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

My investigation is to see the relationship between the T-Total and the T-Number of T-Shapes and to find a rule for it so that the T-Total can be easily found.

Extracts from this document...

Introduction

Sabrina Ul-Hasan 10R

Introduction

My investigation is to see the relationship between the T-Total and the T-Number of T-Shapes and to find a rule for it so that the T-Total can be easily found.

First I am going to draw a 9 by 9 grid and pick T-Shapes out for example the T-Number would be the number witch is at the bottom of the T-Shape.

image00.png

e.g.

N -19

1

N -18

2

N-17image01.png

3

N-9

11

N

20image06.png

image10.png

The T-Total would be the number you would get by adding all the figures inside the T-Shape together.

e.g.

N-19

1

N-18

2

N-17

3

N-9

11

N

20

TN= N+(N-9)+(N-19)+(N-18)+(N-17)

TN=1 + 2 + 3 + 11 +20 = 37  

Therefore the T-Total = 37

Here is the grid and my working out for it: -

A 9 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

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

N-19

2

N-18

3

N-17

N-9

12

N

21

TN= N+(N-9)+(N-19)+(N-18)+(N-17)

TN= 2 + 3 + 4 +12 + 21 =                                    

T21 = 42

N-19

3

N-18

4

N-17

5

N-9

13

N

22

TN= N+(N-9)+(N-19)+(N-18)+(N-17)

3 + 4 + 5 + 13 + 22 =

T22=47

N-19

4

N-18

5

N-17

6

N-9

14

N

23

TN= N+(N-9)+(N-19)+(N-18)+(N-17)

4 + 5 + 6 + 14+ 23=

T23=52 

N-19

5

N-18

6

N-17

7

N-9

15

N

24

...read more.

Middle

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

N-17

1

N-16

2

N-15

3

N-8

10

N

18

TN= N+(N-8)+(N-16)+(N-15)+(N-17)

1 + 2 +N- 3 +10 +18 =

T18=34

N-17

2

N-16

3

N-15

4

N-8

11

N

19

TN= N+(N-8)+(N-16)+(N-15)+(N-17)

2 + 3 + 4 + 11 + 19=

T19=39

N-17

3

N-16

4

N-15

5

N-8

12

N

20

TN= N+(N-8)+(N-16)+(N-15)+(N-17)

3 + 4 + 5 +12 + 20=

T20=44

Here is the results table for the 8 by 8 grid :-

T-Number

T-Total

18

34            

19

39

20

44



The T-Total increase’s by 5 so the rule for the
8 by 8 grid would be found in the similar way to the 9 by 9 grid.

To work out the rule for this grid I multiplied 5 by the T-Number and took away the T-Total.

e.g.

1

2

3

10

18

5 x 18 = 90

90 – 34 = 56

image08.png



image09.png

As a result the rule for the 8 by 8 grid is :-

TN= N+(N-8)+(N-16)+(N-15)+(N-17)

image04.pngimage04.pngimage04.pngimage04.pngimage04.png

image05.png

(By adding together all the n’s you get 5n)

TN= N+(N-8)+(N-16)+(N-15)+(N-17)

image04.pngimage04.pngimage04.png

image11.png

(By doing the equation you get left with –56)

5n – 56

Now I am going to do a 10 by 10 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

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

98

89

90

91

92

93

94

95

96

97

98

99

100

N-21

1

N-20

2

N-19

3

N-10

12

N

22

The working out for the rule

TN= N+(N-10)+(N-20)+(N-21)+(N-19)

1 + 2 + 3 + 12 + 22 =

T22=40image12.pngimage13.png

22 x 5 = 110

110 – 40 = 70

...read more.

Conclusion

Results table

Grid size

Rule

8 by 8

5n -56

9 by 9

5n – 63

10 by 10

5n – 70

11 by 11

5n – 77

g by g

5n – 7g

As you can see from the results the rule increases by 7 in each grid. Also the last figure is obtained by multiplying the grid size by 7.

For example:-

The rule for the 8 by 8 grid is 5n – 56

7 x 8 = 56image20.pngimage21.png


image22.pngimage23.png


image24.png

Therefore to show this in algebraic form it would be:

7gimage25.png

N - (g x 2) +1

N-(g x 2)

N - (g x 2) -1

N-g

N

Were as the algebraic equation for all of it would be:        

5n – 7gimage27.pngimage28.pngimage29.pngimage30.png

Now I am going to test this rule to see if it works on any grid size. I will do this on a 12 by 12 grid.

12 by 12 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

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

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

N-25

1

N-24

2

N-23

3

N-12

14

N

26


image09.pngimage31.png

5t – 7g is my rule here is the working out

5 x 26 =130

7 x 12 =84

Therefore I think the rule for the 12 by 12 grid will be :

130 – 84

N-25

1

N-24

2

N-23

3

N-12

14

N

26

Now I am going to see if I am right

TN=N+(N-12)+(N-24)+(N-23)+(N-25)

TN= 1+ 2+ 3 + 14 + 26=46

5 x 26 = 130

image32.png

image33.png

image35.png

130 – 46 = 84

image37.pngimage36.png

image38.png

Therefore this proves that the rule works on any size grid.

...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

    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 Position 1 Position 2 4 11 12 13

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

    These formulas only apply to the nine by nine grids 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 5tn-63= t-total D 1

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

    = x + x - 4 + x - 9 + x - 8 + x - 7 t = 5x - 28 This formula is the same as the 4x4 grid as it has a "magic number" of 28, identical to a 4x4 grid, we can predict that grid

  2. T- total T -number coursework

    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 The red t-shape has t-number of 33 and the t-total = 7+17+27+25+33 = 109 The difference between the t-number and the rest of the numbers in the t-shape.

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

    Formula Difference 10 by 10 5T - 70 7 9 by 9 5T - 63 7 8 by 8 5T - 56 As you can see the 5 remains constant because there are five boxes in the T - Shape, however the numbers at the end follow the 7 times table.

  2. The object of this coursework is to find the relationship between the total value ...

    The only variable needed after the rule will be N. Values of T = 1 + 2 + 3 + 12 + 22 = 40 Value of N = 22 Value of T = N + N-10 + N-19 + N-20 + N-21 so RULE: Value of T = 5N-70

  1. Investigate the relationship between the T-Total and the T-number for grid widths of different ...

    I then times 54 by 5 because that is how much the T-Total goes up by every time the T-number goes up by 1. then I add the T-Total from the red T and this gives me my T-Total for my green T.

  2. I am going to investigate how changing the number of tiles at the centre ...

    I have drawn pattern number 7 and counted 32 border tiles, which confirms that my formula is correct. Total Tiles I am also going to investigate whether I can find a formula which give the total amount of tiles in my pattern, T, provided I have the pattern number.

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