I taught Algebra II students how to factor quadratics in the form x2 + bx + c, ax2 + bx + c, difference of two squares, and perfect square trinomials with some GCFs thrown in for good measure.

But in the end, I wanted to convince myself that they really learned the difference between each type. I wanted some kind of sorting activity where students had to analyze the problem for which type and then solve. I couldn't really find what I had in mind so ta-da!

I made up 35 problems, seven groups of 5 problems each (with symbols on each to check their answers), and printed them on card stock.

Students cut them up and sorted them into the four main categories without GCFs first. Here are two different flow charts I made to help them. The second one seemed to work better.

Once they had those four groups, I told them that there should be five in each group. That prompted some rearranging. Then I gave them the correct symbols for those four groups. That's 20 problems out of the way.

Now students are left with 15 pieces that all have GCFs. So they had to divide the GCF out of each problem and see which of the original four groups the remaining problem fit with.

Once the last three groups are sorted, I again gave the correct symbols so they could check their answers.

Then they had to actually write down the problems in the correct category on this worksheet and solve.

This can take anywhere from 3-4 class periods depending on how much you are willing to let the students struggle. But they practice telling the different types and then actually working 35 problems.

All files can be found below.