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  • Level: GCSE
  • Subject: Maths
  • Word count: 1249

To Investigate numbers in a letter T drawn on a grid ranging from 6 by 6to 9 by 9.

Extracts from this document...

Introduction

T-total

Aims: To Investigate numbers in a letter T drawn on a grid ranging from 6 by 6to 9 by 9.

Investigation: I will be trying to find formulae for the t-total investigation. I will be drawing a grid.

Tasks:

1) Investigate the relationship between the T-total and the T-number

2) Use the grids of different sizes. Translate the T-shape to different positions. Investigate relationships between the T-total and the T- Number and the grid size.

3) Use grids of different sizes again, try other transformations and combinations of transformations. Investigate relationships Between the T-total and the T-number and the grid size and the transformations.

Key: Red = 1st Formulae, Green= 2nd Formula , Purple= 3rd formula and yellow means that numbers is used in both of the other formula’s

1) Solution:

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Look at the T-shape I Have drawn on the 9 by 9 number grid.

The total of the numbers inside the T-shape is 1+2+3+11+20=37

This is called the T-total.

The number at the bottom of the T-shape is called the T-number.

...read more.

Middle

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If you take the other numbers in the T-Shape away from the T-Number you get a T-Shape like this.

T-13

T-12

T-11

T-6

T

= 5T-42

1) Now to test this formula to see if it works, again

For the T-total I will use the letter X

For the T-Number I will use the letter T

So X = 5T-42

T = 14

X = 5x14-42

= 70-42

= 28

Now I will do two more to check to see if it will work anywhere on the grid.

2)T=22

X=5x22-42 9+10+11+16+22=68

=110-42

= 68

3)  T=35

X=5x35-42 22+23+24+29+35=133

=175-42         =133

I have tested the formula for three different T-numbers and the formula works for a 6 by 6 grid.

The full formula for this size grid is:- X=5T-42

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I can predict that that the formula for the 3 by 3 square will be 21. I will now prove this.

So X = 5T-19

     T = 8

     X = 5x8-19

         = 40-21 = 19

The full formula= X=5T-21  

Below is a grid with parts of the formula in. I will use this to

Figure out a formula for any T-Total on any width grid.

T-2G-1

T-2G

T-2G+1

T-G

T

...read more.

Conclusion

I have also found out by doing these grids that as well as having one rule for each grid to work out the T-totals possible with in it, there can also be overall rules to work out any T-total of any grid size be it a 4 by 4 grid or a 20 by 20 grid. I also worked out that you always multiply the T-number by 5 and to get the number which you have to subtract all you do is multiply the grid size by 7.Which is 5t-7g

Rotations onlyIf you rotate the T shape 90 degrees the formulae is 5t+7 and if you rotate it 180 degrees the formulae is 5t+7G. Also if you rotate it 270 degrees the formulae is 5t-7.

Evaluation:

James Shamim 11G Maths Coursework

...read more.

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