• 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
  • Level: GCSE
  • Subject: Maths
  • Word count: 1902

T-shape - investigation

Extracts from this document...

Introduction

Math’s GCSE Course work

image00.png

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

Task

Translate the T shape to different positions on the grid.

  1. Investigate the relationship between the T-total and the T-number.
  2. Use different sized grids. Translate the T shape to different position and investigate the 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 relationships between the T-total, the T-total, the gridsize and the transformations.

Part 1

1image01.png

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

T-number

20

30

40

50

60

70

80

T-total

37

87

137

187

237

287

337

From my results I would say that every time the T- number goes up by 10 the T-total goes up by 50.

        I am now going to try and work out a formula for the relationships between the T-total and the T-number for anywhere on the grid. I am going to do this by working out all of the numbers in relation to N (T-number.)

1

2

3

n-19

n-18

n-17

11

=

n-9

20

n

Now I will add up all of the N’s and all of the numbers to hopefully get a formula.n+n-9+n-18+n-19+n-17= 5n-63.

...read more.

Middle

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

81image02.png

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

1

2

3

n-21

n-20

n-19

12

=

n-10

22

n

62

63

64

73

83

N=83 83x5-70=345

        62+63+64+73+83=345

36

37

38

47

57

N=57 57x5-70=215

57+47+37+36+38=215

My formula does work anywhere on the grid so now I am going to work out the formula for 8 by 8 and see if I can find something that relates them all together.

This is the first T-shape on an 8by 8 grid:

1

2

3

n-17

n-16

n-15

10

=

n-8

18

n

Adding up all the Ns and the numbers I get: 5n-56. So if N is 18 then the formula becomes 18x5-56=34 and 1+2+3+10+18=34. I shall now test the formula on other points in the grid.

41

42

43

50

58

With this shape n is 58: 58x5-56=234 and 58+50+42+41+43=234. I shall try it with one more shape just to make sure.

14

15

16

23

31

N is 31 so the formula is: 31x5-56=99 and 31+23+14+15+16=99. I have proved now that the formula works for this 8by 8 grid. I am now going to put all of my results into a table and see if there is a link for them.

8 by 8

9 by 9

10 by 10

5n-56

5n-63

5n-70

By looking at my results I can see that each time the grid size goes up by 1 the formula changes as the second number goes up by 7. And also the grid size (g) x7 =the second number. I predict that the formula will be 5n-7g. I am going to check it by working it out the same way as I did the other formulae by working out the T-shape in relation with N but this time I’m going to add G (grid size).

1

2

3

n-2g-1

n-2g

n-2g+1

10

=

n-g

18

n

Adding up all of the Ns and the Gs and the numbers I get: 5n-7g. I am now going to test this formula on the T-shapes I used before. Firstly I will test the 8 by 8 grids.  

1

2

3

10

18

N=18 and G=8 so the formula is 5x22-7x8=34 and 18+10+2+1+3=34

41

42

43

50

58

N=58 G=8. 5x58-7x8=234. 58+50+42+41+43=234.

14

15

16

23

31

N=31 g=8. 31x5-7x8=99 31+23+14+15+16=99

I have now proved that the formula works on an 8 by 8 grid now ill try it on 9 by 9.

9 by 9

55

56

57

65

74

N=74                 5x74-9x7=307

     74+65+56+55+57=307

1

2

3

11

20

5x20-7x9=37 20+11+2+3+1=37

11

12

13

21

30

...read more.

Conclusion

Normal= 5n-7g        Rotated 90o= 5n+7

To see a link I need one more formula so I will work out the formula for a shape rotated by 180o.

34

42

49

50

51

n

n+g

n+2g-1

n+2g

n+2g+1

This become equal to 5n+7g I am going to test this on 2 shapes from each grid size to check if it works.

First I will try 8 by 8.

34

42

49

50

51

34x5+7x8=226 and the sum of T-shape is 34+42+40+49+51=22

22

30

37

38

39

22x5+7x8=166 and the T-total is 22+30+38+37+39=166

Now I will try it 9 by 9.

2

11

19

20

21

2x5+9x7=73 and 2+11+20+21+19=73

34

43

51

52

53

5x34+9x7=233 and 34+43+51+52+53=233 so the formula works on 9 by 9 I will now try it on 10 by 10.

54

64

73

74

75

5x54+7x10=340 and 54+64+74+73+75=340

78

88

97

98

99

5x78+7x10=460 78+88+98+99+97=460 I have now proved that my formula works on all sized gids so now I shall compare the three formulae I have.

Normal=5n-7g        rotated 90o clockwise=5n+7         rotated 180o=5n+7g

Degrees

Formulae

0

5n-7g

5n+7(-g)

90

5n+7

5n+7(1)

180

5n+7g

5n+7(g)

270

5n-7

5n+7(-1)

I predict that 270 is 5n+7. I will now check.

1

n-g-2

9

10

11

=

n-2

n-1

n

17

n+g-2

5n-7so I was correct.

...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

    (7 x 23) - (11 x 10) = 51 161 - 110 = 51 1 + 2 + 3 + 4 + 5 + 13 + 23 = 51 I found out that the formula for a 5by2 on a 10by10 grid is correct. I will now do the same on a 9by9 grid.

  2. The T-Total Mathematics Coursework Task.

    factorised we can create the formula: L-Total = 5 x L-Number + 58 L = 5l + 58 This equation is used to work out any L-shape that has been rotated 180 degrees clockwise on a 9 by 9 number grid.

  1. T-Total Investigation

    numbers, as for as grid width of 5 it is 25, which is 5 x 5, and for a grid width of 9 it is 45 which is 9 x 5. We can also see that translations larger than 1 can be found by a(25)

  2. Objectives Investigate the relationship between ...

    40 41 42 * Tn 22 n 24 31 N+9 33 N+17 N+18 N+19 The image above shows exactly what needs to be done to n, the T-number to find the individual numbers in the T-shape. n+n+9+n+17+n+18+n+19 =n+n+n+n+n+9+17+18+19=5n+63 Check 5n+63 Substitute the T-number into 'n' 5x23+63= 178 As you can

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

    One simple change needs to be made to my horizontal translation equation, that as "a" was also used for the figure by which to translate (the same as the vertical translation), we have to substitute "a" with "b" in the horizontal equation otherwise we can only move the T-Shape, is fixed diagonal positions.

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

    and the N number is 18. I will move my T-Shape across one column. The total of this T-Shape is 39 (2 + 3 + 4 + 11 + 19 = 39) and the N number is 19. I will again move the T-Shape across one column.

  1. Maths GCSE Coursework – T-Total

    We now need to use the same method with different grid size to make a universal equation. I have chosen a grid width of 5 as that has a central number as does a grid width of 9, but make it vertically longer as to allow room to express vertical translations.

  2. T-Total Course Work

    + (T-18) + (T-17) + (T-9) + (T) = 5T - 63 Let T-number = T Let T-total = n T n 20 21 22 37 +(5) = 42 +(5) = 47 Formula = 5T - 63 I tested that when: T = 80 n = 337 337 = 5T - 63 337 = (5 x 80)

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