• 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: 1845

My objective in this investigation is to ~ First investigate the association between the t-total and the t-number. ~

Extracts from this document...

Introduction

Jade chanele rattray

Mathematics coursework: T-shape                                 Bexleyheath secondary school.

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


T-NUMBER

THIS IS AN INVESTIGATION BY JADE CHANELE RATTRAY.

T-TOTAL

T-SHAPE

INTRODUCTION

This particular piece of course work concentrates on numbers that are situated in a grid. In this grid upon these numbers is a‘t’ shape this is made up of three numbers across the top and three numbers down.

My objective in this investigation is to…

~

First investigate the association between the t-total and the t-number.

~

Secondly, utilize grids of various sizes, render the t-shape to different positions as well as examine the relationship between t-number, t-total, and t-shape.

~

And finally, again use grids of various sizes, as well as try other transformations and combinations of transformations. And further more to study connections between the T-total, T-number, grid size and the transformation.

PLAN

I am a student in year nine that has been presented with an investigation to discover with mathematical procedures that different grids have a different results and connection between numbers.

I have been given a basic introductory 9 by 9 grid with a simple 3 by 3 t-shape with a 1:1 aspect ratio. I will study the association between the T-total and T-number.

...read more.

Middle

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

Here is a simple 9 by 9 grid. On this grid I have shaded in three t-shapes. The first one I shades is the one that has the five numbers 40, 41, 42, 50 and 59.

The T-total is 40+41+42+50+59=232. If I alter the position of this shape one space to the left I will have a t-total of 39+40+41+49+58=227. Look at the last t-total of 232 and look at this one, there is a decrease of five, and if I move the T-shape two spaces to the right from the original position I get a T-total of 42+42+44+52+61=242. The T-total increases from the first by 10.

METHOD

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

For the pencil highlighted T-shape the T-number is 20 and the T-total is 37. For the red highlighted T-shape the T-number is 21 and the T-total is 42. Note that the difference is 5. I predict from this information that every time the T-number increases by one, the T-total increase by five just as it did on the grid in the plan. I will investigate in two ways. The first will be to discover the formula and the second shall be to prove the formula. These methods are called ‘relative formula’ and ‘difference in sequence’.

...read more.

Conclusion

41-40

41-39

41-48

.                41-30.

5

5tn-7=198

So lets see if this worked.

T-number=41

T-total=41+40+39+48+30=198

It has proven to work.

So this show that the formula may alter from situation to situation but the basic introductory formula is always its template.

Conclusion

In this project I have found various ways in which to solve the problem that was presented with. This investigation named T-shape was and investigation where I had to find the formula for each circumstance for instance a different grid size, I was expected to work out the correct formula for the T-shape in this grid as well as find another correct formula for any different position that the t-shape could be in like 90  180  270  or its original position.

I found three formulas the first for the original shape position and original grid size was:

5tn-63=T-total

This was my original/introductory formula.

My second was the T-shape 180  from its original position the formula for this was:

5tn+63=T-total

And my third was the T-shape on its side/90 /270 the from its original position formula for this position was:

5tn-7=T-total.

Knowing all of this and presenting this to you as an investigation brings me to the end of the investigation.

...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-Totals Investigation.

    172 217 262 307 +45 +45 +45 +45 +45 +45 These T-totals have an addition of 45. With this I can see that 45�9=5. Next I will try and see if these are similar to the results from an 8 by 8 grid.

  2. T-Shape investigation.

    this sequence perfectly 5n - 63 I will check this by placing a T in the middle of the grid. 29 30 31 32 33 34 35 38 39 40 41 42 43 44 47 48 49 50 51 52 53 56 57 58 59 60 61 62 65 66

  1. T Total and T Number Coursework

    22 23 24 32 41 34 43 52 42 41 24 becomes 52-difference of 28 23 becomes 43-difference of 20 22 becomes 34- difference of 12 32 becomes 42- difference of 10 T number (41)

  2. T-total Investigation

    Using expressions I found out that my formula 5T - 70 is correct. I will now work out the formula for the given 3by2 T on a 9by9 grid. I placed the 3by2 T on the beginning of my 9by9 grid.

  1. Maths GCSE Coursework – T-Total

    can be found by using the equation of t=(5v-2g)-(a(5g))-5b were v is the middle number, g is the grid width, a is the number by which to translate vertically and b is the number by which to translate horizontally. I terms of T-Total (x); Any type of translation (vertical, horizontal or a combination)

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

    - (-1)(12) + 2 - 22} + 7 = 322 2 2 -1 1 61 422 5 { 61 + (-3)(-10) - (-1)(12) + 2 - 22} + 7 = 422 2 2 1 -1 61 442 5 { 61 + (-1)(-10)

  1. Objectives Investigate the relationship between ...

    108 +63 As you can see the increment was '+63' this allows me to build a simple formula. x = current T-total + 63 where 'x' is equal to the new T-total Therefore: x = 45 +63 x =

  2. T-Shapes Coursework

    72 + 82 + 92 + 102] [96]+ [504] 600 3n + 1/2 l {2n + 10(l + 1)} [3 x 32] + [1/2 x 7 x {(2 x 32) + 10(8)}] [96] + [1/2 x 7 x {64 + 80}] [96] + [1/2 x 7 x {144}] [96] + [504] 600 2)

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