• 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
15. 15
15
16. 16
16
17. 17
17
18. 18
18
• Level: GCSE
• Subject: Maths
• Word count: 1852

# T shapes. I then looked at more of these T-Shapes from the grid in sequence and then by tabulating these results I could then work out a formula.

Extracts from this document...

Introduction

Tushyam Sonecha        Maths T- Shape Coursework        10B

For this coursework I have been asked to investigate and in turn solve t e relationship between two numbers. These numbers are the T-Total and T-Number. Then further more on different sized grids and with different transformations

9 * 9 Grid

 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 will start by trying to find the relationship between the T-Total and T- Number in a 9 by 9 grid.

 1 2 3 11 20
 5 6 7 15 24

I then looked at more of these T-Shapes from the grid in sequence and then by tabulating these results I could then work out a formula.

Here is a table of my results:

 T- Number T-Total 20 37 21 42 22 47 23 52 24 57 25 62

From this set of data it is shown that there is a change in the T-Total by 5 each times      so I then times the T-Number by 5 each time and then correspond to the T-Total so here is another set of results to show this.

 T- Number times 5 T-Total 100 37 105 42 110 47 115 52 120 57 125 62

From these results I can now predict that relationship formula is that 5 times the T-Number – 63. To help prove that this is true I will now rather than calling it the T-Number I will call it ‘n’. This then means that:

Formula= 5n – 63

 n-19 n-20 n-21 n-9 n

Middle

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

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

 1 2 3 12 22
 5 6 7 16 26

As I have already shown in the previous grid through calculation, I have determined that 5n is the constant difference so that to repeat a table showing data from the T- total against the T- Number will be pointless.

 5n 110 115 120 125 130 135 T- Total 40 45 50 55 60 65

From the above table of results I can tell that the difference is 70 therefore for a 10 y 10 grids the formula will be 5n – 70. Again to prove this I will use ‘n’.

 N – 21 N - 20 N – 19 N – 10 N

 Grid Size Formula for the T- Total 8 * 8 5n - 56 9 * 9 5n – 63 10 * 10 5n - 70

Now for the three grids that I have already done I will tabulate the formulas.

Now, by just looking at the differences and relations in the numbers I can see a pattern and that it will always be the formula 5n – 7 * Grid Width (G).

Now I will combine both ‘n’ and ‘G’ into one formula.

 N – 2G-1 N – 2G N – 2G-1 N – G N

T-Total = 5n – 7G

Now I will look at different transformations

Translation

Now I will look at the relationship between the T- Number and T-Total as the T shape is moved onto different vectors on grid.

9 * 9 Grid Translations

 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

 N – 2G-1+4 N – 2G+4 N – 2G+1+4 N – G+4 N+4

I will now translate the T- shape to the vector

 N – 2G-1+36 N – 2G+36 N – 2G+1+36 N – G+36 N+36

With the above formula I can predict that the general formula for vectors is

N + A –BG

As I did more example of vector translating I found that horizontally the number change increased only by one each time. I then found out that as the shape moved vertically, the numbers changed by 9 each time, so I called IT ‘BG’.

I then, to prove my prediction used the terms in a T-shape.

 n-(2G-)+A-BG n-(2G+9-BG) n-(2G+1)+A-BG n-G+A-BG n+A-BG

Conclusion

No I will look at the Horizontal line of reflection.

 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

Image 1- T-Number= 29      +9      T-Total =82     +171

Reflect 1-T-Number=38                 T-Total =253

Image 2 – T-Number=25     +27      T-Total=62    +261

Reflect 2 – T-Number=53               T-Total=323

As in the vertical reflection another pattern has emerged and this time for each square that the shape moves down 9 is gained onto the T-Total. With the relationships compiled from previous calculations I can also work out the T-Total.

The formula for a normal T-shape on a 9*9 grid is 5N – 63 then the formula for a reflected t shape can be worked out and adapted by just flipping it over.

 n n+9 N+19 N+18 N+17

It is from this depiction that we see that the formula is 5n + 63. Now to combine both together.

5N +5(G5) +63. Like before, I will change the ‘+63’to ‘+7G’. I WILL NOW USE ‘Reflect 1 and 2@ to check my formula.

Checking:

T-Total = 52 +61 +69 + 70

=  323

Formula =5(N+GS) +7G

=5(25+ (9*3) +63

= (5*52) +63

=260+63

=323

9 * 9 Grid Rotations

Finally I am going to look at the relationship between the T-Total and T-Number as they are rotated clockwise up to 270 degrees on a 9*9 grid.

 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

 N-2G-1 N-2G N-2G-1 N-G-2 N-9 N-G+2 N-2 N-1 N N1 N+2 N+G+2 N+9 N+G+2 N+2G-1 N+2G N+2G

The formula for a 90 degrees=5N +7

The formula or 180 degrees= 5N+7G

The formula for 270 degrees= 5N-7

Page  of

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

# Related GCSE T-Total essays

1. ## T-Total Maths

the pattern of the sequence, which goes up by 5 each time. Formula: T=5N-49 I tested that when: T-number = 48 T-total = 191 Below is a T-shape, and in each cell how number is connected with T-number on a 7by 7 number grid.

2. ## Maths GCSE Coursework &amp;amp;#150; T-Total

on another grid size with another type of a combination translation, to verify that it is correct, I have chosen a grid width of 5, extended vertically to accommodate the combination translation: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

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. ## Mathematics Coursework - T Shapes

81 Testing Prediction Now that I have a certain formula, which has been tested, I can take any T-shape at random from any random Grid Size and use any random vector to create a final T-shape. 1 2 3 4 5 6 7 8 9 10 11 12 13 14

1. ## T-Shapes Coursework

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 Tt = (5 x 47)

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

We can state that: The T-Total (t) can be found by using the equation t = 5v - 2g, were v is the middle number (x -g) and g is the grid width, on any grid with, with a standard T-Shape.

1. ## T totals - translations and rotations

see in my 8by8 grid above and I will be representing this as N in my equation. My T-total is 18+10+2+1+3 = 34. The number in my T-shape directly above my T-number is 8 places back on my grid so it is N-8.

2. ## Maths Coursework T-Totals

width of 9 the T-Total (t) is -45 smaller than the previous T-Total (t) (the origin) As when v = 32, t = 142 and with a translation vertically by -1 v = 23, t = 97, and 97 - 142 = -45, therefore the above statement it correct.

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