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

Investigate the relationship between the T-total and the T-number.

Extracts from this document...

Introduction

Sonny Kumar        Maths Coursework

        T-Totals

Tasks

1) Investigate the relationship between the T-total and the T-number

2) Use the grids of different sizes. Translate the T-shape to different positions. Investigate relationships between the T-total and the T- number and the grid size.

3) Use grids of different sizes again, try other transformations and combinations of transformations. Investigate relationships between the T-total and the T-number and the grid size and the transformations.

Investigation into T-shapes

Looking at the 10-10 grid below and the T-shape drawn on it,

The total number of the numbers on the inside of the T-shape is called the T-total

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

...read more.

Middle

88

89

90

91

92

93

94

95

96

97

98

99

100

Using random examples I am going to show the relationship between the T-total and T-number.

T-number69-50+48+49+59+69=275(t-total)

T-number32-11+13+12+22+32=90(t-total)

T-Number

T-total

22

40

23

45

24

50

25

55

26

60

27

65

28

70

29

75

As you can see from this table every time the t-number goes up 1 the t-total goes up 5. From this I can tell that to find formula connecting these two together I will have to multiply one of them by 5. So then I decided to multiply the t-number by 5.

T-Number

T-number times 5

Difference between 5 times t-number and t-total

T-total

22

110

70

40

23

115

70

45

24

120

70

50

25

125

70

55

26

130

70

60

27

135

70

65

28

140

70

70

29

145

70

75

This table shows that 5 times the t-number minus 70 equals the t-total.

So the formulae relating the t-number and the t-total is-

T-number=N        T-total=T

T=5N-702) Different sizes and relationship between the T-total and the T- number and the grid size

I know this works for the grid 10 by 10 but I'm not exactly sure if it'll work for any other grids because there are more intervals in between the first number of each line. So I might have to change a value in my formula. I will try my formula with two different sized grids.

Here is a 9 by 9 grid for which I will test my formula

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

...read more.

Conclusion

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

T- Number =20

Orange T-Total = 7+8+9+14+20=58

Gold T-Total = 20+21+22+28+16=107

Orange-Gold=49

This shows that I have to add 49 to the formula for my relationship to work.

 So now my formula will become- T=5N-7W+49

Next I am going to use a 7 by 7 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

T- Number =23

Orange T-Total = 8+9+10+16+23=66

Gold T-Total = 23+24+25+32+18=122

Orange-Gold=56

This shows that I have to add 56 to the formula for my relationship to work.

 So now my formula will become- T=5N-7W+56

I am going to show my results in a table.

Grid width

Orange T-Total

Gold T-Total

Difference between the two T-Total

5

25

67

42

6

58

107

49

7

66

122

56

Conclusion

My formula’s had to be changed each time I started the next task. Which I found confusing at first but then I ‘got  into it’.

For my final formula I have made it to be

Where T=T-total, N=T=number, W=Grid width

T=5N-7W

For example-

The t-number=26 in 7 by 7 grid

T=(5x26)-(7x7)

T=130-49

T=81

Then if there’s a transformation-

T= (5N-7W)+((W+1)x7)

For example-

The t-number=25 in 8 by 8 grid and then rotated 90 degree’s clockwise.

T= (5N-7W)+((W+1)x7)

T=(125-56)+(9x7)

T=169+63

T=232

...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 and T Number Coursework

    Looking at what the formula is for a translation on a 9x9 grid I should be able to find the formula. T=5n-7g+5x-5gy. If I add the 14g to this then I should have the final formula for a 180 degree rotation.

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

    to the t-total of the rotated t-shape. The t-total of a t-shape that has been rotated and then translated can therefore be written as: * Rotate 90� clockwise and translate T = 5 ( n + c - dg -d -cg + a - bg )

  1. Objectives Investigate the relationship between ...

    I have used an equation method to find my formula; I could have used the algebraic difference method, to find it. T22 1 2 3 11 12 13 21 22 23 Tn n-21 n-20 n-19 n-10 n As you can see from the above T-shape, we now know how to find all the individual values of the T-shape.

  2. T-Shapes Coursework

    Where n = 177, w = 23, l = 14, g = 40 Total Sum = = = = Total Sum = = = = = = Wing + Tail [166 + ... 175 + 176 + 177 + 178 + 179 + ...

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

    The red t-shapes formula is 5tn- 63= t-total. The blue t-shapes formula is 5tn + 7= t-total. If we add the 63 and the 7 together from the two formulas we get 70. This is the difference in the t-total between the two t-shapes. The t-number for both t-shapes is 41.

  2. T-Shapes Coursework

    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 As we can see, the T-Shapes that have been dotted, do

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

    This will also work in reverse, as we can find any T-Number's value at any time by using v-g. Translations Vertical Again, we shall use our standard gird size and position to establish our basic starting point; 1 2 3 4 5 6 7 8 9 10 11 12 13

  2. T-Total Maths coursework

    = 9 = 7x9 = 63 I now have enough data to prove that my formula works 5N - 7G = 10 + 63 = 73 So my Formula works because T = 73. The formula has worked for the 9x9 grid.

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