• 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.

    When: T=T-total t=T-number The formula is T = 5t - 70 Normal T-shapes on a 4 by 8 number grid T-number Bottom of T-shape T-total All numbers in T-shape added T-number Bottom of T-shape T-total All numbers in T-shape added 10 22 22 82 11 27 23 87 14 42

  1. T-Shapes Coursework

    + g(l + 1)} Although this was not found by the methods in other sections, for the purposes of spotting patterns, the use of knowledge from other sections is not detrimental to the investigation. Here is a table that shows this formula to apparently work, fulfilling the pattern from the previous section: Middle Number (n)

  2. Objectives Investigate the relationship between ...

    28 29 37 38 39 47 48 49 29+39+49+38+37=192 T-shape T-total Increment T37 115 T37 (90�) 192 +77 We also have an increment of '+77', therefore we know that, to find the T-total of a 90� rotated T-shape, we would be able to do so by simply adding '77' to the current T-total.

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

    100 If we note the same form of table we have used before, we can find the "magic number", the above table shows a vertical translation of the T-Shape by +4, were v=45, t =205 which translates to, v=49, t=225.

  2. Maths Coursework T-Totals

    T=(205-18)+15 T=187-15 T=172 Using our equation found in the preliminary work we can work out the real value of the translated shape, (it has a v number of 38); T=(5x38)-(2x9) T=190-18 T=172 Thus proving our theory right that the equation can be used for any type of translation, vertical, horizontal or a combination of the both.

  1. The object of this coursework is to find the relationship between the total value ...

    and the N number is 62. This proves my prediction and the pattern was correct. Rule I am now going to try and find a rule for this question on a 10 by 10 grid, which I am going to change from T into terms of N.

  2. Maths GCSE Coursework – T-Total

    we generalize this straight away using the same method's used in before for a 9x9 grid we achieve the formula: t = x - 8 + x - 17 + x - 16 + x - 15 t = 2x - 8 + 3x - 48 t = 5x -

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