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

I am investigating the relationship between the T-total and the T-number.

Extracts from this document...

Introduction

Dan Bloom        

Introduction

I am investigating the relationship between the T-total and the T-number.

I am going to move the T until I find a pattern.

Collect the results

I started with 22.

The T-Number is 22.

The T-Total is 47 (3 + 4 + 5 + 13 + 22).

I then moved the T-Number along 1.

The T-Number is 23.

The T-Total is 52 (4 + 5 + 6 + 14 + 23).

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

I then moved the T-Number along to 24.

The T-Number is 24.

The T-Total is 57 (5 + 6 + 7 + 15 + 24).

I then moved the T-Number along to 25.

The T-Number is 25.

The T-Total is 62 (6 + 7 + 8 + 16 + 25).

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

This is my table of my results:

T- Number

T-Total

22

47

23

52

24

57

25

62

Patterns

I have noticed that the T- Number’s and the T-Total’s are linked. To get from 47 to 52 to 57 to 62 in the T-Total column, I have to plus 5.

...read more.

Middle

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

If we add up the numbers in the T, it should add up to 67.

7 + 8 + 9 + 17 +26 = 67

This shows that the equation works.

Also there is another way of finding out if the equation works.

If you call the T-Total ‘N’ then the number above that, would be N – 9 and so on. I will show this on a diagram:

image00.png

                N – 19        N – 18        N – 17

                        N – 9

                        N

If you then put the numbers from the T, (N-19) + (N-18) + (N-17) + (N-9) + (N) = 5N – 63.

This is another way of showing that the equation works.

I will now do the same only this time I will change my grid size from 9 to 10 across. This is to see if there is a pattern.

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

...read more.

Conclusion

I will now change the grid from 10 to 11. Everything else will stay the same.

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

T-Number = 24

T-Total = 43

T-Number = 25

T-Total = 48

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

T- Number = 26

T- Total = 53

24

48

25

53

26

58

27

55

T- Number = 27

 T- Total = 58

This is my table of results:        

T- Number

T-Total

Because the T-Total is going up in fives I know that it is T = 5N.

5 x 24 = 120

This does not fit so if you take 72 away from 120. That fits.

Therefore the equation must be: T= 5N -72

To prove this equation works, I will use another way to show it.

image02.png

        N -         21    N - 22        N -23

             N - 11

             N

If you then put the numbers from the T, (N-11) + (N-22) + (N-23) + (N-21) + (N) = 5N – 72.

This is another way of showing that the equation works.

I will now do the same, expect the grid size will be 12 instead of 11.

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

    When I moved out the next like I noticed that I missed out two T-numbers (26, 27), this is why I have separated the table into two. The reason being was that the T- shape does not fit onto the grid.

  2. Urban Settlements have much greater accessibility than rural settlements. Is this so?

    This gives an indication as to the approximate percentage of residents in an area. I will use this to determine the percentage of residents that are probably at a driving age. It is only a rough outline in my case, because the length of the count was not long enough.

  1. T-Total investigating monitoring

    pattern in these tables is plus one every time in the T - Number and for the T - Total it is plus five very time.

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

    B 8 12 16 20 24 +4 +4 +4 +4 B= 4n + 4 To get 4N at the start of the formula, you have to put the added outer borders into a table ( see above ). Each pattern number is counted as N and the squares in that outer most border is counted as B.

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

    If we say that 20 is the T-number and the T-number is then represented by x. We can use x to replace 20 so that it would fit in with any T-shape: t = (x - 19) + (x - 18)

  2. 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

  1. Investigating the relationship between the T-total and the T-number.

    13 14 15 23 32 If the T-shape is then translated by the vector 2 , the new T-number and the T-total will -2 be changed to 40 and 137 respectively. 21 22 23 31 40 A formula of this translation of the T-shape can be worked out by working the vectors with the original T-number.

  2. Investigating the links between the T-number and the T-total on a size 9 grid

    I believe the formula will be: - 5n+7 = T-total 34 41 42 43 52 3 10 11 12 21 21 28 29 30 39 5n+7 = T-total 5(10)+7 = T-total 57 = T-total Also: 10 + 11 + 12 + 21 + 3 = 57 5n+7 = T-total 5(28)+7

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