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  • Level: GCSE
  • Subject: Maths
  • Word count: 1668

Investigate the relationship between the T-Total and the T-Number. Use grids of different sizes. Translate the T-Shapes to the different positions. Investigate

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Introduction

09th January 2006

GCSE Mathematics Coursework

T-Totals

  • Investigate the relationship between the T-Total and the T-Number.
  • Use grids of different sizes. Translate the T-Shapes to the different positions. Investigate relationships between the T-Total, the T-Number and the grid sizes.
  • Use grids of different sizes again. Try other transformations and combinations of transformations. Investigate the relationships between the T-Total, the T-Number, the grid size and the transformations.

T-Total Grid

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

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64

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72

73

74

75

76

77

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79

80

81

T-Numbers  (T)

20

21

22

23

24

T-Total

 37

42

47

52

57

                                                          +5            +5            +5             +5    

5 x 20 = 100

 100 – 37 = 63

The difference between the T-Totals is 5 this makes the first part of the formula: 5T

To work out the second part takes the T-Number and multiplies by the difference.

5T - 63

The 50th Term is:

...read more.

Middle

5 x 16 = 80

 80 – 31 = 49

5T – 49

The 50th Term is:

5 x 50 = 250

 250 - 49 = 201

To Test:

T Number 40

5 x 40 = 200        

200 – 49 = 151

T-Total Grid

1

2

3

4

5

6

7

8

9

10

11

12

13

14

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16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

T-Number

14

15

16

17

18

T-Total

28

33

38

43

48

                                                +5                       +5                      +5                      +5

5 x 14 = 70

 70 – 28 = 42

5T – 42

The 50th Term is:

5 x 50 = 250

 250 - 42 = 208

To Test:

T Number 30

5 x 30 = 150

150 – 42 = 108

Relationships and Master Formula Working Out

Formulae’s

9 x 9 Grids: 5T - 63

8 x 8 Grids: 5T - 56

7 x 7 Grids: 5T – 49

6 x 6 Grids: 5T – 42

  • Smaller the Grid Size the less you have to take away from the T-Total
  • The Larger the grid size the more you have to take away from the T-Total
  • All The Formulas have gaps of 7

    (Ex. 63 – 56 = 7. 56 – 49 = 7. 49 – 42 = 7.)

I found out that the master formula is 5T-(7xG)

I got the 5 by looking at the differences of the number.

The T stands for the T-Number (which is always 5; as there are 5 squares in the T; and it is current throughout.)

...read more.

Conclusion

T-Number 30

5 x 30 = 150

150 – -63 = 213

8 x 8 Grids: Transformation

T-Number

11

12

13

14

15

T-Total

48

53

58

63

68

5 x 11 = 55

 55 – 48 = 7

5T - 7

The 50th Term is:

5 x 50 = 250

 250 – 7 = 243

To Test:

T-Number 30

5 x 30 = 150

150 – 7 = 143

7 x 7 Grids: Transformation

T-Number

8

9

10

11

12

T-Total

47

52

57

62

67

5 x 8 = 40

 40 - 47 = -7

5T - -7

The 50th Term is:

5 x 50 = 250

 250 – -7 = 257

To Test:

T-Number 30

5 x 30 = 150

150 – -7 = 157

7 x 7 Grids: Transformation

T-Number

2

3

4

5

6

T-Total

59

64

69

74

79

5 x 2 = 10

 10 - 59 = -49

5T - -49

The 50th Term is:

5 x 50 = 250

 250 – -49 = 299

To Test:

T-Number 30

5 x 30 = 150

150 – -49 = 199

7 x 7 Grids: Transformation

T-Number

2

3

4

5

6

T-Total

59

64

69

74

79

5 x 2 = 10

 10 - 59 = -49

5T - -49

The 50th Term is:

5 x 50 = 250

 250 – -49 = 299

To Test:

T-Number 30

5 x 30 = 150

150 – -49 = 199

6 x 6 Grids: Transformation

T-Number

7

8

9

10

11

T-Total

42

47

52

57

62

5 x 7 = 35

 35 - 42 = -7

5T - -7

The 50th Term is:

5 x 50 = 250

 250 – -7 = 257

To Test:

T-Number 30

5 x 30 = 150

150 – -7 = 157

6 x 6 Grids: Transformation

T-Number

2

3

4

5

6

T-Total

52

57

62

67

72

5 x 2 = 10

 10 - 52 = -42

5T - -42

The 50th Term is:

5 x 50 = 250

 250 – -42 = 292

To Test:

T-Number 30

5 x 30 = 150

150 – -42 = 192

6 x 6 Grids: Transformation

T-Number

9

10

11

12

13

T-Total

38

43

48

53

58

5 x 9 = 45        

 45 - 38 = 7

5T - 7

The 50th Term is:

5 x 50 = 250

 250 – 7 = 243

To Test:

T-Number 30

5 x 30 = 150

150 – 7 = 143

Relationships

...read more.

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