• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  10. 10
    10
  11. 11
    11
  12. 12
    12
  • Level: GCSE
  • Subject: Maths
  • Word count: 2979

T-Total and the T-Number.

Extracts from this document...

Introduction

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

Aim:

My aim is to investigate the relationship between the T-Total and the T-Number.  I will first do so using a 9x9 grid. After that, I shall use grids of different sizes. Using algebra, I will find the formula for finding the T-Total using the T-Number for all grid sizes.  For further investigation, I plan to translate the "T" into different directions. I plan to put all my formulas in a "Formula Table" at the end of my investigation.

9x9:

T-Number

20

23

31

44

57

62

T-Total

37

52

92

157

222

247

This is a 9x9 grid with 6 "T" shapes inside it. Some of the "T"s are overlapping but this does not really matter. Next to it is a table showing each of the "T"s properties, (T-Number & T-Total). The first pattern being spotted is obviously that as the T-Number increases so does the T-Total. This meaning that the T-Total is directly proportional to the T-Number. I now need to figure out a formula for finding the T-Total using T-Number in a 9x9 grid, which I've done below showing the routes of my formula.

image00.pngn-19 + n-18 + n-17 + n-9 +n = 5n - 63 = T-Total

Above is a "T" representing itself in a 9x9 grid, and next to it as you can see is the formula for working out the T-Total knowing the T-Number.

...read more.

Middle

121

171

186

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

 This is a 7x7 grid with 6 "T" shapes inside it. Again they're overlapping which does not matter. Next to the grid is a "T" property table. I now have to figure out a formula for working out any number in the "T" knowing the T-Number in a 7x7 grid. The formula for working this out is shown below.

image11.png n-15 + n-14 + n-13 + n-7 +n = 5n – 49 = T-Total

Thisis a "T" representing itself in a 7x7 grid, and next to it as you can see is the formula for working out the T-Total knowing the T-Number.

I am now going to test the formula I have found.

234(5 x 17) -49 = 85-49 = 36 = T-Total              FORMULA WORKS

10

17

101112(5 x 25) -49 = 125-49 = 76 = T-Total              FORMULA WORKS

18

25

192021(5 x 34) -49 = 170-49 = 121 = T-Total              FORMULA WORKS

27

34

By now, I have found 4 formulas for working out any numbers in 7x7, 8x8 and 9x9 grids, knowing the T-Number. Another pattern I have now spotted in the formulas being discovered by myself is that as the grid size decreases by a size the formulas decreases by 7. Basically the formula is 5n takeaway the grid size multiplied by 7.

9 x9 Grid

8 x 8 Grid

7 x 7 Grid

n-19 + n-18 + n-17 + n-9 +n = 5n - 63

n-17 + n-16 + n-15 + n-8 +n = 5n – 56

n-15 + n-14 + n-13 + n-7 +n = 5n – 49

5n –(9x7) = 5n - 63

5n –(8x7) = 5n – 56

5n – (7x7) = 5n - 49

Now that I know that the formula goes up and down in 7s, I am going to attempt to predict the formula for a 10 x 10 and a 5 x 5 grid.

10x10:

Knowing the pattern for the formulas, I predict that the formula for a 10 x 10 grid will be 5n – 63 plus 7. Therefore it will be 5n – 70, because 63 + 7 = 70 and because 10 x 7 = 70. I will know check my prediction. Below is a part of a 10 x 10 grid.

T-Number

22

26

28

32

T-Total

40

60

70

90

image12.png

Above is part of a 10 x 10 grid and next to it is a table showing the properties of the 4 "T"s present in the part of the grid. Below is the working out for the formula, so then I can check if my predictions were correct.

image13.pngn-21 + n-20 + n-22 + n-10 +n = 5n – 70 = T-Total

The formula I have found matches the one I predicted it would be. But that's not it; I now have to check if the formula is correct and works positively.

Prediction check:

image14.png(5 x 22) -70 = 110-70 = 40 = T-TotalPREDICTION CORRECT

image15.png(5 x 26) -70 = 130-70 = 60 = T-TotalPREDICTION CORRECT

image16.png(5 x 32) -70 = 160-70 = 90 = T-TotalPREDICTION CORRECT

image17.png(5 x 28) -70 = 140-70 = 70 = T-TotalPREDICTION CORRECT

As you can see, my predicted formula totally matched the one I found by investigating the 10 x 10 grid, and positively worked. Just to make sure, I am now going to do the same for a 5 x 5 grid as mentioned earlier on.

5x5:

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

13

17

24

T-Total

25

30

50

85

...read more.

Conclusion

Conclusion:

I can conclude that in the time available to me, two weeks precisely, I think I have succeeded in investigating the relationship between the T-Total and the T-Number. I have used grids of different sizes and translated the "T"s to different directions and positions on the grids. By doing so I have found a number of formulas for working out any number including the T-Total knowing the T-Number in a number of grids.

Evaluation:

I would say that this investigation has been a success. I managed to find a number of rules and formulas to work out numbers in a "T". I do believe that I followed the guidelines given pretty well.

Unfortunately, my investigation was hindered by 1 thing – this was my lack of time to carry out the investigation as far as possible ( i.e. use more grids and test each of the formulas present in my formula page a few more times).

If I were to redo this investigation, I would make sure that I set aside enough time to do a proper job of it.

image09.png

Wais Naeemi        10E        Y-Band

...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. T-total Investigation

    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 82 83 84 85 86 87 88

  2. T-totals. I am going to investigate the relationship between the t-total, T, and ...

    (1 + g) - (d - b) (g - 1) + a - bg } - 7 Validation To thoroughly validate these formulae, all forms of and need to be tested. As there are sixteen combinations of the two vectors, using only an 11�11 grid will be sufficient for our test.

  1. In this section there is an investigation between the t-total and the t-number.

    The blue shape is the opposite of the red t-shape so therefore the formula for the blue t-shape is 5tn - 70 = t-total. The sign has become the opposite of what it use to be. This has happened in many cases before.

  2. For my investigation, I will be investigating if there is a relationship between t-total ...

    I then can simplify this to: T-total = 5N-98 Using the results from the other grid sizes I have constructed the table below Grid size value (multiplied by itself) Relative value to be subtracted in equation Similarity 7 47 Grid size X 7 8 54 Grid size X 7 9

  1. For my investigation, I will be investigating if there is a relationship between t-total ...

    find a rule which can find the t total of any grid size. I noticed that every time the grid size is increased by 1 the variable at the end of the formula becomes another minus seven to what it already was before, e.g. 5N-21, 5N-28, 5N-35...... and so on.

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

    + ( 2 x 9 ) 45 (187 - 142) 32 142 t = (5 x 32) + ( 2 x 9 ) 45 (142 - 97) 23 97 t = (5 x 23) + ( 2 x 9 ) 45 (97 - 52) 14 52 t = (5 x 14)

  1. In this investigation Im going to find out relationships between the grid sizes and ...

    T-Number (n) T-Total (t) 30 87 39 132 48 177 57 222 66 267 When going vertically on the 9x9 grid the table of result shows a ratio of 1:5 between the T-Number and the T-Total. So no matter how the T-Shape is moved, either horizontally or vertically the T-number and the T-Total are in the same ratio of 1:5.

  2. My aim is to see if theres a relation between T total and ...

    So the 50th value would be: 5 x 50 - 7 x 12 = 160 PART 3: Now I am going to rotate my T - shapes in different grid sizes to 90� anticlockwise, 180�, and 90� clockwise to see if I would get a different algebraic expression.

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