• 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
  • Level: GCSE
  • Subject: Maths
  • Word count: 2271

T-Total. I can work out a formula to find the T-total on a 9 by 9 grid.

Extracts from this document...

Introduction

Maths Coursework

T-Total

1.

Here is a 9 by 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

The total of the numbers within the T shape is 1+2+3+11+20=37

I will call this the T-total. T would represent this.

The 20 at the bottom of the T shape will be called the T-Number. N would represent this.

1

2

3

11

20

Here is the T shape by itself. As you can see the middle column is going down in 9’s because the grid size is 9 by 9.

N-19

N-18

N-17

N-9

N

Here is a converted version of the original. This is so I can work out a formula to find the T-total on a 9 by 9 grid.

T = N-19+N-18+N-17+N-9+N

T = 5N-63

Time for me to check if this formula works:

N means T-Number.

N = 20

T = 5x20-63

T = 100-63

T = 37

To make sure it is not a fluke, I will do 2 more checks on the same grid size.

16

17

18

26

35

T = 112

T = 5x35-63

T = 175-63

T = 112

48

49

50

58

67

T = 272

T = 5x67-63

T = 335-63

T = 272

So now you know the formula for the 9 by 9 grid is T =5N-63

2.

I will now find the formula for a 5 by 5 grid.

Here is the 5 by 5 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

The total of all the numbers inside the T-shape is 1+2+3+7+12=25

As you can see, the middle column is going down in 5’s because of the grid size.

1

2

3

7

12

T = 25

N-11

N-10

N-9

N-5

N

Here is a converted version of the original.

...read more.

Middle

The total amount of numbers inside the T-Shape is 3+8+12+13+14=50

The 3 at the top of the T-Shape will be called the T-Number.

3

8

12

13

14

Here is the T-Shape by itself. As you can see the numbers in the middle is going up in 5’s because the grid width is 5.

Here is the converted version so I can work out the formula for the T-Total.

N

N+5

N+9

N+10

N+11

T = (N)+(N+5)+(N+10)+(N+9)+(N+11)

T = 5N+35

Now to check if the formula works:

3

8

12

13

14

T = 50

T = 5x3+35

T = 15+35

T = 50

Here is another check to make sure.

14

19

23

24

25

T = 105

T = 5x14+35

T = 70+35

T = 105

Now I will see another formula for another grid size, which is 4 by 6.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

That will be the T-Shape I will be finding the T-Total formula.

Firstly here is the formula I need to use.

N

N+4

N+7

N+8

N+9

That is the converted version of the 4 by 6 grid size.

T = (N)+(N+4)+(N+8)+(N+7)+(N+9)

T = 5N+28

Now to check if the formula works:

7

11

14

15

16

T = 63

T = 5x7+28

T = 35+28

T = 63

Here is another example for that formula:

14

18

21

22

23

T = 98

T = 5x14+28

T = 70+28

T = 98

Now I will figure out a formula to find the T-Total for an inverted T-Shape on any size grid.

N

N+G

N+2G-1

N+2G

N+2G+1

G = Grid Width

Here is the full formula to work when solving out the formula for an inverted T-Shape on any size grid.

T = (N)+(N+G)+(N+2G)+(N+2G+1)+(N+2G+1)

T = 5N+7G

Now lets try that formula on the 5 by 5 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

T = 5N+7G

T = 5N+7x5

T = 5N+35

As you can see if you go up to page 5-6 you will find that it works out as the same formula as the one on this page.

Now for a different sized grid I haven’t used before.

I will use a 3 by 7 grid size.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

T = 5N+7G

7G = 7xGrid width

T = 5N+7x3

T = 5N+21

To make sure this formula works I will find an inverted T-Shape on the 3 by 7 grid and see if that formula works.

8

11

13

14

15

T = 61

T = 5x8+21

T = 40+21

T = 61

Now that has been completed I will convert the T-Shape 90° to the right.

Here is a 5 by 5 grid to test on.

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

The Total amount of numbers inside the T shape is 11+12+13+8+18=62

The 11 at the left of the T-Shape will be called the T-Number.

8

11

12

13

18

Here is the T-Shape by itself. As you can see the numbers on the right are going down in 5’s due to the grid size, which is 5.

Here is the converted version so I can work out the formula for the T-Total.

N-3

N

N+1

N+2

N+7

T = (N)+(N+1)+(N+2)+(N-3)+(N+7)

T = 5N+7

Now to check if this formula works:

8

11

12

13

18

T = 62

T = 5x11+7

T = 55+7

T = 62

Here is another T-Shape to make sure:

15

18

19

20

25

T = 97

T = 5x18+7

T = 90+7

T = 97

Here is another grid size to find out what formula I need to use for that specific grid size.

The grid size I’ll use will be 7 by 4.

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

Firstly here is the formula I’ll need.

N-5

N

N+1

N+2

N+9

T = (N)+(N+1)+(N+2)+(N-5)+(N+9)

T = 5N+7

Now to check if the formula works:

5

10

11

12

19

...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

This will be the T-Shape I will be using to find out if my formula works. I will firstly need to figure out a formula.

N-6

N-2

N-1

N

N+2

T = (N)+(N-1)+(N-2)+(N-6)+(N+2)

T = 5N-7

Let me try this formula on my T-Shape:

10

14

15

16

18

T = 73

T = 5x16-7

T = 80-7

T = 73

Now let’s try this on another T-Shape in the same grid size:

17

21

22

23

25

T = 108

T = 5x23-7

T = 115-7

T = 108

Now this has been completed I will now try to find a formula to all T-Shapes rotated 270° to the right on any size grid. Although I should solve the full working out, I found that the formula 5N-7 could be worked for all grid sizes. Here is an example on a 9 by 8 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

T = 158

T = 5x33-7

T = 165-7

T = 158

Here is another example:

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

T = 123

T = 5x26-7

T = 130-7

T = 123

So now you understand that for the first T-Shape the formula to work out a formula to solve any T-Total on any size table is –

T-Total=5N-7G

Now you understand that for the inverted T-Shape the formula to work out a formula to solve any T-Total on any size table is –

T-Total=5N+7G

Now you understand that for the first sideways T-Shape the formula to work out a formula to solve any T-Total on any size table is –

T-Total=5N+7

Now you understand that for the second sideways T-Shape the formula to work out a formula to solve any T-Total on any size table is –

T-Total=5N-7

...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 Maths

    +56 = 15+56 = 71 As expected, the equation has produced yet another correct answer. Another example is below. N = 4 T = (5 x 4) +56 = 20 + 56 = 76 Here is the last equation I will show from the 8 by 8 grid to show that the equation is correct.

  2. The T-Total Mathematics Coursework Task.

    added T-number Bottom of T-shape T-total All numbers in T-shape added 22 40 42 140 23 45 43 145 24 50 44 150 25 55 45 155 26 60 46 160 27 65 47 165 28 70 48 170 29 75 49 175 32 90 52 190 33 95 53

  1. T-Total Course Work

    - 56 259 = 259 Formula works. Below is a t-shape, and in each cell how the number is connected with T on an 8x8 grid T-17 T-16 T-15 T-8 T Check the formula: (T-17) + (T-16) + (T-15) + (T-8) + (T) = 5T - 56 So this is correct 9x9 Grid 1 2 3 4

  2. To prove that out of town shopping is becoming increasingly popular with shoppers, and ...

    the day, where more females are around, whom usually do the shopping in the household. The next most popular shop was Matalan with 15.9% along with McDonalds which got the same. Matalan always was going to be popular as I pointed out in my prediction; it sells a wide range of clothes for all ages and is good value.

  1. Objectives Investigate the relationship between ...

    n+n-1+n-2+n-12+n+8 =n+n+n+n+n+8-1-2-12=5n-7 My formula for finding the T-total of any 180 rotated T-shape is therefore '5n-7' Let's check to see if it works. I will use the T-shape, T23 to test if this works. 5x23 - 7 = 108 The formula works, just as expected.

  2. T-Shapes Coursework

    + 1/2 l {2n + 10(l + 1)} [3 x 29] + [1/2 x 8 x {(2 x 29) + 10(9)}] [87] + [1/2 x 8 x {58 + 90}] [87] + [1/2 x 8 x {148}] [87] + [592] 679 7)

  1. T-shapes. In this project we have found out many ways in which to ...

    64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 The t-shapes above holds more formulas as the rest they all work the same. The red t-shape has a t-number of 32 and a t-total of 32+42+52+60+44= 230 This t-shape has a

  2. Maths Coursework T-Totals

    generalizations bar; When a T-Shape is rotated by 90, 180 or 270 degrees, its T-Total is larger. If we try the same rotations on a different grid width and plot the results in a table, patterns might become easier to see.

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