# My task is to find out the relationship between the T-total and the T-number.

Extracts from this document...

Introduction

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11/05/05T – TotalsPrashant Sawlani

Coursework

Introduction:

I am looking at this T-shape drawn on a 9 by 9number grid.

The total of the number 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 20.

This is called the T-number.

My task is to find out the relationship between the T-total and the T-number.

In doing this investigation I hope to find out if there is a pattern between the T-total and the T-number.

Method & Planning:

To do this investigation I will start off by using a 9 by 9 grid then I will draw T-shapes.

I will begin by moving my T-shape step by step to the right and I will work my way down to the 3 by 3 grid in order.

I will show drawing and working out, I will show my results in a table of results, I will look for patterns and rules from my results.

I will write my rules in sentences and algebra.

Prediction:

When I’ve finished the task I think I will find that if I

Middle

11/05/05T – TotalsPrashant Sawlani

Coursework

Workings:

If I add these two together we have our formula.

5tn-63=t-total

### Here is an example of using the formula

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5*57-63=t-total

5*57-63= 222

Check

T-total = 38+39+40+48+57=222

I will now be using grids of different sizes and then translating the t-shape to different positions. Then investigation of the relationship between the t-total, the t-number and the grid size. Here I will be finding out more about the grid size and what it is capable of doing.

11/05/05T – TotalsPrashant Sawlani

Coursework

Workings:

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T-total = 1+2+3+13+24 = 43

T-number = 24

The t-total and the t-number have risen even though the t-shape looks to be in the same place. The t-number has risen by four and the t-total has risen by six. If we use the same rules we made in the last section it works. Here is the longer method

Difference

24-1= 23

24-2 = 22

24-3 =21

24-13 =11

TOTAL =77

Or the shorter way

7* 11 (grid size) = 77

Try out the new formula

5tn – 77= t-total

11/05/05T – TotalsPrashant Sawlani

Coursework

Workings:

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.

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T-number = 10

T-total = 1+2+3+6+10= 22

7 * 4 (grid size) = 28

5tn- 28= t-total

5*10-28=22

Conclusion

Coursework

Workings:

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5tn + 7 = t-total

5* 70 + 7 = 357

Check

T-number = 70

T-total = 70+71+72+63+81 = 357

If we were to put the t-shape diagonally on the grid we find that the same rule applies again apart from you can not use the 2nd rule were you times the grid size by seven.

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11/05/05T – TotalsPrashant Sawlani

Coursework

Workings:

The t-shape has t-number of 33 and the t-total = 7+17+27+25+33 = 109

The difference between the t-number and the rest of the numbers in the t-shape.

33-25= 8

33-7= 26

33-17= 16

33- 27 = 6

TOTAL= 56

5tn+56= t-total

5 * 33 - 56 =109

The reverse triangle the sign should be reversed to a plus.

T-number is 13

T-total = 19+29+39+21+13 = 121

5tn+56= t-total

5*13+ 56= 121

11/05/05T – TotalsPrashant Sawlani

Coursework

Conclusion:

In this project I have found out many ways in which to solve the problem I have with the t-shape being in various different positions with different sizes of grids. The way I have made the calculations less difficult is by creating a main formula that changes for all the different circumstances.

Here I have put all the formulas I have come up with. These formulas only apply to the nine by nine grids

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5tn-63= t-total D

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5tn+63 = t-total U

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5tn-7= t-total R

The different size of grid changes means the formula has to change slightly.

This is what happened.

T-shapes | number to x by 7 |

D & U | Grid size |

L & R | nothing |

DL & UR | Grid size -1 |

DR & UL | Grid size +1 |

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

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