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• Level: GCSE
• Subject: Maths
• Word count: 1138

# To find the relationship between the T-Total and the T-Number I must investigate the relationship between the T-number and the other numbers in the T-shape.

Extracts from this document...

Introduction

T-Totals

Part 1

## T-number = 23

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

To find the relationship between the T-Total and the T-Number I must investigate the relationship between the T-number and the other numbers in the T-shape.

To do this I will take all the numbers in the T away from the T-number to produce the formula.

Formula for the relationship between the T-number and T-total in a 9 by 9 grid = T + (T – 9) + (T – 18) + (T- 19) + (T – 17) = 5T – 63

To test this formula I will use another T on the 9 by 9 grid.

T-number = 62

T-Total = 5T – 63

= (5 x 62) – 63

= 247

43 + 44 + 45 + 53 + 62= 247

The formula has been tested and found to be correct as 5T-63.

### Part 2

#### I will now use grids of different sizes to investigate the relationship between the T-total, the T-numbers and the grid size.

I will start with a six by six gird and find the relationship between the T- total and the T-number.

T-number = 21

T- total = 63

As before I will show the relationship between the T-number and the other numbers in the T.

Formula for the relationship between the T-number and T-total in a 6 by 6 grid = T + (T – 6) + (T – 12) + (T – 13) + (T – 11) = 5T – 42

Middle

To prove this formula I will show the relationship between the T-total and the T-number but I will involve the grid size.

Formula for the relationship between the T-number, T-total and grid size = T + (T – g) + (T – 2g) + (T – 2g + 1) + (T  - 2g – 1) = 5T - 7g

I will test this formula on a different grid.

T- number = 67

T-total = (5 x 67) – (7 x 12) = 251

42 + 43 + 44 + 55 +67 = 251

The formula is correct.

I shall now investigate formulas showing the relationship between the T-number, the T- number and the grid size when they are rotated through 90° c/w, 180° and 90° a-c/w.

T- number = 32

T- total = 32 + 41 + 49 + 50 +51 = 223

As before to show a formula I must investigate the relationship between the T-number, T- total and the grid size.

Formula for the relationship between the T-number, T-total and grid size at a 180° rotation =

T + (T + g) + (T + 2g) + (T + 2g –1) + (T + 2g + 1) = 5T + 7g

I note that this formula is the opposite of the formula for the vertical rotation (5T – 7g).

I will now investigate a formula showing a relationship between the T-number the T-total and the grid size at a 90° c/w rotation.

T-number = 72

T- total = 72 + 73 + 74 + 61 + 87 = 367

Conclusion

This T will be called T1.
T-number = 55

T-total = 390

I will transform the T to new a new position by moving it 3 along and

2 up. (-3

2)

This T will be called T2

T-number = 75

T-total = 305

To investigate the relationship between the T-total, the T-number, the grid size and the transformations I will need to show the effects of moving the T two up and 3 along and how this relates to the numbers in the T and the grid size.

• If you move the T up or down one each number in the T increases by the grid size
• If you move the T left or right one each number increases by one.

With the bullet points above I can construct a formula, which show the relationship between the two transformed T’s.

T-total of the original T – ((number moved up or down x amount of numbers in the shape x grid size) + (number moved left or right x amount of numbers in the shape)) = The T-total of the second, transformed T.

To test this formula I will use the T’s from above.

390 – ((2 x 5 x 10) + (-3 x 5)) = 305

305 is the T-total of T2 confirming the formula.

This formula will work for a transformation of a rotated T or a different shape.

This student written piece of work is one of many that can be found in our GCSE T-Total section.

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# Related GCSE T-Total essays

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

To begin with, I will first find the T-totals of these 3 T-shapes. * T20 1 2 3 11 20 1+2+3+11+20 = 37 * T21 2 3 4 12 21 2+3+4+12+21 = 42 * T22 3 4 5 13 22 3+4+5+13+22 = 47 Table of results T-shape T-total Increment T20

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

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

Moving to the left: The same approach is taken as moving the T shape to the left as moving the T shape to the right except for a minor adjustment. When moving the T shape to the left, instead of adding 5 x amount of squares moved across, a minus is used.

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

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1. ## T totals - translations and rotations

5 5 5 5 Un= n+5 My general expression for my 9by9 grid is: N-19 N-18 N-17 N-9 N N+ (N-9) + (N-18) + (N-18+1) + (N-18-1) = N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

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

= 28 5tn- 28= t-total 5*10-28=22 This has proven to work on a smaller scale. We can see that by changing the grid size we have had to change the formula but still managing to keep to the rule of how you get the number to minus in the formula.

1. ## T- total T -number coursework

= 77 Try out the new formula 5tn - 77= t-total 5*24-77=43 The same formula works with only changing the last number in the formula. This will be tried on a smaller grid size to make sure it is not if the grid size is bigger.

2. ## Maths Coursework T-Totals

x 7 From this a grid of a T-Number based on the relationships between x (T-Number) and g (grid size); x-(2g-1) x-2g x-(2g+1) x-g x In addition, from this we can simplify the above and generate the formula of:. t = 5x - (g � 7 )

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