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• Level: GCSE
• Subject: Maths
• Word count: 1668

# Investigate the relationship between the T-Total and the T-Number. Use grids of different sizes. Translate the T-Shapes to the different positions. Investigate

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Introduction

09th January 2006

GCSE Mathematics Coursework

T-Totals

• Investigate the relationship between the T-Total and the T-Number.
• Use grids of different sizes. Translate the T-Shapes to the different positions. Investigate relationships between the T-Total, the T-Number and the grid sizes.
• Use grids of different sizes again. Try other transformations and combinations of transformations. Investigate the relationships between the T-Total, the T-Number, the grid size and the transformations.
 T-Total 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
 T-Numbers  (T) 20 21 22 23 24 T-Total 37 42 47 52 57

+5            +5            +5             +5

5 x 20 = 100

100 – 37 = 63

The difference between the T-Totals is 5 this makes the first part of the formula: 5T

To work out the second part takes the T-Number and multiplies by the difference.

#### 5T - 63

The 50th Term is:

Middle

5 x 16 = 80

80 – 31 = 49

## 5T – 49

The 50th Term is:

5 x 50 = 250

250 - 49 = 201

To Test:

## T Number 40

5 x 40 = 200

200 – 49 = 151

 T-Total 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
 T-Number 14 15 16 17 18 T-Total 28 33 38 43 48

+5                       +5                      +5                      +5

5 x 14 = 70

70 – 28 = 42

## 5T – 42

The 50th Term is:

5 x 50 = 250

250 - 42 = 208

To Test:

## T Number 30

5 x 30 = 150

150 – 42 = 108

### Relationships and Master Formula Working Out

Formulae’s

9 x 9 Grids: 5T - 63

8 x 8 Grids: 5T - 56

7 x 7 Grids: 5T – 49

6 x 6 Grids: 5T – 42

• Smaller the Grid Size the less you have to take away from the T-Total
• The Larger the grid size the more you have to take away from the T-Total
• All The Formulas have gaps of 7

(Ex. 63 – 56 = 7. 56 – 49 = 7. 49 – 42 = 7.)

I found out that the master formula is 5T-(7xG)

I got the 5 by looking at the differences of the number.

The T stands for the T-Number (which is always 5; as there are 5 squares in the T; and it is current throughout.)

Conclusion

## T-Number 30

5 x 30 = 150

150 – -63 = 213

8 x 8 Grids: Transformation

 T-Number 11 12 13 14 15 T-Total 48 53 58 63 68

5 x 11 = 55

55 – 48 = 7

5T - 7

The 50th Term is:

5 x 50 = 250

250 – 7 = 243

To Test:

## T-Number 30

5 x 30 = 150

150 – 7 = 143

7 x 7 Grids: Transformation

 T-Number 8 9 10 11 12 T-Total 47 52 57 62 67

5 x 8 = 40

40 - 47 = -7

5T - -7

The 50th Term is:

5 x 50 = 250

250 – -7 = 257

To Test:

## T-Number 30

5 x 30 = 150

150 – -7 = 157

7 x 7 Grids: Transformation

 T-Number 2 3 4 5 6 T-Total 59 64 69 74 79

5 x 2 = 10

10 - 59 = -49

5T - -49

The 50th Term is:

5 x 50 = 250

250 – -49 = 299

To Test:

## T-Number 30

5 x 30 = 150

150 – -49 = 199

7 x 7 Grids: Transformation

 T-Number 2 3 4 5 6 T-Total 59 64 69 74 79

5 x 2 = 10

10 - 59 = -49

5T - -49

The 50th Term is:

5 x 50 = 250

250 – -49 = 299

To Test:

## T-Number 30

5 x 30 = 150

150 – -49 = 199

6 x 6 Grids: Transformation

 T-Number 7 8 9 10 11 T-Total 42 47 52 57 62

5 x 7 = 35

35 - 42 = -7

5T - -7

The 50th Term is:

5 x 50 = 250

250 – -7 = 257

To Test:

## T-Number 30

5 x 30 = 150

150 – -7 = 157

6 x 6 Grids: Transformation

 T-Number 2 3 4 5 6 T-Total 52 57 62 67 72

5 x 2 = 10

10 - 52 = -42

5T - -42

The 50th Term is:

5 x 50 = 250

250 – -42 = 292

To Test:

## T-Number 30

5 x 30 = 150

150 – -42 = 192

6 x 6 Grids: Transformation

 T-Number 9 10 11 12 13 T-Total 38 43 48 53 58

5 x 9 = 45

45 - 38 = 7

5T - 7

The 50th Term is:

5 x 50 = 250

250 – 7 = 243

To Test:

## T-Number 30

5 x 30 = 150

150 – 7 = 143

##### Relationships

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