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  • Level: GCSE
  • Subject: Maths
  • Word count: 1922

T-Totals. Use grid of different sizes. Translate the T-shape to different position. Investigate relationships between the T-total, the T-numbers and the grid size.

Extracts from this document...

Introduction

Maths Course Work

T-Totals

Introduction

Looking at a grid of 9*9, with a t-shape you can see that the totals inside the T-shape.=37 E.g.1+2+3+11+21=37.

This is called a T-total =37

 And T-number is the number on the T-shape =20

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Task

I have been set a task to: -

  1. Investigate the relationship between the T-total and the T-number.
  1. Use grid of different sizes. Translate the T-shape to different position. Investigate relationships between the T-total, the T-numbers and the grid size.
  1. Use grids of different sizes again. Try other transformation and combinations of transformations. Investigate relationship between the T-total, the T-numbers, the grid size and the transformations.

Standard T-shapes

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If I input the results from several T-shape into a table it look something like this

T-number

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T-total

37

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67

From this table I can quite clearly see that there is a difference of 5 between adjacent T-numbers.

I can now a simple process of trial and improvement to obtain what I believe the formula to be I will then test my theoretical formula to see if it is correct.

Because there is a difference of 5 I believe that is a logical place to begin the formula.

...read more.

Middle

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T-number

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T-total

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From this table I can see that the difference between the T-total is still 5 so the first bit of the formula is the same. Now to save time I will use a shorter method to work out the total difference between the T-totals and all the other numbers in the shape. in the last formula this number was 63.

24-1=23

24-2=22

24-3=21

24-13=11

TOTAL=77

Know I presume that this number is the variable that changes when the grid size does. I now have to change the formula to allow the grid size to be times or added to another number to reach my difference of 77. So I did this and obtained the formula, g being grid number.

5t-(7g)

I will now try this on another grid size to test my formula.

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With my formula our will work out the T-total for T-number 22 on a 6*6 grid

5*22-(7*6)

=68

My formula has been proven to work on grids of a smaller size. I have now workout how to work out any upright t on any size grid just by working out how to obtain the last number in the formula.

I will now rotate the T-shape on its sun and see what part of the formula changes. I will then try to work out a formula for all rotations.

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 I have to conclude that my formula will be changed in some way. There is no numbers change so I will try and change the minus sign to a plus and I will see if that works. The formula will be

5t+63 or 5t+(7*g)

I will now test this formula on another t-shape and on a different grid.

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...read more.

Conclusion

T-number=12

12+11+10+19+1=53

My formula has been proven to work.

If I now rotate the shape through 180 degrees. I predict that the formula will be the same ecept I now will change the minus in the formula to a plus.

I will now test this theory

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So the formula I will use is

5*10+7=57

T-number=10

10+11+12+3+21=57

This formula has been proven to be correct

I will now try to work a formula that I can use with vectors to work out the T-number and then use the formulas that I have already obtained to work out the rest.

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This shape has been translated by a vector of  +4.

                                           -3

Now if my original T-number is 20 and I have moved I across right by 4 for every one square across I have added one to my original t- number. The same is for the other vector but for every one square up or down the grid number is added or subtracted.

So in this case

X- along in 1’s

Y- up r down in g

Therefore

(t+x)+(yG)

I will now test this

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This T-shape has been moved by vector +3

                                        -4

So if I use my formula

Red T-number=32

(32+3)+(4*9)=71

Which is the Blue T-number now t work out the T-total all I have to do I use my formula from the first section.

...read more.

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

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