I found out that going across the grid once and adding 5 to the next t-total gives you the next t-total.
Then I found out that going down the grid once, and adding 45 to the last t–total gives you the next t–total.
If you multiply the difference going across by the gridsize you get the difference going down.
5 * 9 = 45
10 by 10 grid going down and across.
I found out that going across the grid once and adding 5 to the next t-total gives you the next t-total.
Then I found out that going down the grid once, and adding 50 to the last t–total gives you the next t–total.
If you multiply the difference going across by the gridsize you get the difference going down.
5 * 10 = 50
Equations
I worked out some equation for each T.
Here are my results:-
8 by 10 grid.
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In this T is equal to 18 so 18-10 is equal to T-8.
9 by 10 grid.
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In this T is equal to 20 so 20-11 is equal to T-9.
10 by 10 grid.
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In this T is equal to 22 so 22-12 is equal to T-10.
The equations here are T – the gridsize.
More Equations
I worked some more equations but instead of using I used G instead because G is the gridsize.
In these equations I predict that the end equation will be the same on all of them. I could take a t out of any size grid and still get the same equation.
8 by 10 grid.
= =
In my equation I used G for the gridsize so T-8 is equal to T-G because G is equal to 8 and 8 is the gridsize.
9 by 10 grid.
= =
In my equation I used G for the gridsize so T-9 is equal to T-G because G is equal to 9 and 9 is the gridsize.
10 by 10 grid.
= =
In my equation I used G for the gridsize so T-10 is equal to T-G because G is equal to 10 and 10 is the gridsize.
I added all the T’s up to make 5T and then added 2G + 2G + 2G + G and found out that it is equal to 7g. The equation is 5T – 7G.
I got the 5T by adding all the T’s up inside the T. I got -56, -63 and -70 by adding all the numbers up inside the T. Then I realized that it went up in 7’s. I had to make an algebra equation to fit all of the T’s. I done 7 times the grid size to get the number after the 5T, so the equation is 5T – 7G.
My prediction was right, now I now that I can take a T out of any size grid and still get the end equation.
Using a Different Gridsize
If I where to do this on a 12 * 12 grid the equation would still be the same, you would get 5T – 7G. I can prove this by taking a T out of a 12*12 grid and adding up all the T’s then by adding up all the G’s.
= =
When I add all the T’s up I still get 5T and when I add all the G’s up I get 7G. The equation is still 5T – 7G.
Rotations
I did some T’s using rotation. I found out each T-Total and each T-Number. Then I did the algebra for the T’s. Here are my results:-
Algebra
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= 5T-56
In this T is equal to 20 so T – 8 is equal to 12.
= =5T+7
In this T is equal to 29 so T – 1 is equal to 30.
=5T+56
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In this T is equal to 36 so T + 8 is equal to 44.
=5T-7
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In this T is equal to 5 so T - 1 is equal to 12.
I found out a pattern that is when you rotate the T 180 you get the same number but with a different sign.
E.g.
=5T-56
Multiples
I drew a 10*10 grid going up in the two times table. I took a T out of the grid and then done the algebra for it. Here are my results:-
Algebra
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In this t is equal to 44 so 44 – 24 is equal to T – 20.
Then I did the equation using G for the grid size.
= =
In my equation I used G for the gridsize so T-20 is equal to T-2g because G is equal to 10 and 10 is the gridsize.
Then I put M into the algebra. M meaning multiple. I am using a multiple of 2 because that is what the grid was going up in.
= =
=
=
Multiples
I drew a 10*10 grid going up in the three times table. I took a T out of the grid and then done the algebra for it. Here are my results:-
Algebra
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In this T is equal to 75 so 75 – 45 is equal to T – 30.
Then I did the equation using G for the grid size.
= =
In my equation I used G for the gridsize so T-30 is equal to T-3g because G is equal to 10 and 10 is the gridsize.
Then I put M into the algebra. M meaning multiple. I am using a multiple of 3 because that is what the grid was going up in.
= =
=
I looked at both equations for the grids going up in 2’s & 3’sand found out a pattern. The pattern is that on the multiple equations it is the same for both of them apart from the number at the end. On the 2 equation it is + 2 & - 2 and on the 3 equation it is + 3 & - 3.
The equation here is 5T because I added all the T’s and then I got 7MG because I added up MG + 2MG + 2MG + 2MG. Therefore the equation is 5T – 7MG.
