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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.

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:

 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 44 45 46 47 48 49 50 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

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.

Middle

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

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

## 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

 1 2 3 4 5 6 7 8 9

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

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

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

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