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.

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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.

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. here are some examples.

This is a 4by4 square grid.

This is a 6by6 square grid.

This is an 8by8 square grid.

These are some of the examples. But in this coursework I am going to start from 6by6 and carry on to 12by12 grid. I am going to show you all the diagrams and then give you a table of results. I am going to work out everything hen you will also come to know some rules. You need rules for these things. From this I will make a prediction and then test it to show whether it is true or false. You will also need formulas. Then in the end there is going to be a conclusion. And I will explain you everything in a summary. Now I will start explaining in detail.

This is the 6by6 square grid. And you will know everything about it.

This is the 6by6 square grid. There is the T-Shape drawn in red in the square grid.

This is the T-shape drawn out from the square grid above. Now I will show you the T-Total and the T-Number of this shape. This is position number 1.

T-Total= 1+2+3+8+14=28.

T-number=14.

Now I move the shape right. So the shape in blue is the moved shape. Every shape has different T-Total and T-Number.

So now the T-Total = 2+3+4+9+15 =33.

T-Number = 15.

This is position number 2.

Now I move the shape right. So the shape in yellow is the moved shape. This shape will have different T-Total and T-Number.

T-Total= 3+4+5+10+16= 38.

T-number = 16

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.

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+23. 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 = 4+5+6+11+17 = 43.

T-Number = 17. Suppose this as position number 4.  Now let us check this by putting it in the table of results.

Now look at the position number 4. It is proved that the formula is right because it works properly.

No I will show you the other example of 7 by 7 square grid and I will show everything that I did in the 6 by 6 square grid.

This is a 7 by 7 square grid and the T-Shape is drawn for you in ...

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