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• Level: GCSE
• Subject: Maths
• Word count: 5173

# In this coursework, I am going to show you the workings and give you the information about the T-Shapes and the different things about transformations. Transformation is about moving shapes on a Square Grid.

Extracts from this document...

Introduction

PRATIK MEHTA        GSCE COURSWORK

GCSE COURSEWORK

In this coursework, I am going to show you the workings and give you the information about the T-Shapes and the different things about transformations. Transformation is about moving shapes on a Square Grid. There are different types of transformations. For example, rotation, translation etc. a square grid is a grid, which has number of square shapes put together and makes a big square. This big square is called a square grid. T- Shapes are shapes of T drawn on a square grid. They have five numbers inside it. A T-Total is the total of all the numbers inside the T-Shape, added together. Every T-Shape has a T-Number. A T-Number is the number at the bottom of the T-Shape. This is an example of all the things that I have told you above.

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The shape in red is called a T-Shape. The grid, in which the shape is drawn, is called a square grid. In this shape the T-Total is 6+7+8+11+15=47. The T-Number is the shape is 14. In this grid the shape can be moved. Look at one of the example in the diagram. The shape in blue is the moved shape. This is called transformation. There can be many different types of grids. For example, 4 by 4, 6 by 6, 8 by 8 etc.

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This is a 9 by 9 square grid. And the T-Shape is drawn for you in blue colour.

T-Total= 3+4+5+13+22 = 47.

T-Number = 22.

Call this position number 1.

Now I move the shape and I move it right so the T-Total and The Number will change. The shape in red is the moved shape.

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T-Total=4+5+6+14+23 =52.

T-Number = 23.

This is position number 2.

Now I move the shape right again so the T-Total and the T-Number will change as well. The shape in colour green is the moved shape now.

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T-Total=5+6+7+15+24=57.

T-Number = 24.

This is position number 3.

Now I will show you the Table of Results to show you what I explained you in the whole process. This will sum up the whole example and will help you to understand.

 Position No. T-Total T-Number 1 47 22 2 52 23 3 57 24

By this table of results, the rule comes out as, the T-Total goes up by 5, and the T-number goes up as 1. Therefore the formula should be, N=5p+42. Now let Us test this rule and formula.  I move the shape right again. So the shape in yellow is the moved shape.

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T-Total=6+7+8+16+25=62.

T-Number = 25.

Suppose this is position number 4.

Now look at the table below.

 Position No. T-Total T-Number 1 47 22 2 52 23 3 57 24 4 62 25

In this table of results the formula fits in correctly so it is proved that the formula is right.

No I will show you the other example of 10 by 10 square grid and I will show everything that I did in the other square grids.

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This is a 10 by 10 square grid. And the T-Shape is drawn for you in blue colour.

T-Total =

4+5+6+15+25 = 55.

T-Number = 25.

This is position number 1.

Now I move the shape right so the T-Total and the T-Number change as well. The shape in colour red is the moved shape.

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T-Total =

5+6+7+16+26 = 60.

T-Number = 26.

This is position number 2.

Now I move the shape right again. So the T-total and the T-Number will change again. The shape is the colour yellow is the moved shape.

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T-Total =

6+7+8+17+27= 65.

T-number = 27.

This is position number 3.

Now I will show you the Table of Results to show you what I explained you in the whole process. This will sum up the whole example and will help you to understand.

 Position No. T-Total T-Number 1 55 25 2 60 26 3 65 27

By this table of results, the rule comes out as, the T-Total goes up by 5, and the T-number goes up as 1. Therefore the formula should be, N=5p+50. Now let Us test this rule and formula.  I move the shape right again. So the shape in green is the moved shape.

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Conclusion

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T-Total = 4+5+6+17+29 = 61.

T-Number = 29.

This is position number 3.

Now I will show you the Table of Results to show you what I explained you in the whole process. This will sum up the whole example and will help you to understand.

 Position No. T-Total T-Number 1 51 27 2 56 28 3 61 29

By this table of results, the rule comes out as, the T-Total goes up by 5, and the T-number goes up as 1. Therefore the formula should be, N=5p+46. Now let Us test this rule and formula.  I move the shape right again. So the shape in green is the moved shape.

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T-Total = 5+6+7+18+30 = 66.

T-Number = 30.

Suppose this is position number 4.

Now let’s check this by putting it in the table of results.

 Position No. T-Total T-Number 1 51 27 2 56 28 3 61 29 4 66 30

In this table of results the formula fits in correctly so it is proved that the formula is right.

Now I will show you all the formulas that I got from all the examples:

 Grids Formula 6 by 6 N=5P+23 7 by 7 N=5P+26 8 by 8 N=5P+29 9 by 9 N=5P+42 10 by 10 N=5P+50 11 by 11 N=5P+48 12 by 12 N=5P+46

Now this was the entire example I was meant to show you. Now you should be able to understand what this T-Shape is all about. I showed you the examples in 6 by 6, 7 by 7, 8 by 8, 9 by 9, 10 by 10, 11 by 11, and 12 by 12 square grids.  I have also shown you the formulas of all the grids. This is how you work out the T-Total and the T-Numbers.

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

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