• 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
  • Level: GCSE
  • Subject: Maths
  • Word count: 1456

T-shapes.I will investigate and find rules that connect the t-total to the t-number and the grid size.

Extracts from this document...

Introduction

MATHS COURSEWORK : t-shapes.

I will investigate and find rules that connect the t-total to the t-number and the grid size.

T = t number

X = grid size

To investigate and find a rule I will use a 4 x 4 grid as starting of with a smaller grid and going up can help spot a rule with much more ease.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

The t-number is 10 and the t-total is 1+2+3+6+10=22

I will try and investigate a rule by working out the difference between the t-total and the t-number, and then I will use an algebraic expression to work out the rule for grids of different sizes.

T-number = 10

T-total = 1+2+3+6+10= 22

7 x 4 (grid size) = 28

5tn- 28= t-total

5 x 10-28=22

Now I will investigate if this formulae works on different positions on a 4 x 4 grid.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

I will try a different t-shape.

The t-number is 11

The t-total is 27 (2+3+4+7+11)

I will substitute the following values into the formulae 5t – 7x (grid number)

5 X 11 = 55

7 X 4 = 28

55 – 28 = 27

This has proven to work on a 4 x 4 grid.

...read more.

Middle

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

I am first going to try and rotate the t-number 180 degrees so it is upside down.

I will do this as we already have a formula for the t-total (5t-63). I have used a 9x9 grid as this is the grid which the formula works on.

The t-shape I am going to use has a t number of:

T- number: 2

The old formula stated that we had to minus 63 away from 5 x the t-number but as this is upside down (rotated 180 degree) I am going to try and add the 63.

So 5 x t number makes 10 and + 63 = 73

To see if the formula has worked I will add all the numbers in the t-shape:

2+11+19+20+21 =73         THIS NOW PROVES THAT THE MINUS SIGN

                                                                         HAS WORKED

We have now found a formula for both the upright and upside down T- shape.

The next step is to move the shape on its side (90 degrees from the upright position) I move the t-number 90 degrees to the left.

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

an="1">

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

The formula for this t-shape must be:

5t-number +7 = t – total as the one above is the opposite.

I will now test this 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

 5 x 70 + 7 = 357

T-number = 70

T-total = 70+71+72+63+81 = 357

This formula works for all grid sizes and anywhere on the grid.

CONCLUSION

During this project we have learned how to find data and summaries it into smaller parts.

We have learnt to find and make rules and have put them into practice. This project has taught us how to make algebraic rules which can be put into use.

Here are the various rules we found out:

PART 1

T-total is 5t – 63

(This only works for 9x9 grid anywhere)

PART 2

5tn – 7x(grid number)

(This works for all grid sizes anywhere.

PART 3

Normal way up – 5t – 7x

90 degrees to the left – 5t – 7 x

90 degrees to the right- 5t + 7 x

180 degrees from upright : 5t + 7 x

...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

    +80y -40y -80y +5x +10x -5x -10x Looking at this formula again I can see that the formula for an 8x8 grid using the vectors above is T=5n-56+5x-40y.

  2. The T-Total Mathematics Coursework Task.

    12 118 39 253 13 123 40 258 14 128 41 263 15 133 42 268 16 138 43 273 17 143 44 278 19 153 46 288 20 158 47 293 21 163 48 298 22 168 49 303 23 173 50 308 24 178 51 313 25 183

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

    Towards Dartford... Under 18: 19-30: 31-45: 46-60: 61+: | Total: 0 Total: 0 Total: 1 Total: 0 Total: 0 Third count performed in New Rd at 14:35 on Sunday. Away from South Darenth... Under 18: 19-30: 31-45: 46-60: 61+: Total: 0 Total: 0 Total: 0 Total: 0 Total: 0 Fourth count performed in New Rd at 14:35 on Sunday.

  2. Objectives Investigate the relationship between ...

    = 40 + 50 = 90 If translated twice, it would be 40 + (2x50) = 40+ 100 = 140. This is the T-total of T42 I will now use the formula I found earlier to work out the T-total of this same T-shape (T32), just to prove that it

  1. T-Shapes Coursework

    = = Mean = Mean = 25 + 35 + 45 + 55 + 65 225 225 = 45 The conventional method of finding the mean of any set of numbers 5 25 + 65 = 90 = 45 A method of finding the mean of an arithmetic progression 2

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

    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

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

    The T shape below will make this clearer:- From the investigations I have done so far I have found the information for my formula and need to assemble it and make sure it works. The formula I put together, using all the relevant information, is 5x - y.

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

    - a multiple of 7 with a value dependent on the grid size. We should now try and find the rule that governs the "magic number" that has to be taken from 5x to gain t. If we say g is the grid size (e.g.

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