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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.

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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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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 20 21 22 23 24 25 26 T-total 37 42 47 52 57 62 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.

Middle

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 T-number 24 25 26 27 28 29 30 T-total 43 48 53 58 63 68 73

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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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.

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 ...

New T-total = 34 + (2*5) = 34 + 10 = 44 As you can see the T-total of T20 is '44' Algebraic Formula While my formula above, will be able to find the T-total of T-shapes translated horizontally, it is not extensive enough and requires a current T-total number

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

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 Red t-shape 5tn- (7*G)+7= t-total 5*41 - 63+7 = 149# Blue t-shape 5tn- (7*G)

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Also there is transformations and combinations of transformations. The investigation of the relationship between the t-total, the t-numbers, the grid size and the transformations. If we turned the t- shape around 180 degrees it would look like this. When we have done this we should realise if we reverse the t-shape we should have to reverse something in the formula.

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

(The grid is on the next page) 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

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

* A translation of 1 square upwards of the T-Number leads to a T-total of -45 of the original position. * A translation of 1 square downward of the T-Number leads to a T-total of +45 of the original position.

2. ## T totals - translations and rotations

The two remaining numbers in the T shape are N-18+1 and N-18-1. Thus the T total is: N+ (N-9) + (N-18) + (N-18+1) + (N-18-1) = 5N-63 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

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

Now to work out the difference between the t-number and the rest of the numbers in this t-shape Working Out: - 70-51=19 70-52=18 70-53=17 70-61=9 TOTAL=63 Again the number turns out to be 63. This is where the 63 came from in this equation.

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