@tnorman1236 I cruised through school the whole way, doing very little other than listen, and sometimes amusing myself by trying to prove something by an alternative method.
A prime example is in how to convert degrees Centigrade to degrees Fahrenheit. I was taught to divide the number by 5, then multiply it by 9 and then add 32, which is how almost the whole world does it. Initially, I realised that multiplying by 9 and then dividing by 5 was actually multiplying by 1.8, and there's an easy way to do that in your head. Double it and knock off 10%. eg. 12 degrees doubled is 24, less 10% (one tenth) makes 24 minus 2.4 which is 21.6. Easy! Now all I needed to do was add 32, to get an answer of 53.6 degrees Fahrenheit. But my amusement continued. Since minus 40 Centigrade equals minus 40 Fahrenheit, all we have to do is add 40 to bring both numbers to zero. So if I added 40 to 12 degrees Centigrade, I got 52, which doubled made 104 degrees. One tenth of that is 10.4, so subtract 10.4 from 104 and I got 93.6 degrees Fahrenheit. Now subtract the 40 so that the two scales again crossed over at minus 40 and there was my answer, worked out in my head - 53.6 degrees. The beauty is that it works exactly the same way for converting Fahrenheit to Centigrade, provided you divide by 1.8 instead of multiplying. When I proudly used this on a test, my maths teacher said my method was an approximation, which just luckily gave the correct answer for that particular question. I disagreed and the maths teacher gave me zero marks. Two days later, he apologised. He had been sounding off in the staff common room, when my physics teacher burst out in delight at my logic and explained that this method was 100 percent accurate and valid.
However, he advised me to still show my workings in the slow, traditional way for exams!
However, the add 40, multiply or divide by 1.8, subtract 40 method is much easier to programme for a computer.