# My objective in this investigation is to ~ First investigate the association between the t-total and the t-number. ~

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Introduction

Jade chanele rattray

Mathematics coursework: T-shape Bexleyheath secondary school.

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T-NUMBER

THIS IS AN INVESTIGATION BY JADE CHANELE RATTRAY.

T-TOTAL

T-SHAPE

INTRODUCTION

This particular piece of course work concentrates on numbers that are situated in a grid. In this grid upon these numbers is a‘t’ shape this is made up of three numbers across the top and three numbers down.

My objective in this investigation is to…

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First investigate the association between the t-total and the t-number.

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Secondly, utilize grids of various sizes, render the t-shape to different positions as well as examine the relationship between t-number, t-total, and t-shape.

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And finally, again use grids of various sizes, as well as try other transformations and combinations of transformations. And further more to study connections between the T-total, T-number, grid size and the transformation.

PLAN

I am a student in year nine that has been presented with an investigation to discover with mathematical procedures that different grids have a different results and connection between numbers.

I have been given a basic introductory 9 by 9 grid with a simple 3 by 3 t-shape with a 1:1 aspect ratio. I will study the association between the T-total and T-number.

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Here is a simple 9 by 9 grid. On this grid I have shaded in three t-shapes. The first one I shades is the one that has the five numbers 40, 41, 42, 50 and 59.

The T-total is 40+41+42+50+59=232. If I alter the position of this shape one space to the left I will have a t-total of 39+40+41+49+58=227. Look at the last t-total of 232 and look at this one, there is a decrease of five, and if I move the T-shape two spaces to the right from the original position I get a T-total of 42+42+44+52+61=242. The T-total increases from the first by 10.

METHOD

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For the pencil highlighted T-shape the T-number is 20 and the T-total is 37. For the red highlighted T-shape the T-number is 21 and the T-total is 42. Note that the difference is 5. I predict from this information that every time the T-number increases by one, the T-total increase by five just as it did on the grid in the plan. I will investigate in two ways. The first will be to discover the formula and the second shall be to prove the formula. These methods are called ‘relative formula’ and ‘difference in sequence’.

Conclusion

41-40

41-39

41-48

. 41-30.

5

5tn-7=198

So lets see if this worked.

T-number=41

T-total=41+40+39+48+30=198

It has proven to work.

So this show that the formula may alter from situation to situation but the basic introductory formula is always its template.

Conclusion

In this project I have found various ways in which to solve the problem that was presented with. This investigation named T-shape was and investigation where I had to find the formula for each circumstance for instance a different grid size, I was expected to work out the correct formula for the T-shape in this grid as well as find another correct formula for any different position that the t-shape could be in like 90 180 270 or its original position.

I found three formulas the first for the original shape position and original grid size was:

5tn-63=T-total

This was my original/introductory formula.

My second was the T-shape 180 from its original position the formula for this was:

5tn+63=T-total

And my third was the T-shape on its side/90 /270 the from its original position formula for this position was:

5tn-7=T-total.

Knowing all of this and presenting this to you as an investigation brings me to the end of the investigation.

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

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