• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

T- Total. When trying to fine out the T-Total in a 6 by 6-number grid, If you take the other numbers in the T-Shape away from the T-Number you get a T-Shape like the one shown below the 6x6 grid.

Extracts from this document...

Introduction

T- Total

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

Look at the T-shape drawn on the 9 by 9 number grid.

The numbers in this shape are added together to make the T-Total, which would be in this case 1+2+3+11+20=37. So the T-Totals number would be 37.

As I go on I am sure I will find a pattern which may help me find a rule.

T-Totals

T-Number

2+3+4+12+21=42

21

3+4+5+13+22=47

22

4+5+6+14+23=52

23

The number at the bottom of the T-shape is called the T-number.

The T-number for this T-shape is 20.

If you take the other numbers in the T-Shape away from the T-Number you get a T-Shape like this.

T-17

T-18

T-19

T-9

T

You will notice that the centre column of the T-Shape is going up in 9’s this is because of the table size. With the table set out like this a formula can be worked out to find any T-Total on this a 9x9 grid. This is done in the working below: -

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

= 5T-63

Now I will test this formula to see if it works for the 9x9 Grid

For T-Total I will use the letter X

For the T-Number I will use the letter T

So X = 5T-63

T = 20

X = 5x20-63

= 100-63

= 37

...read more.

Middle

T

This time the centre column of the T-Shape is going up in 6’s because of the table size. The formula for this size grid is T-Total = T-13+T-12+T-11+T-6+T= 5T-42

Now to do as I did before I will test my formula out: -

With X = T-Totals and T= T-Number

T = 35

So X= 5x35 – 42

This means X should equal 133

The numbers in the T-Shape are 22,23,24,29,35 and if you add them all together this makes 133 which shows my formula is true, but just to make sure I will test it again.

T = 16

So X = 5x16 – 42

So X= 32

3 + 4 + 5 + 10 + 16 = 32

This shows that my formula is correct!

I have tested the formula for two different T-Numbers and the formula works on a 6x6 grid.

The full formula for this size grid is: - X=5T-42

Below is a grid with parts of the formula in. I will use this to figure out a formula for any T-Total on any width grid.

T-2G-1

T-2G

T-2G+1

T-G

T

T-total = T-2G-1

T-2G

T-2G+1

T-G

T

X=5T-7G

If the Grid Width (= G), and the T-Number (= T), the T-Total (= X) is calculated by

X=5T-7G

Now I’m going to try the grid that I drew earlier which was G=9

The formula is X=5T-7G

Which changes to X=5T-7x9

X=5T-63, this shows that this rule has a relationship between itself and the rule for the grid.

I will now try the formula on a 7 by 7 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

X=5X17-49(2+3+4+10+17=36) – This is what the numbers in the T-Shape added together equals.

X=85-49

X=36

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

I am now going to try this formula on a 3 by 5 grid.

X=5X8-21 (1+2+3+5+8=19) – This is what the numbers in T-Shape added together equals.

X=40-21

X=19

I am now going to try this formula on a 6 by 10 grid.

X=5X33-42 (20+21+22+27+33=123

X=165-42

X=123

Now I have worked the formula out for the T-Shape in the one position, I am going to translate the T-Shape to different positions and investigate the relationships between the T-Total, the T-number and the grid size.

As you can see below the T-Shape can be set out just like the previous one I drew but the formulas are flipped over.

T

T+G

T+2G+1

T+2G

T+2G-1

T + (T+G) + (T+2G+1) + (T+2G) + (T+2G-1) = 5T + 7G

As you will see the rule is fairly similar but instead of a take-away sum it is an additional sum, I think this happens because usually when you flip something it is the opposite to what it was and when you flip the T-Shape it flips the rule.

I will now try this new formula on a 4 by 7 grid, using 10 as 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

...read more.

Conclusion

>=56+10

=73

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

I have tried this new formula for an inverted T and it works, the formula is: X=+5T

I will now find out a formula that has been translated 90 degrees anti-clockwise

T-1-G

T-2

T-1

T

T-2 + G

T

T-1

T-2

T-2-G

T-2+G

5T-7 this is what all the squares added above equals and this should be the rule.

I will use this rule on a 5by5grid this should not affect any outcome of the end result, I will use 8 as my T-Number though

X= 5T-7=5x8-7

X= 40-7=33     (Numbers In T-Shape = 1+6+11+7+8= 33)

So my rule is correct!

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

I have tested this new formula for a side ways T the formula works it is: X=5T-7

Before I write the formula I will predict what it will be 5T+7

T+2-G

T

T+1

T+2

T+2+G

T

T+1

T+2

T+2+G

T+2-G

5t+7

The formula is 5T+7 My Prediction was correct!

I have tested this new formula for a side ways T the formula works it is: 5T+7

The formula for a this way up is: X=5T-7G

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

The formula for a this way up is: X=7G+5T

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

The formula for a this way up is: X=5T+7

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

The formula for this way up is: X=5T-7

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

...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 and T Number Coursework

    I will test my formula on a 9x9 grid. I will choose the vectors(1,2) for this test. The original shape will be green and the new shape red. I will use this formula T=5n-7g+5x-5gy. I predict that the t-total of the new shape will be 55*5-70+5-100=110.

  2. Objectives Investigate the relationship between ...

    Let's refer to the T-number as 'n' * T35 27 28 29 35 36 37 43 44 45 * Tn 27 28 n-6 n n+1 n+2 43 44 n+10 The image above shows exactly what needs to be done to n, the T-number to find the individual numbers in the T-shape.

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

    the problem we have with the t-shape being in various different positions with different sizes of grids. The way we have made the calculations less difficult is by creating a main formula that changes for all the different circumstances. Here I have put all the formulas I have come up with.

  2. T-Total. I will take steps to find formulae for changing the position of the ...

    From this I have found that the formula for moving the T shape down is 5x - y + 5bz (z is the variable for the grid width and b is the variable for the vertical movement). Moving the T shape up: the same formula is used for moving the

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

    or irregular (e.g. 5x101), with the two variables of grid width (g) and the T-Number (x) for a Tb T-Shape. Tc and Td shapes As we know that a 180-degree flip will be a "negative" equation of the other flip, we only need to work out one kind of shape, therefore we shall work out formulas for Tc shapes.

  2. T-Totals. We have a grid nine by nine with the numbers starting from 1 ...

    64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 The t- shape has a t-number of 32. Now to work out the difference between the t-number and the rest of the numbers in this t-shape Working out: - 32-13=19 32-14=18 32-15=17

  1. From the table I have noticed that when that when you move a T ...

    I am now to investigate the total by moving the T shape down the grid 9 10 11 18 26 T total=9+10+11+18+26=74 26x5=130-56=74 17 18 19 26 34 T total=17+18+19+26+34=114 34x5=170-56=114 25 26 27 34 42 T total=25+26+27+34+42=154 42x5=210-56=154 Sum Total Increase 1+2+3+10+18 34 9+10+11+18+26 74 40 17+18+19+26+34

  2. T- total T -number coursework

    in this t-shape Working Out: - 70-51=19 70-52=18 70-53=17 70-61=9 TOTAL=63 Again the number turns out to be 63. This is where the 63 came from in this equation. There is also another place this 63 comes from. This is 9*7=63.

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