• 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
  • Level: GCSE
  • Subject: Maths
  • Word count: 2069

T-total Coursework.

Extracts from this document...

Introduction

Lauren Willis

 T-total Coursework

In this piece of coursework im going to investigate the relationship between the T-total and the T-number. I will do this by using different grid sizes and I will translate the T-shape to different positions on the grid. I will also try other transformations and combinations of transformations.

Here im going to try one T-shape on this 9 by 9 grid and see if I can find a relationship between the T-total and the T-number.

T-total=1+2+3+11+20= 37

T-number= 20

T-total=4+5+6+14+23= 52

T-number= 23

T-total=7+8+9+17+26= 67

T-number= 26

T-total=28+29+30+38+47= 172

T-number= 47

T-total=31+32+33+41+50= 187

T-number= 50

T-total=34+35+36+44+53= 202

T-number= 53

T-total=55+56+57+65+74= 307

T-number= 74

T-total=58+59+60+68+77=332

T-number= 77

T-total=61+62+63+71+80= 337

T-number= 80

This was too difficult to see a pattern so I decided to only use the first three rows of the 9 by 9 grid and then I will see if I can see a pattern.

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

T-total =1+2+3+11+20 = 37

T-number= 20

T-total= 2+3+4+12+21 = 42

T-number=21

T-total= 3+4+5+13+22= 47

T-number=22

T-total= 4+5+6+14+23= 52

T-number=23

T-total= 5+6+7+15+24=57

T-number=24

T-number

T-total

20

37

21

42

22

47

23

52

24

57

From this I can see that each time the T-number goes up by one the T-total goes up by five. This is because there are five numbers in the T-shape and they are all being moved up each time. I think the number five will be important in this investigation.

I also looked at the relationship between the T-total and the T-number by finding the difference between them.

T-total

T-number

Difference

37 -

20 =

17

42 -

21 =

21

47 -

22 =

25

52 -

23 =

29

57 -

24 =

33

...read more.

Middle

13 =

17

35 -

14 =

21

From this I can see a pattern that each time the T- number goes up by one. The difference between the T- numbers to the T- total goes up by four.

Because five is an important number in this investigation I will multiply the T- number by 5 times table then take away the T- total to see if this shows a pattern.

T-number

T-total

Difference

(12x5)=65 -

25=

35

(13x5)=65 -

30=

35

(14x5)=70 -

35=

35

It was a five by five grid and 35 is in the five times tables is it is 7x5. So seven is important in this investigation because before I found that the difference was 63 and that was 7x9.

From this I can see my formula will work  

5n – T-total = 7x5 (grid size multiplied by seven)

5x12– 60=35

5x13- 60=35

5x14- 60=35                

Now I will try a six by six grid to see if my formula works.

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

T-total= 1+2+3+8+14=28

T-number= 14

T-total= 2+3+4+9+15=33

T-number=15

T-total= 3+4+5+10+16=38

T-number=16

T-total= 4+5+6+11+17=43

T-number=17

Here is a table to show the T-total and the T-number of this six by six grid.

T-number

T-total

14

28

15

33

16

38

17

43

I will now find the difference between the T-total and the T-number.

T-total

T-number

Difference

28 -

14 =

14

33 -

15 =

18

38 -

16 =

22

43 -

17 =

26

From this I can see that each time the T-number goes up by one the difference goes up by four.

Because five is an important number in this investigation I will multiply the T-number by five then take away the T-total and see if I can see a pattern.

I will try my formula on each of these T-numbers and multiply them by five then minus 63 to see if I get the T-total for each one.

5n-63

5x20-63=37

5x21-63=42

5x22-63=47

5x23-63=52

5x24-63=57

I will now predict what I will get for 25,26 and 27.

For 25 I think the answer will be 62

For 27 I think the answer will be 67

For 28 I think the answer will be 72

I will now try my formula and see if I am correct.

5n-63

5x25-63=62 The T-total for 25= 6+7+8+16+25 = 62

5x26-63=67 The T-total for 26= 7+8+9+17+26 = 67

5x27-63=72 The T-total for 27= 8+9+10+18+27=72

This proves that my formula does work.

I will now try and see if this formula works on the T-numbers on a five by five grid. Here is a table to show the T-totals and the T-numbers.

 Vdvrsbg gbtwrrtg

T-number

T-total

25

12

30

13

35

14

I am going to use the Formula 5n-35. I will use 5 because there is five numbers in the T-shape and I will minus 35 because that was the difference between the T-total and the T-number each time.

Here is a table to show how I found the difference between the T-number and the T-total. I did this by multiplying the T-number by five each time then I would I minus the T-total and I would get the same answer for the difference each time.

T-number

T-total

Difference

(12x5)=65 -

25=

35

(13x5)=65 -

30=

35

(14x5)=70 -

35=

35

...read more.

Conclusion

5n-63

                5x2-63=-53

This will not work so I will try adding instead of misusing

5n+63

5x2+63=73, which was our T-total

T-total= 2+11+19+20+21=73. I will now check this on the other T-totals I did.

5n+63

5x3+63=78 which was the T-total 3+12+20+21+22=78

5x4+63=83 which was the T-total 4+13+21+22+23=83

5x4+63=88 which was the T-total 5+14+22+23+23=88

5x5+63+93 which was the T-total 6+15+23+24+25=93

To make sure my formula works I will try this on a 7by7 grid. I predict my formula will be 5n+49

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

T-total=2+9+16+15+17=59

T-number=2

T-total=3+10+16+17+18=64

T-number=3

T-total=4+11+17+18+19=69

T-number=4

T-total=5+12+18+19+20=74

T-number=5

T-total=6+13+19+20+21=79

T-number=6

I will now try the formula I predicted which was 5n+49.

5x2+49=59 which was the T-total 2+9+16+15+17=59

5x3+49=64 which was the T-total 3+10+16+17+18=64

5x4+49=69 which was the T-total 4+11+17+18+19=69

5x5+49=74 which was the T-total 5+12+18+19+20=74

5x6+49=79 which was the T-total 6+13+19+20+21=79

For both of these grids I have found that the number you add is the grid number multiplied by 7 so my formula is 5n+the grid number multiplied by seven. So for a…

5by5 grid the formula will be 5n+35

6by6 grid the formula will be 5n+42

7by7 grid the formula will be 5n+49

8by8 grid the formula will be 5n+56

9by9 grid the formula will be 5n+63

I will now try and find a formula for the T-shape on its side.

5by5grid the formula will be 5n+35

6by6 grid the formula will be 5n+42

7by7 grid the formula will be 5n+9

8by8 grid the formula will be 5n+6

9by9 grid the formula will be 5n+3

...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. Marked by a teacher

    T-total coursework

    5 star(s)

    then y = 1, while the horizontal translation is also 1 (the T-shape is moved right by 1) then x = 1. The diagram below left shows what n-2w-1 n-2w n-2w+1 10 n-w 12 19 n 21 (n+x+wy-2w)-1 n+x+wy-2w (n+x+wy-2w)+1 10 n+x+ wy-w 12 19 n+x+wy 21 happens to the

  2. Magic E Coursework

    e+3g e+4g e+4g+1 e+4g+2 ----- e+4g+(x-1) To get the final formula for arm length we need to add up the formulae from each of the rows and add up the 2 squares in between.

  1. T-totals. I am going to investigate the relationship between the t-total, T, and ...

    - (d - b) (g+1) + a - bg } + 7 * Translate and rotate 180� T = 5 {n + 2 (c - a) - 2g (d - b) + a - bg } + 7g * Translate and rotate 270� clockwise T = 5 { n + (c - a)

  2. Objectives Investigate the relationship between ...

    40 41 42 * Tn 22 n 24 31 N+9 33 N+17 N+18 N+19 The image above shows exactly what needs to be done to n, the T-number to find the individual numbers in the T-shape. n+n+9+n+17+n+18+n+19 =n+n+n+n+n+9+17+18+19=5n+63 Check 5n+63 Substitute the T-number into 'n' 5x23+63= 178 As you can

  1. T-Shapes Coursework

    Again, I believe 5 calculations are enough to display any patterns. 3) Data Collection 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

  2. In this section there is an investigation between the t-total and the t-number.

    Also there is transformations and combinations of transformations. The investigation of the relationship between the t-total, the t-numbers, the grid size and the transformations. If we turned the t- shape around 180 degrees it would look like this. When we have done this we should realise if we reverse the t-shape we should have to reverse something in the formula.

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

    now I will move onto rotations. Rotations When rotating the T shape 90� to the right. It is the exact same process as working out the formula for the first 9x9 grid I did first. The only difference is that the T is on its side.

  2. The investiagtion betwwen the relationship of the T-number and T-total

    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 I fist tried reflections in the y-axis.

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