T-Totals. Aim: To find the relationship between the T-Total and the T-number. To find a formula that works for every grid size. To find how rotating the T-shape effects the T-Total To find a formula that works f

GCSE Maths

T-Totals

Aim:

To find the relationship between the T-Total and the T-number.
To find a formula that works for every grid size.
To find how rotating the T-shape effects the T-Total
To find a formula that works for every translation.

T-Total 1=1+2+3+11+20

=37

T-Number=20

T-Total=2+3+4+12+21

=42

T-Number=21

T-Total=3+4+5+13+22

=47

T-Number=22

T-Total=4+5+6+14+23

=52

T-Number=23

I have noticed that the difference off the T-totals is 5:

37 42 47 52 57

5 5 5 5

(This is because there are 5 numbers in the T-totals and they are going up 1 every time)

The formula must equal T=5n+C (T=T-Totals n=T-number C=Constant)

We know the T-totals and T-numbers so we need to find what the constant is, there is too ways of doing this by going back to the 0th formula or just imputing the other totals into the formula. I will use the second method to succeed in finding the Constant.

T-total 1=37

37=(5*20)+C C=37-5*20 C=37-100 C= -63

T-number=20

Therefore T=5n-63

I will try this formula on T-Number 50:

Using my formula, T-number=69 so

T=(5*69)-63

=345-63

=282

Now I need to show it is correct:

T=50+51+52+60+69

=282

My prediction was correct so my formula is right. This is my first aim.

I will now use Grid size 8 to see if there is any difference in the formula I have found for Grid size 9 and if there is to work out the connection between the Grid size and the formula.

I used terms of n to figure out the ...