• 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
  • Level: GCSE
  • Subject: Maths
  • Word count: 2322

T-Totals - All the things T said

Extracts from this document...

Introduction

Chan-woo Kim

Mathematics coursework

T-Totals - All the things T said

-Word definition

*T-Total

eg)

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

Looking at T-shape drawn on 5 by 5 number grid.

The sum of the numbers inside the shape is 1+2+3+7+12=25

25 is called 'T-Total'.

*T-Number

The number at the bottom of the shape (the number which is shown by the shaded square) is called 'T-Number'.

The T-Number for the T-shape above is 12.

-The aim of this project is to investigate the relationship between T-Total and T-Number.

-I use 9 by 9 number grid to investigate the relationship.

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

-Then I pick some samples to find what I am going to find.

Sample 1)

1

2

3

11

20

T-Number = 20

T-Total = 1+2+3+11+20 = 37

Sample 2)

2

3

4

12

21

T-Number = 21

T-Total = 2+3+4+12+21 = 42

Sample 3)

3

4

5

13

22

T-Number = 22

T-Total = 3+4+5+13+22 = 47

-I arrange these samples in the table.

T-Number

20

21

22

T-Total

37

42

47

-As we notice, when T-Number increases by 1, its T-Total also increases by 5. It shows that there is a certain pattern.

-If I define T-Number = N

N-19

N-18

N-17

N-9

N

T-Total = N+N-9+N-18+N-19+N-17 = 5N-63

-To check whether it is right, I substitute N for 20.

5N-63 = 5*20-63 = 100-63 = 37.

...read more.

Middle

T-Number

22

23

24

T-Total

40

45

50

-As we can see, when T-Number increases by 1, T-Total also increases by 5. It is obvious that there is a certain pattern.

-If I define T-Number = N

N-21

N-20

N-19

N-10

N

T-Total = N+N-10+N-20+N-21+N-19 = 5N-70 = 5N-70

-To check whether it is right, it is easy and quick that I substitute N for 22.

5N-70 = 5*22-70 = 110-70 = 40

-When T-Number is 22, T-total is 40 and equation fits. Consequently the relationship between T-Number and T-Total is :

T = 5N-70

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

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

-Now I use 11 by 11 number grid to find the relationship between T-Number and T-Total.

Sample 1)

1

2

3

13

24

T-Number = 24

T-Total = 1+2+3+13+24 = 43

Sample 2)

2

3

4

14

25

T-Number = 25

T-Total = 2+3+4+14+25 = 48

Sample 3)

3

4

5

15

26

T-Number = 26

T-Total = 3+4+5+15+26 = 53

-I arrange the samples in the table.

T-Number

24

25

26

T-Total

43

48

53

-Again we notice, when T-Number increases by 1, T-Total also increases by 5. Now it is certain that there is a pattern.

-If I define T-Number = N

N-23

N-22

N-21

N-11

N

T-Total = N+N-11+N-22+N-23+N-21 = 5N-77

-Now I am going to check whether it it true. To do it, I substitute N for 24.

5N-77 = 5*24-77 = 120-77 = 43

-When T-Number is 24, T-Total is 43 and the equation does make 43 when N is 24. Therefore the relationship between T-Number and T-Total is :

T = 5N-77

-Now, I arrange these 3 equations that I have found from my the investigation.

Grid

9*9

10*10

11*11

Equation

5N-63

5N-70

5N-77

-Look at the numbers -63, -70, and -77. They increase by -7 when the size of grid increases by 1.

-From these numbers, we can find a certain interesting point.

-63 = -7*9

-70 = -7*10

-77 = -7*11

-When we look at these results, we can notice that - 7 is constant and the number which we use to multiply it is the same as grid number. For example, -63 is from the equation of 9 by 9 grid and - 63 = -7*9. The same relationship is found in all the examples and therefore the relationship between T-Number, T-Total, and number grid is :

T-Number = N, T-Total = T, Grid =G

T = 5N-7G

-Now, I turn T-shape 90 degree clockwise and investigate the relationship between T-Number and T-Total.

*

*

  Original                   Rotated one

* = T-Number

-I use 9 by 9 grid to find the relationship.

Sample 1)

3

10

11

12

21

T-Number = 10

T-Total = 10+11+12+3+21 = 57

Sample 2)

4

11

12

13

22

T-Number = 11

T-Total = 11+12+13+4+22 = 62

Sample 3)

5

12

13

14

23

T-Number = 12

T-Total = 12+13+14+5+23 = 67

-I arrange these samples in the table.

T-Number

10

11

12

T-Total

57

62

67

-It shows that there is a certain pattern as when T-Number increases by 1, T-Total increases by 5.

-If I define T-Number = N

N-7

N

N+1

N+2

N+11

T-Total = N+N+1+N+2+N+11+N-7 = 5N+7

-I check whether it is a suitable equation, by substituting N for 10

5N+7 = 5*10+7 = 57

-As I checked above, it is the right equation. Therefore the relationship between T-Number and T-Total is :

T = 5N+7

-I Change the grid to 10 by 10 and investigate the relationship.

Sample 1)

3

11

12

13

23

...read more.

Conclusion

3

14

24

25

26

T-Number = 3

T-Total = 3+14+25+24+26 = 92

Sample 3)

4

15

25

26

27

T-Number = 4

T-Total = 4+15+26+25+27 = 97

-I arrange these results in the table.

T-Number

2

3

4

T-Total

87

92

97

-As we can notice, it is possible that there is a certain pattern because when T-Number increases by 1, T-Total increases by 5.

-If I define T-Number = N

N

N+11

N+21

N+22

N+23

T-Total = N+N+11+N+22+N+21+N+23 = 5N+77

-To check whether it is the right equation, I substitute N for 2.

5N+77 = 5*2+77 = 87

-The result above shows that this equation does make 87 when N is 2 so that it is the right equation. Therefore the relationshio between T-Number and T-Total is :

T = 5N+77

-Now, I arrange these 3 equations that I have found from the investigation.

Grid

9*9

10*10

11*11

Equation

5N+63

5N+70

5N+77

-Look at the numbers 63, 70, 77. They increase by 7 when the size of grid increases by 1.

-From these numbers, we can find an interesting point.

63 = 7*9

70 = 7*10

77 = 7*11

-When we look at these results, we can notice that 7 is constant and the number which we use to multiply it is the same as the grid number. For example, 63 is from the equation of the 9 by 9 grid and 63 = 7*9. The same relationship is found in all the examples and therefore the relationship between T-Number, T-Total, and number grid is :

T-Number = N, T-Total = T, Grid = G

T = 5N+7G

-What I have found from the investigation is that T-Total increases by a certain algebraic pattern linked with T-Number and Grid number and algebraic pattern is changed when number grid is changed and/or T-shape is rotated. Therefore the relationship between T-Number and T-Total is variable.

...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. The T-Total Mathematics Coursework Task.

    * I will round off by evaluating my coursework. Step One Here are some different types of T-shapes that could be drawn on the 9 by 9 grid. Please see the next page for the T-shapes written equations. 1 2 3 4 5 6 7 8 9 10 11 12

  2. T-totals, Main objective of this project of T-totals coursework is to find an inter-relationship ...

    used the T-number to work out the rule by subtracting the T-number with the other minor numbers inside the T-shape; This equals 5n-63 Then I calculated an overall rule that shows a relationship Between the T-total and the T-number alongside the grid number.

  1. T-Shapes Coursework

    is the First Term in the Tail, because it is always "g more" than n. (n + gl) is the Last Term in the Tail because there are always "l" number of "g"s in it. A) Justification of Sum of Wing This is really the same justification that was in

  2. T-Total Investigation

    again it will be easier to find generalizations: Center of Rotation (v) Rotation (degrees) Direction T-Total (t) Difference compared to original T-Total 14 0 N/a 52 0 14 90 Clockwise 72 +20 14 180 Clockwise 88 +36 14 270 Clockwise 68 +16 It is hard to make any immediate generalizations

  1. Maths Coursework - T-Total

    adds on 'a' to every part of the 't', like pictured in red in the table below.

  2. Maths Coursework:- T-Total

    + ( ( t + 3 ) - ( 2g - 1 ) ) + ( ( t + 3 ) - ( 2g + 1 ) ) t + 3 + t - g + 3 + t - 2g + 3 + t + 3 - 2g + 1 + t + 3 - 2g

  1. Maths Coursework T-Totals

    - 56 t = 180 - 56 t = 124 Which is the same answer as before proving this formula works. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 On a 4x4 grid we can try the same method of generalization to

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

    We need now to combine the two equations, only take one instance of 5v-2g as only one T-Shape is being translated; WRITE YOUR RULES USING ALGEBRA t=(5v-2g)-(a(5g))-5b To prove this equation we need to again start with our stand grid and position and try it on a combination translation.

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