# T-shapes.I will investigate and find rules that connect the t-total to the t-number and the grid size.

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Introduction

MATHS COURSEWORK : t-shapes.

I will investigate and find rules that connect the t-total to the t-number and the grid size.

T = t number

X = grid size

To investigate and find a rule I will use a 4 x 4 grid as starting of with a smaller grid and going up can help spot a rule with much more ease.

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The t-number is 10 and the t-total is 1+2+3+6+10=22

I will try and investigate a rule by working out the difference between the t-total and the t-number, and then I will use an algebraic expression to work out the rule for grids of different sizes.

T-number = 10

T-total = 1+2+3+6+10= 22

7 x 4 (grid size) = 28

5tn- 28= t-total

5 x 10-28=22

Now I will investigate if this formulae works on different positions on a 4 x 4 grid.

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I will try a different t-shape.

The t-number is 11

The t-total is 27 (2+3+4+7+11)

I will substitute the following values into the formulae 5t – 7x (grid number)

5 X 11 = 55

7 X 4 = 28

55 – 28 = 27

This has proven to work on a 4 x 4 grid.

Middle

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I am first going to try and rotate the t-number 180 degrees so it is upside down.

I will do this as we already have a formula for the t-total (5t-63). I have used a 9x9 grid as this is the grid which the formula works on.

The t-shape I am going to use has a t number of:

T- number: 2

The old formula stated that we had to minus 63 away from 5 x the t-number but as this is upside down (rotated 180 degree) I am going to try and add the 63.

So 5 x t number makes 10 and + 63 = 73

To see if the formula has worked I will add all the numbers in the t-shape:

2+11+19+20+21 =73 THIS NOW PROVES THAT THE MINUS SIGN

HAS WORKED

We have now found a formula for both the upright and upside down T- shape.

The next step is to move the shape on its side (90 degrees from the upright position) I move the t-number 90 degrees to the left.

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Conclusion

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The formula for this t-shape must be:

5t-number +7 = t – total as the one above is the opposite.

I will now test this formula:

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73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 |

5 x 70 + 7 = 357

T-number = 70

T-total = 70+71+72+63+81 = 357

This formula works for all grid sizes and anywhere on the grid.

CONCLUSION

During this project we have learned how to find data and summaries it into smaller parts.

We have learnt to find and make rules and have put them into practice. This project has taught us how to make algebraic rules which can be put into use.

Here are the various rules we found out:

PART 1

T-total is 5t – 63

(This only works for 9x9 grid anywhere)

PART 2

5tn – 7x(grid number)

(This works for all grid sizes anywhere.

PART 3

Normal way up – 5t – 7x

90 degrees to the left – 5t – 7 x

90 degrees to the right- 5t + 7 x

180 degrees from upright : 5t + 7 x

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

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