• 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: 2633

# T Total Investigation

Extracts from this document...

Introduction

Razvan Alexa 11R10th March 2002

### Math’s Coursework

T-Total

I have been given a task to translate the T-Shape to different positions on the 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

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

The total of the numbers inside the T-shape is

1+2+3+11+20=37

This is called the T-total.

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

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

1. Investigate the relationship between the T-Total and the T-Number.
 N

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

 N-19 N-18 N-17 N-9 N
 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

T. NumberT. Total

20                        37

32                        97

26                        67

56                        217

71                        292

77                        322

1+2+3+11+20=37

13+14+15+23+32=97

7+8+9+17+26=67

37+38+39+47+56=217

52+53+54+62+71=292

58+59+60+68+77=322

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

T-Total = 5T-63

Now to test this formula to see if it works

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

Middle

X=5T-49

T. NumberT. Total

16                                   31

20                                  51

44                                 171

48                                 191

1+2+3+9+16=31

5+6+7+13+20=51

29+30+31+37+44=171

33+34+35+41+48=191

 1 2 3 9 16

## X=5x16-49 (1+2+3+9+16=31)

X=80-49

X=31

I will now try it for two more of my t-shapes to make sure the formula works correctly.

 5 6 7 13 20

## X=5x20-49 (5+6+7+13+20=51)

X=100-49

X=51

 33 34 35 41 48

## X=5x48-49 (33+34+35+41+48=191)

X=240-49

X=191

I will now try the formula on a 6 by 6 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

The formula is X=5T-7G

Which changes to X=5T-7x6

X=5T-42

T. NumberT. Total

14                                          28

23                                        73

33                                       123

1+2+3+8+14=28

10+11+12+17+23=73

20+21+22+27+33=123

 1 2 3 8 14

## X=5x14-42 (1+2+3+8+14=28)

X=70-42

X=28

I will now try it for two more of my t-shapes to make sure the formula works correctly.

 10 11 12 17 23

## X=5x23-42 (10+11+12+17+23=73)

X=115-42

X=73

 20 21 22 27 33

## X=5x33-42 (20+21+22+27+33=123)

X=165-42

X=123

I have tried this formula out on three different grid sizes and the formula works, the formula is: X=5T-7G, when Grid Width (= G), the T-Number (= T), and the T-Total (= X)

3) Grids of different size using other transformations and combinations of transformations to Investigate relationships between the T-Total, the T-Numbers, the Grid sizes and the transformations.

Below is a grid with parts of the formula in. I will use this in a minute to figure out a formula.

 1 2 3 . G G+1 G+2 G+3 . 2G 2G+1 2G+2 2G+3 . 3G

For a “ T ” in the grid

 1 2 3 4 5 ... G G+1 G+2 G+3 G+4 G+5 ... 2G 2G+1 2G+2 2G+3 2G+4 2G+5 ... 3G 3G+1 3G+2 3G+3 3G+4 3G+5 ... 4G 4G+1 4G+2 4G+3 4G+4 4G+5 ... 5G

2 squares right

1 square down

From 2G+2 to 3G+4

This looks like adding numbers of squares down to the number of G’s and the number of squares right to the other number. If we start with a T-number (T) then moving 4 right and 3 down

The new T-number is:

T+3G+4

We can use “h” for the number of places right and “Y” for the number of places down.

We could write this as (h/y), a column vector:

Now X+(4/3)=X+3G+4

And X+(h/y)=X+yG+h

For all of the “ T’s ” the T-number is the same as shown below:

The other “ T’s ” that I can work out the formula for are shown bellow.

A 9 by 9 grid can be used for the other 3.

 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

T. NumberT. Total

1.  142

41                         198

41                         212

41                         268

22+23+24+32+41=142

30+39+48+40+41=198

34+43+52+42+41=212

58+59+60+50+41=268

I will now try to find out the formula for my t-shape when the T is 90° from it upright position when (T=T. Total) and (G=grid size).

 T+2-G T T+1 T+2 T+2+G

All of the formulas in the grid above added together gives me an overall formula of:

T+(T+1)+(T+2-G)+(T+2)+(T+2+G)

5T +7

Now that I know the formula for the T-Shape 90° from it upright position, I will now test it 3 times, with different sized grids.

I will test my new formula, in an 8 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

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 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

7G+5T

=7x8+5x29 (T. Total: 44+45+46+37+29=201)

=56 + 145

=201

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

7G+5T

=7x7 + 5x18 (T. Total: 31+32+33+25+18=139)

=  49 + 90

= 139

Also, now on a 6 by 6 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

7G+5T

=7x6 + 5x15 (T. Total: 26+27+28+21+15=117)

=  42 + 75

=  117

I will now try to find out the formula for my t-shape when the T is 260° from it upright position when (T=T. Total) and (G=grid size).

 T-2-G T-2 T-1 T T-2+G

All of the formulas in the grid above added together gives me an overall formula of:

T+(T-1)+(T-2+G)+(T-2)+(T-2-G)

5T-7

Now that I know the formula for the T-Shape 260° from it upright position, I will now test it 3 times, with different sized grids.

I will test my new formula, firstly on 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

5T-7

=5x30 – 7 (T. Total: 19+28+37+29+30=143)

=150 – 7

=143

I will now try it on an 8 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

5T – 7

=5x29 – 7 (T. Total: 19+27+35+28+29=138)

=145 – 7

=138

I will now try it 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

5T – 7

=5x40 – 7 (T. Total: 31+38+45+39+40= 193)

=200 – 7

=193

Whilst doing this investigation I found out that for the 2 T’s which were sideways like this:

Had the formula’s 5T – 7 and 5T + 7 which did not have a G (Grid Size) in the formula, because they would cancel each other out thus telling me that this formula was not affected by the grid size in order for me to find the T. Total with my formula’s.

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

# Related GCSE T-Total essays

1. ## T-total Investigation

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

2. ## T-Shapes Coursework

Section 5: w x l "T" on Width g Grid 1) Introduction Throughout this section, the variable w will be used to represent the width of the "wing" of the "T" and the variable l will be used to represent the length of the "tail" of the "T".

1. ## The T-Total Mathematics Coursework Task.

we can say that the formula for this table is as follows. When: T=T-total t=T-number The formula is T = 5t + 7 T-shapes rotated 180 degrees to the right on a 10 by 10 number grid T-number Top of T-shape T-total All numbers in T-shape added T-number Top of

2. ## T-Total Investigation

T=5v-18 We can even say that; T=5v-2g As 9 is the grid size, and all numbers in our relationship grid were related around 9, so we can concluded that it is related to the grid size. We can test this on different positions on the 9x9 grid.

1. ## Objectives Investigate the relationship between ...

n n+6 26 27 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-1+n-2+n-10+n+6 =n+n+n+n+n+6-1-2-10=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.

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

a positive figure its T-Total is less than the original T-Total If we table these results along with all the horizontal translation results from 41 to 44 (for v), we should easily see a pattern (on a grid width of 9), also adding a column for the difference between the number in that column and the once below.

1. ## Maths Coursework T-Totals

T=105-70 T=35 CHECK YOUR RULE WITH EXAMPLES This proves my equation correct as; the correct translated T-Total is generated, thus we can state; Any combination translation (vertically and horizontally), can be found by using the equation of t=(5v-2g)-(a(5g))-5b were v is the middle number, g is the grid width,

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

and the N number is 20. I will move the T-Shape across one column again. The value of this T-Shape is 42 (2 + 3 + 4 + 12 + 21 = 42 and the N number is 21. To continue the sequence, I will move the T-Shape across another column again.

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