• 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
  • Level: GCSE
  • Subject: Maths
  • Word count: 1554

Investigating a T shape which will be on a 9x9 grid and have an area of 5 squares.

Extracts from this document...

Introduction

image00.png

image01.png

T-Total

Maths Coursework February 2004

Introduction

In this piece of coursework I will be investigating a T shape which will be on a 9x9 grid and have an area of 5 squares. The T-total is all the numbers in the T shape added up together and the T-number is the bottom number in the T highlighted in green below.

2

3

4

12

21

In this T there are five numbers 2, 3, 4, 12 and 21 if you add these numbers up it makes the T-total    

                           2+3+4+12+21=42

The highest number in this T is 21 so 21 would be the T-number.

Once I have investigated that I will investigate whether or not using grids of different sizes would make a difference to the formulae and any relationship found. I will try and find a relationship between the T-Total, the T-Number and the grid size.

In the third part of this coursework I will use different transformations and combinations of transformations. I will investigate the relationship between the T-Total, the T-Number, the grid size and the transformations.  

After that I drew a table of the first few T-Numbers and T-Totals for the first few T’s.

      T20

      T21

      T22

      T23

T-Total

       37

       42

       47

       52

T-Number

       20

       21

       22

       23

The first T is the T shown in the introduction, the second T is

   2    

   3

   4

  12

  21

And so on.

In the table there is a pattern, when the T-Number goes up one the T-Total goes up five, this pattern also works for T’s anywhere on the grid

This pattern occurs because each number inside the T goes up one as you move it across the grid and there are five numbers in the T. This pattern also works for every T on the grid.

       T50

       T51

       T52

       T53

T-Total

      187

      192

      197      

      202

T-Number

       50

       51

       52

       53

The next thing I did was name each of the squares in relation to the T-Number  

 N-19

 N-18

 N-17

  N-9

    N

The N stands for the T-Number and the other numbers are in relation to it and it works for every T. This helps because it makes it easier for me to work out a piece of algebra to solve the problem for every T.  

In this T I have noticed that the first difference from N is 9 which is also the width of the grid.

I’ll put that idea into another T. Note W= Width Number (9)

N-

(2W-1)

  N-2W

N-(2w+1)

   N-W

     N  

...read more.

Middle

  86

  87

  88

  89

  90

  91

  92

  93

  94

  95

  96

  97

  98

  99

 100

I have highlighted the first T that can be made on this grid. The T-Number is 22. If the formula works for this T then the T-Total should be 40. The T-Total is 1+2+3+12+21= 40.

This formula works on that T but does it work on any otherT’s in the 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

  82

  83

  84

  85

  86

  87

  88

  89

  90

  91

  92

  93

  94

  95

  96

  97

  98

  99

 100

This T’s T-Number is 69. If the formula works for this T the    T-Total should be 275. The T-Total is 48+49+50+59+69= 275.

The formula seems to work for this size grid.

As there are 10 in each row it’s obvious that the row above will be 10 less than the row below. So 59 is 10 less than the T-Number 69. If you calculate the whole T you realise that row 2 is 10 less than row 1 and row 3 is 20 less than row 1, but there are three relevant numbers in row 3 which are 19 less, 20 less and 21 less that the T-Number. The 19 and the 21 can both be changed into 20’s because if you take the 1 from 21 and put it on the 19 they both make 20.  

  N-21

  N-20

  N-19

  N-10

    N  

...read more.

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

 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

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

This T will be called ST 64 as it starts at 64, it is a stretch of 2 in both directions.

 26

 27

 28

 29

 30

 40

 52

 64

ST 64=26+27+28+29+30+40+52+64= 296

I think I can work out the formula using my previous method so:

12+24+ (36x5) =216

Now if I see how many times 12 goes into 216

216/12 = 18

This means the formula is:

8N-18W= T-Total

8N=   8=number of integers in the T shape N= T-Number

18W=  18= Number calculated  W=Width

Just to make sure this formula works here is another T.

ST 142 = 104+105+106+107+108+118+130+142= 920

Using the formula the T-Total would be (8x142) + (18x12) = 920

You would be able to use this way of finding out the formula for any T.

Conclusion

In conclusion I have found that the number of integers in the T calculates the number before the N in the formula and the width of the grid calculates the value of W. The number before the W is found by looking at the numbers in the rows and relating them to the T-Number. When the T is regular the W-Number is negative e.g.

-18W

                        8N    

Whereas if the T is flipped upside down the W-Number is positive.                        

...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. Relationship between T-total and T-number I am going to investigate T-totals and T-numbers ...

    = 56 I have tested my prediction and I can see that it is correct. As the T number increases by 9, the T total increases by 45. Across : Down : I have made a table, which shows the increase in the T total when the T number increases.

  2. Black and white squares

    -38 28 8 2 7 -18 20 8 1 1 -6 12 8 0 -1 -2 4 8 d = -1 Now that I have obtained the value of (d) I will be able to find the rest of the values. I would however need to cancel out both (c)

  1. T-Shapes Coursework

    + 93 + 94 + 95 + 96 + 97 + 98) + (112) (1196) + (112) 1308 n(w + 1) + 20 92(13 + 1) + 20 (92 x 14) + 20 1288 + 20 1308 2) Where n = 128 and w = 15 Total Sum = =

  2. For my investigation, I will be investigating if there is a relationship between t-total ...

    + (N-18) + (N-17) + (N-9) + (N) I then can simplify this to: T-Total = 5n-63 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

  1. For my investigation, I will be investigating if there is a relationship between t-total ...

    first T-number to get the gap which in this case was 63. The formula can be used on any of the T number in the 9x9 grid. I have found a general rule which will work out the T total of a given T number.

  2. T-Shapes Coursework

    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 7th T-Shape: T-Total 55

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

    If we rotate our T-Shape by 180 and 270 degrees clockwise, again it will be easier for us to build up a profile, and some generalizations. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

  2. T-Totals (A*) Firstly I have chosen to look at the 9 by 9 grid. ...

    I found this out by doing the table seen below: Nth term 1 2 3 4 5 T-number 30 31 32 33 34 T-total 87 92 97 102 107 Difference +5 +5 +5 +5 This table shows us that 5 multiplied by the nth term added to 82 will give us the t-total.

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