• 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: 3688

# T- total T -number coursework

Extracts from this document...

Introduction

Abdul Anwar

Maths Coursework

PART 1

I have a grid nine by nine with the numbers starting from 1 to 81. There is a shape in the grid called the t-shape. This is highlighted in the colour red. This is shown below: -

 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

The number 20 at the bottom of the t-shape will be called the t-number. All the numbers highlighted will be called the t-total. 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 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 is 20

And the

T-total is37

## For this t-shape the

T-number is 21

and the

T-total is 42

As you can see from this information is that every time the t-number goes up one the t-total goes up five.

Therefore the ratio between the t-number and the t-total is 1:5

This helps us because when we want to translate a t-shape to another position. Say we move it to here

 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 all ready know the answer to the one in red. To work out the one in green all we have to do is work out the difference in the t-number and in this case it is 54. We then times the 54 by 5 because it rises 5 ever time the t- number goes up. Then we + the t-total from the original t-shape and I come out with the t-total for the green t-shape. This is another way to work out the t-total.

What I need now is a formula for the relationship between the t-total and the t-number. I have found a formula which is 5t-number-63 = t-total.

Middle

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

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

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. The t-number has risen by four and the t-total has risen by six. If I use the same rules I made in the last section it works. Here is the longer method

Difference

24-1= 23

24-2 = 22

24-3 =21

24-13 =11

TOTAL =77

Or the shorter way

7* 11 (grid size) = 77

Try out the new formula

5tn – 77= t-total

5*24-77=43

The same formula works with only changing the last number in the formula. This will be tried on a smaller grid size to make sure it is not if the grid size is bigger.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

T-number = 10

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

7 * 4 (grid size) = 28

5tn- 28= t-total

5*10-28=22

This has proven to work on a smaller scale. I can see that by changing the grid size I have had to change the formula but still managing to keep to the rule of how I get the number to minus in the formula.

PART 3

In this next section there is change in the size of grid. Also there is transformations and combinations of transformations. The investigation of the relationship between the t-total, the t-numbers, the grid size and the transformations.

If I turned the t- shape around 180 degrees it would look like this. When I have done this I should realise if I reverse the t-shape I should have to reverse something in the 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

It is obvious that I will have to change the minus sign to a different sign. I should try the opposite of minus which is plus

5tn + 63=t-total

5 * 2 + 63 = 73

Check to see if the formula has worked

T-number = 2

T-total = 2+11+19+20+21 =73

The reverse in the minus sign has worked.

The next step is to move the shape on its side. Again we nearly keep the same formula as I had at the beginning. Again I change the minus number. I can work out the number to minus by working out the difference in the t-number to each number in the t-shape.

 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

Difference

12-1 =11

12-10= 2

12-19= -7

12-11 = 1

TOTAL = 7

Formula

5tn - 7 =t-total

5*12 - 7= 53

Check to see if the formula is right

T-number = 12

T-total = 1 +10 +19 +11 +12 = 53

This formula has worked. If I rotated the t-shape 180 degrees, the same will happen, as what happened when the t-shape was turned 180 degrees from it is first original position. This is proven below.

 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

5tn + 7 = t-total

5* 70 + 7 = 357

Check

T-number = 70

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

If I were to put the t-shape diagonally on the grid I find that the same rule applies again apart from I can not use the 2nd rule were I times the grid size by seven.

 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

Conclusion

 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

Red t-shape

5tn- (7*G) + 133 = t-total

5* 41 –63+ 133= 275

Blue t-shape

5tn- (7*G) -7 = t-total

5*41-63-7 = 135

I now have a formula for seven different rotations. The number at the end of the formula I plus by or in one case minus buy again is divisible by seven. I could say that the magic number for this piece of coursework is seven.

If there are formulas for rotation then surly there is for reflection. Here I have simply only done one type of reflection just to prove that reflection actually works. Here is the formula 5tn+ (12gm) = t-total. How do I get this formula is what we need to know.

 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

The answer to this is that I need to think of what I’m doing to each of the numbers in the t-shape from the blue t-shapes t-number. For the number 29 I have a grid movement of one so we get (tn+gm). For the number 38 I have a grid movement of two so I get (tn+2gm). For the numbers 46, 47 and 48 I have a grid movement of three and a total of three numbers, se I get 3(tn+3gm). The total of all of them together is (5tn +12*gridsize) = t-total.

This formula should be tested. The t-total of the blue t-shape is 37 and the t-total of the red t-shape is 208.

Formula

5tn+(12*gridsize)= t-total

5*20+ 12* 9 = 208

The formula has worked.

#### CONCLUSION

In this project I have found out many ways in which to solve the problem I have with the t-shape being in various different positions with different sizes of grids. The way I have made the calculations less difficult is by creating a main formula that changes for all the different circumstances.

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 coursework

5 star(s)

(n) + (n-w) + (n-2w) + (n-2w-1) + (n-2w+1) = 5n - 7w This calculation shows that the sum of the 5 terms within the T-shape is 5n - 7w, so I can make a formula which shows the relationship between the T-total, the T-number and the grid size: T = 5n - 7w where T is

2. ## T-Total Maths coursework

N = 14 T = (5 x 14)-7 = 70-7 = 63 Rotation of 900 8 by 8 T-number and T-total table T-number T-total 9 52 10 57 11 63 12 67 Here I have added a prediction of mine when I realized the pattern of the sequence, which goes up by 5 each time.

1. ## T Total and T Number Coursework

For this example I will use a 9x9 grid. 60 61 62 70 79 Using this example we can work out what the total for this equation will be. It will be as follows: (n-2g-1)+(n-2g)+(n-2g+1)+(n-g)+(n). This is equal to 5n-7g.

2. ## Maths Coursework - T-Total

I used a 7x7 number square again and made a t-formula-shape again (in green). n n+7 n+13 n+14 n+15 I saw the same thing as before where the 7 in the t-formula-shape is the same as the grid width so came up with this new one (in turquoise).

1. ## Magic E Coursework

. . + 2 = 1 2R = x + x + x . . . + x + x = x(x - 1) R = 1/2 x(x - 1) Now I need to e's there are in the row, as these will be added onto this number.

2. ## 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.

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

Another area that we can investigate is that of differing grid such as 4x7 and 6x5 will make a difference to 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

2. ## Objectives Investigate the relationship between ...

So the algebraic formula would be n-21+n-20+n-19+n-10+n = '5n-70' As you can see I have arrived at exactly the same formula of '5n-70' Now I will test this formula, on T22 5x22-70=40 This formula will find the T-total of any T-shape on a 9x9 grid, as long as it is

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