• 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
  • Level: GCSE
  • Subject: Maths
  • Word count: 1189

T-Totals. I am going to investigate the relationship between the T-total and the Tnumber. I will use a 9 x 9 grid. I will draw different Tshapes onto the grid.

Extracts from this document...

Introduction

MATHS COURSEWORK

T-TOTALS

BY EMMET MURPHY 11K

Aim:   I am going to investigate the relationship between the     T-total and the T–number.  I will use a 9 x 9 grid.  I will draw different T–shapes onto the grid.  Then I will find the T–total and the T–number.  I will put the answers into a table of results. I will try to find the relationship between these numbers.

Method:   To find the T-total I had to add up all the numbers in the T- shape.  For example:

1+2+3+11+20 = 37

2+3+4+12+21 = 42

3+4+5+13+22 = 47

4+5+6+14+23 = 52

5+6+7+15+24 = 57

6+7+8+16+25 = 62

7+8+9+17+26 = 67

10+11+12+20+29 = 82

11+12+13+21+30 = 87

12+13+14+22+31 = 92

13+14+15+23+32 = 97

14+15+16+24+33 = 102

15+16+17+25+34 = 107

16+17+18+26+35 = 112

17+18+19+27+36 = 117

18+19+20+28+37 = 122

Table of Results  

     T-number

          T-total        

      Difference

                    20

                      37

            5

                    21

                      42

                    22

                      47

            5    

                    23

                      52

                    24

                      57

            5

                    25

                      62

                    26

                      67

            5

                    29

                      82

                    30

                      87

            5  

                    31

                      92

                    32

                      97

            5

                    33

                     102

                    34

                     107

            5

                    35

                     112

                    36

                     117

            5      

                    37

                     122

The relationship between the T-number and the T-total is:

...read more.

Middle

5n – 63.

I will substitute 3 terms in for n:

The first term:

(5 x 20) – 63

100 – 63

 = 37      

The seventh term:

(5 x 26) – 63

130 – 63

 = 67

The fifteenth term:

(5 x 36) – 63

180 – 63

 = 117

10x10 grid:

1+2+3+12+22 = 40

2+3+4+13+23 = 45

3+4+5+14+24 = 50

4+5+6+15+25 = 55

5+6+7+16+26 = 60

6+7+8+17+27 = 65

7+8+9+18+28 = 70

8+9+10+19+29 = 75

Table of Results:

      T-number

         T-total

      Difference

22

40

              5

23

45

24

50

              5

25

55

26

60

              5

27

65

28

70

              5

29

75

Analysis of Results:  In order to find the formula for the T-shape on a 10x10 grid I took the first T-number, 22 and multiplied it by 5(the difference).  This totalled 110.  To get the T-total I subtracted 70 from 110 which equalled 40.  When put into a formula it looks like this:

5n – 70

I will substitute three numbers in for n:

The first term:

(5 x 22) – 70

110 – 70

 = 40

The seventh term:

(5 x 28) – 70

140 – 70

 = 70

The eighth term:

(5 x 29) – 70

145 – 70

 = 75

Step 2:

Now I will investigate the relationship between the T-number and the T- total using a 10x10 grid and rotating the T- shape 90o clockwise.

Method:

...read more.

Conclusion

(5 x 2) + 70

10 +70

 = 80

The seventh term:

(5 x 8) + 70

40 + 70

 = 110

The fifteenth term:

(5 x 16) + 70

80 + 70

 = 150

Conclusion:   Using the 10x10 grid I have found a pattern in the formulae.

Upright T:       5n – 70

Rotated 90o:   5n + 7

Rotated 180o: 5n + 70

I noticed that all the formulae started with 5n. However for the T-shape rotated 180 o the function sign was opposite to the upright T-shape i.e. 5n – 70 and 5n + 70. Based on this I predict that a T-shape rotated 270o will have the opposite function sign to the T-shape rotated 90o ie. 5n – 7

To test my prediction, I will look at three T-shapes:

1+11+21+12+13 = 58

2+12+22+13+14 = 63

3+13+23+14+15 = 68

(5 x 13) – 7 = 58

(5 x 14) – 7 = 63

(5 x 15) – 7 = 68

From these results I can see that my hypothesis correct.

To conclude my investigation I have shown that the difference is always 5 for a T-total in any grid size.  Also when the T-shape is rotated 180o   (reflected) the function signs are opposite.

...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-totals. I will be doing three grids, a 10 x 10 grid, a 9 ...

    Size Of Grid Formula 10x10 5N - 7G 9x9 5N - 7G 8x8 5N - 7G G is the size of the Grid Summary Using the formula 5N - 7G, I think I can

  2. The T-Total Mathematics Coursework Task.

    L-Shapes (Step 2) Here are L-shapes rotated 90 degrees clockwise. There are L-shapes that have been randomly placed anywhere over the 9 by 9 grid. View the written equations of these T-shapes on the next page. 1 2 3 4 5 6 7 8 9 10 11 12 13 14

  1. T-Totals.Plan: ...

    I predict that if the T-number is 40, with the formula of 5n - 63 = T for a 9x9 grid, T will equal: 137 T = 5n - 63 = (5 x 40) - 63 = 200 - 63 T = 137 To prove that the T-total for the

  2. T-Total Investigation

    and a Rotation through v, can be found by using the equation of 5((v+b)-ag) + y were v is the Middle number is the amount to translate horizontally, a is the amount to translate vertically, g is the grid width, and y is to be substituted by the ending required by the type of rotation, these are : Rotation (degrees)

  1. T-Shapes Coursework

    not work, simply because they cannot fit all the squares they require to make a T, into this 9x9 grid.

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

    Number 1: 23 24 25 34 44 The t-number in this case will be 44. The t-total is 44+34+24+23+25 which will give us 150. T-number: 44 T-total: 151 Number 2: 24 25 26 35 45 The t-number in this case will be 45.

  1. For this piece of GCSE maths coursework, I am aiming to find out the ...

    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 N-15 N-14 N-13 N-7 N 1 2 3 9 16 The formula for the T-Total is:- T-Total = N-15+N-14+N-13+N-7+N=5N-49 T= 5x16-49=31 Now I

  2. Investigation – T-Shapes

    Diagram 9. I will return to my predicted answer example, Diagram 8 and use the formula to work out its T-Total. T-number of Diagram 8 = 26 For the purpose of developing algebraic formulae, the T-Number will be expressed as n. T-total = (n) + (n - 9)

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