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• Level: GCSE
• Subject: Maths
• Word count: 1115

# t-totals. I will be doing three grids, a 10 x 10 grid, a 9 x 9 and an 8 x 8. Doing three will give me the evidence more than if I just did one or two

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Introduction

Maths Coursework – T-Totals

What I am trying to do in this coursework is trying to find a link between two parts of a T. The two parts are the T number (the bottom number) and the T total (all the numbers in the T added together). I will now try and find a connection and hopefully be successful. I will be doing three grids, a 10 x 10 grid, a 9 x 9 and an 8 x 8.  Doing three will give me the evidence more than if I just did one or two and would make sure that I was right.

The first grid I did was the 10 x 10:

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 11 12 13 22 32

11 + 12 + 13 + 22 + 32 = 90

 12 13 14 23 33

12 + 13 + 14 + 23 + 33 = 95

 13 14 15 24 34

13 + 14 + 15 + 24 + 34 = 100

 14 15 16 25 35

14 + 15 + 16 + 25 + 35 = 105

T-Total and T-Number grid

 T-Number 32 33 34 35 T-Total 90 95 100 105

I have done 4 T’s so that I can be sure of the pattern I come across.

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 4 5 6 14 23

4 + 5 + 6 + 14 + 23 = 52

 5 6 7 15 24

5 + 6 + 7 + 15 + 24 = 57

 6 7 8 16 25

6 + 7 + 8 + 16 + 25 = 62

 7 8 9 17 26

7 + 8 + 9 + 17 + 26 = 67

T-Total and T-Number grid

 T-Number 23 24 25 26 T-Total 52 57 62 67

I have come across the same formula in this grid that I did before of:

T Total = 5N +?

N is the T Number.

This is a formula which I believe is the true pattern but I needed to do the 8 x 8 gird to be sure. I also think that I have come across a new formula which can only be proven if the next formula goes down 7 in its T total. The last two have been:

5t -70 = 10 x 10 grid

5t -63= 9 x 9 grid

Conclusion

 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

Where N is 16 then the T Total will be equal to 5N-7G =5 x 16 – 7 x 7

=80 – 49

=31

Also this can be worked out by adding the number 1+2+3+9+16=31. As I demonstrated this works.

Conclusion

From the very first grid, I found the right sum but everything that is found out still needs to be checked unless 100% right. I had made a prediction and I turned that into an answer after looking at two more grids. After completing the three grids (10x10, 9x9 and 8x8), I found that every time that the T-Number goes up 1, the T-Total will go up by 5. I have also worked the general rule:

• 5t-70= 10x10 grid
• 5t-63= 9x9 grid
• 5t -56= 8x8 grid

So I can work out any T Total in any sized grid which gives a T number.

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

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