=5X33-42 (20+21+22+27+33=123

X=165-42

X=123


Now I have worked the formula out for the T-Shape in the one position, I am going to translate the T-Shape to different positions and investigate the relationships between the T-Total, the T-number and the grid size.

A 3 by 3 grid can be used for the other 3.

1

2

3

4

5

6

7

8

9

T

T+G

T+2G+1

T+2G

T+2G-1

T

T+G

T+2G

T+2G-1

T+2G+1

7G+5T

X=7G+5T=7x3+5x2

=21+10 (2+5+7+8+9=31)

=31

I will now try this new formula on a 4 by 7 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

7G+5T

x=7x4+5x10 (17+18+19+14+10=78)

=28+50

=78

I will now try it on a 8 by 3 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

7G+5T

x=7x9+5x2 (19+20+21+11+2=73)

=56+10

=73

I have tried this new formula for an inverted T and it works, the formula is: 7G+5T

1

2

3

4

5

6

7

8

9

T-1-G

T-2

T-1

T

T-2+G

T

T-1

T-2

T-2-G

T-2+G

5T-7

X= 5T-7=5x6-7

=30-7 (1+4+7+5+6=23)

=23

I will now try the new formula on a 4 by 4 grid

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

5T-7

X=5x11-7 (5+9+13+10+11=48)

=48

And on a 4 by 9 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

5T-7

x=5x19-7 (13+17+21+18+19=88)

=88

I have tested this new formula for a side ways T the formula works it is: 5T-7

1

2

3

4

5

6

7

8

9

T+2-G

T

T+1

T+2

T+2+G

T

T+1

T+2

T+2+G

T+2-G

5t+7

The formula is 5T+7

X=5T+7=5x4+7

=20+7 (3+6+9+5+4=27)

=27

I will now try the new formula on a 6 by 6 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

...read more.

Conclusion

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

T- Number = 12

Purple T-Total = 25

Grey T-Total = 67 a difference of 42….. The formula 5T - 7G + 42

Now I'm going to see what happens on a 6 by 6 width 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

T- Number = 14

Purple T-Total = 33

Grey T-Total = 82 a difference of 49….. The formula 5T - 7G + 49

7 by 7 width 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

T- Number = 16

Purple T-Total = 41

Grey T-Total = 97 a difference of 56….. The formula 5T - 7G + 56

Table of Results

Grid width

Purple T-Total

Grey T-Total

Difference between the two T-Total

5

25

67

42

6

33

82

49 Goes up in 7's

7

41

97

56

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

Now I will rotate it again 180° from it's original place

T- Number = 12

Purple T-Total = 25

Grey T-Total = 95 a difference of 70….. The formula 5T - 7G + 70

Now I'm going to see what happens on a 6 by 6 width 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

T- Number = 14

Purple T = 28

Grey T = 112 a difference of 84….. The formula 5T - 7G + 84

7 by 7 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

T- Number = 16

Purple T-Total = 31

Grey T-Total = 129 a difference of 98….The formula 5T - 7G + 98

Conclusion: The amount of numbers in the T decide the number before N in my formula. The number before the W is found by
(T-total - 2T) divided by the top right number of the grid.

By Gary Holmes

...read more.

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

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE T-Total essays

  1. Number Stairs

    finding my formula algebraically as well I can see that the formula should be correct. However just to make sure I will test the formula using 3 different numbers. 2 step stair : Testing By using my formula 3n+11 I'm going to test this formula in three different positions referring to the number in the left hand corner.

  2. Number Stairs

    This works for the entire bottom row except N=1 because it doesn't have a total before it, and N=9 and 10, because they don't have totals. You can also see that the step stair consists of 6 numbers each of these numbers moves 1 position to the right, e.g.

  1. T-Total Investigation

    105 and of the translated shape is 55, using the formula we get, t= 5((23+1)-(3x5)) + 2x5 t= 5(24-15) + 10 t= (5x9) + 10 t= 55 Thus proving my theory correct therefore we can state The T-Total any combination of a translation (vertically, horizontally, or both)

  2. Objectives Investigate the relationship between ...

    98 +56 As you can see the increment was '+56' this allows me to build a simple formula. x = current T-total + 56 where 'x' is equal to the new T-total Therefore: x = 42 +56 x = 98 New T-total = 98 Although a good formula an algebraic

  1. T totals. In this investigation I aim to find out relationships between grid sizes ...

    We know with will not make a difference to the final answer as proved in question 2. 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

  2. T-totals, T-numbers and T-shapes.

    in the table above every time you minus the T-number and the T-total together the answer goes in order of 4. Proof that my result works: 3 4 5 13 22 The T-number for this T-shape is 22. Using the same method, I believe if I add all the 5

  1. Maths GCSE Coursework – T-Total

    + 5 + 6 + 14 + 23 T= 52 Thus proving this method on a grid with of 9. We now need to try it on a grid width of 6 for example, 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

  2. T-Total. I will take steps to find formulae for changing the position of the ...

    Moving to the left: The same approach is taken as moving the T shape to the left as moving the T shape to the right except for a minor adjustment. When moving the T shape to the left, instead of adding 5 x amount of squares moved across, a minus is used.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work