# The mathematical key

I gave my first official quiz today in my Algebra II class. Since so many of my students have 50% extra time accommodations, I designed a 30-35 minute quiz and let the class take the entire 50 minutes. Usually there are a number of students who finish early.

Before students turn in their quiz, I tend to say “are you absolutely, absolutely sure you want to turn this in? Once it’s in my hands, I won’t hand it back, and it tends to be exactly 1 second after students hand in a quiz that they realized they made a mistake and want to check over the test again.” Except for those with some sense of usually false bravado, they wisely go back and check over their work.

But I’ve come up with a good way to keep students occupied once they’ve finished their test. I put up a problem — somewhat based on what we’ve been doing but *just* different enough that students will be forced to make a new conceptual leap on their own. If they show me the right answer, with correct work, I let them leave class a few minutes early. A luxury, for sure. The solution to the problem becomes their key out of my class.

Today in Algebra II, we had a quiz that covered — among other topics — inequalities. Students learned simple linear inequalities and how to solve them. So, for the challenge problem, I put:

Find and write in interval notation where: $x^2+4x+3 \leq 0$.

Two of them got it. Most of the rest of the class wanted to get it. I liked them thinking about problems that are just beyond what we’ve done.