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

T-Totals Maths

Extracts from this document...

Introduction

T-Totals Coursework

My aim is to investigate the relationship between the T-Number and the T-shape on a varying size of grid.

1

2

3

4

5

To the left is a basic T-shape. In this investigation, the number in bold which is “5” is the T-Number.  

The sum of the all the numbers in the T-shape is the T-Total.

For Example:

                1+2+3+4+5 = 10.

                         Therefore the T-Total for this T-Shape is 10.

Using this information I can now begin my investgation.

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

I am going to start my investiation on a 9 by 9 grid. This shows all the numbers from    1 to 81.

Firstly in my investigation, I am going to find a formula that relates my T-Number to my T-Total, firstly with a 9x9 grid and then onto a grid of any size.

To work out my formula I have drawn two T-Shapes on my grid. The first t-shape in green has a T-Number of 20. The other T-Shape highlighted in pink has been translated one number to the right giving it a T-Number of 21.

I then worked out the T-Total for both shapes.

Green T-Shape: 1+2+3+11+20 = 37

                                               Pink T-Shape:  2+3+4+12+21 = 42        

T-Number

T-Total

20

37              +5

21

42              +5

22

47              +5

23

52              +5

24

57

...read more.

Middle

T-Total would be 57.

I then calculated this and my prediction turned out to be correct.

This is because there is 5 numbers in the T-Shape and each number in the T-Shape has to go up by one when it it translated to the right therefore adding five more onto the total. For this same reason, five has to be included as the main focus of my algebraic formula.

The Algebraic Formula

I could then, using the process of elimination and trial and error come up with an algebraic formula. However, I concluded that there must be a more logical way.

I therefore looked at my grid again.

Starting from my T-number, which in this case is called n, I have calculated this algrbraic t-shape. in the boxes of the shape, the numbers inside are related to the T-Number (n).

n - 19

n - 18

n - 17

n – 9

n

In this case on my 9x9 grid, the square directly above the T-Number (which is 20)  is nine less. This makes that square n-9.

...read more.

Conclusion

5n – 7t = T-Total.

I will now go back to the T-Totals from my 9 x 9 grid and try my new and improved  formula on both of them.

9 x 9 T-Shape One.

T-Number = 20

T-Total = 37

For this Formula  I am going to explain why this works.

image20.png

(5 x 20) – (7 x 9) = 37.image03.pngimage04.pngimage02.pngimage05.pngimage06.png

image07.pngimage08.pngimage10.pngimage09.png

9 x 9 T-Shape Two.

T-Number = 21

T-Total = 42

(5 x 21) – (7 x 9) = 42.

So far, with the 9 x 9 grid, the formula works. I am now going to try it out on the 8 x 8 grid T-Totals.

8 x 8 T-Shape One.

T-Number = 18

T-Total = 34

(5 x 18) – (7 x 8) = 34

image11.png

image13.png

8 x 8 T-Shape Two.

T-Number = 19

T-Total = 39

(5 x 19) – (7 x 8) = 39.

As the formula has worked on both grids.

This has indefinatly proved again that my formula is correct.

To prove this fianally I am going to test my formula on two T-Shapes from a 7x7 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

I have chosen two T-Shapes to try my formula on.

7 x 7 T-Shape One.

T-Number = 16

T-Total = 31.

(5 x 16) – (7 x 7) = 31image15.pngimage14.png

7 x 7 T-Shape Two

T-Number = 17

T-Total = 36

(5 x 17) – (7x7) = 36.

I now have a formula that relates the T-Number to the T-Shape regardless of the T-Shapes size as long as the formula is followed corectly.

Vikki Baker 10 Bragg.

...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. Connect 4 - Maths Investigation.

    14L - 22 In order to form an over all rule for any connect 3 with any height and any length. I will have to tabulate all the current total rules so that I can use the difference method to work it out.

  2. Objectives Investigate the relationship between ...

    n+n-1+n-2+n-12+n+8 =n+n+n+n+n+8-1-2-12=5n-7 My formula for finding the T-total of any 180 rotated T-shape is therefore '5n-7' Let's check to see if it works. I will use the T-shape, T23 to test if this works. 5x23 - 7 = 108 The formula works, just as expected.

  1. T-Shapes Coursework

    x Number of Terms The "1/2{2n + 10(l + 1)}" part of the formula gives us the mean, and so this is multiplied by l because l is the length of the tail, and therefore the number of boxes (or terms)

  2. T-Shapes Coursework

    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

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

    We can test this on different positions on the 9x9 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

  2. T totals - translations and rotations

    see in my 8by8 grid above and I will be representing this as N in my equation. My T-total is 18+10+2+1+3 = 34. The number in my T-shape directly above my T-number is 8 places back on my grid so it is N-8.

  1. T-Totals. We have a grid nine by nine with the numbers starting from 1 ...

    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

  2. T-Total Maths coursework

    + 7 = 55+7 = 62 As expected, the equation has produced yet another correct answer. Another example is below, N= 12 T= (5x 12) + 7 = 60+7 = 67 Here is the last equation I will show from the 9 by 9 grid to show that the equation N=13 T= (5x13)

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