• 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
  12. 12
    12
  13. 13
    13
  14. 14
    14
  • Level: GCSE
  • Subject: Maths
  • Word count: 2630

1) Investigate the relationship between the T-total and the T-number. 2) Use grid of different sizes. Translate the T-shape to different position. Investigate relationships between the T-total, the T-numbers and the grid size.

Extracts from this document...

Introduction

T-Totals

Introduction

If you look at the 9x9 grid with the T-shape, you can see that the total of the numbers added together is 37 because it is1+2+3+11+21 which equals 37.

This is what we call the T-total (37)

And T-number is the number at the bottom of the T-shape which in this case is 20

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

My tasks

The tasks I have been set are:

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

2) Use grid of different sizes. Translate the T-shape to different position. Investigate relationships between the T-total, the T-numbers and the grid size.

3) Use grids of different sizes again. Try other transformation and combinations of transformations. Investigate relationship between the T-total, the T-numbers, the grid size and the transformations.

Standard T-shapes

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

If I place the results from 7 T-Shapes into a table then it would look like this.

T-number

20

21

22

23

24

25

26

T-total

37

42

47

52

57

62

67

This table clearly shows that the numbers go up by 5 every time the T-number goes up by 1.

Now I can use trial and error to try to find the formula, I will then test what I believe to be the correct formula to see if it is.

Because there is a difference of 5 between the T-totals I think that it is a logical place to start the formula.

...read more.

Middle

24-1=23

24-2=22

24-3=21

24-13=11

TOTAL=77

I can now take an educated guess that this is the number that changes as the grid size alters. I now have to alter the formula to allow the size of the grid to be multiplied or added to another number to reach the difference of 77 I require. So I did this and I found the formula, with g representing the grid number.

5T-(7g)

I shall now test this formula on another grid size to make sure that it is correct.

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

With my formula I have calculated that the T-total for T-number 22 on a 6 by 6 grid will be 5x22-(7x6) =68

After studying the T-shapes for some time now and studying my formula, I have realize that A always equals T - 2 x The grid size (g) – 1, B equals T -  2g, C = T – 2g + 1, and D = T – gimage00.png

As the T-Total is A+B+C+D+T I can conclude therefore that the

T-total = T – 2g – 1 + T – 2g + T – 2g + 1 + T – g + T

This can be simplified to 5T – 7g my prior formula.

I have now proven that my formula works on smaller sized grids.

...read more.

Conclusion

Remainder- this is the column of the T-number. We know this is correct because 9-2= 7 so the middle seven columns are valid and two is in the centre.

So the three steps to validating a T-number are:

1. T/S - The T-Number (T) is divided by the Grid Size (S) , the answer will be a number and a remainder (R=Row, C=Column).

T / S = R .C

2. Row - The row number +1 must be higher then 2 and lower then the grid size +1

(The inequality 2 > (R+1) < S+1)

3. Column - The column number must be lower then one and also lower then the grid size -1

(The inequality 1 > C < S-1)

If the two numbers fit the inequalities then the T-Number will fit inside the grid. I will now test the formula using random figures.

T-Number

Manually

Using Formula

2

No

No

11

No

No

20

Yes

Yes

28

No

No

63

No

No

42

Yes

Yes

Conclusion

In conclusion I have worked out many different formulae, including how to work out the T-total from just the T-number, how to work out a rotated T’s T-total from the T-number, working the T-total out by using vectors, checking if all of a T-shape is in a grid, and checked everything I have done. I enjoyed this work as it used a lot of formulae and think I explained my method to the best of my abilities.

By Keir Wyndham-Ayres

...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

    So the general formula for the three separate rotations is as follows: +90 degrees; 5n+7 -90 degrees; 5n-7 180 degrees; 5n+7g These can be used to work out the rotations on any grid size. Part Four; A Rotation and a Translation.

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

    We can now perform transformations on the t-shape and investigate it's affect on this relationship. Translation by the vector The t-number can be translated by the column vector where a is the horizontal distance (positive to the right and negative to the left)

  1. Objectives Investigate the relationship between ...

    to work, in other words I need a T-total to find out the other T-totals... I aim to find an algebraic formula, which I can use to find the T-total of any T-shape translated on an 8x8 grid, regardless of its translation direction.

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

    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

  1. For my investigation, I will be investigating if there is a relationship between t-total ...

    I began this part by rethinking my initial formula. If I am to test the T-Shape in different rotations of 0�, 90�, 180� and 270� then the formula '5N-7G' will only work for 0� as this is the angle the formula was based upon.

  2. T-shapes. In this project we have found out many ways in which to ...

    101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 T-total = 1+2+3+13+24 = 43 T-number = 24 The t-total and the t-number have risen even though the t-shape looks to be in the same place.

  1. T-Total. I will take steps to find formulae for changing the position of the ...

    I substituted the T number of 18 with x and changed the rest of the numbers appropriately. Here are my results :- x-17 x-16 x-15 x-8 x I added up the numbers as I did with the other T shape, and got the answer of 56.

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

    9 + 52 - 19 + 52 - 18 + 52 - 17 = 197 Thus proving this equation can be used to find the T-Total (t) by substituting x for the given T-Number. The equation can be simplified more: t = x + x - 9 + x -

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