My students have had a really tough time with factoring this year. It's definitely been a different group than in years past, but I haven't been able to put a finger on the problem. If I give them a context (ie. perfect square trinomial, difference of two squares, etc.), then they do fine, but when we got into simplifying polynomial fractions, the wheels fell off.
It became pretty clear that my students were not very good at identifying what they were up against. Are we factoring monomials, binomials or trinomials? Do I use distributive property, diamond problems or "bottom's up?"
You have to know what you're dealing with before you can pick a strategy to defeat it.
So I put on my cool shoes, gave a few hugs and went with the ELA approach:
I'm already noticing that identifying the opponent and choosing the strategy has helped with simplifying poly fractions. Let's hope it sticks.