If you suspect that the whole triangle is a 45-45-90 (which does turn out to be true) that also gives some test Polynomials you can divide out and see if there is a remainder.
Apropos of nothing in particular: My model of learning is that more knowledge/instruction can never hurt and usually helps. I need solid evidence and some sort of working thesis to change my mind.
blog.mathoffthegrid.com/2019…
I also went back. To this problem a few years back and blogged about it.
I tend to work in small spurts in the evening rather than one long block.
From time to time I have posted videos on YouTube of myself solving maths problems in real time. Here are some more, with the difference that they are six videos all devoted to the same problem, with a total length of around five hours. 1/
youtube.com/watch?v=fl4xw829…
Formulas are useful for reducing computational load when doing the same calculation but they also make it easier to extend the learning. If you continually have to go back to first principles for everything, you rarely can move beyond.
Math teachers: I’d love opinions on this.
I didn’t teach my kids an explicit formula for permutations or combinations this year. We used logic to find the solutions and looked for patterns.
Should I being showing them the explicit formulas? #mtbos#iteachmath