This year in Accelerated Algebra 2, I decided to make new assignment sheets. My assignment sheets are 10 questions long and assigned once every 7 day cycle. They are collected and graded and can be on any material. I do these to keep the math discussion going outside of the classroom and outside of what we are working on at the moment. I got these new problems from SAT, ACT, and math team questions. I don't remember where this particular problem came from, but it has been one of my favorites so far:
In class, we have not done recursive functions yet, but we have done function notation. This really checks their understanding. They think they start to figure it out and do f(2) but then they just use "2" for f(2). They also want to try to find a shortcut to get to f(10). I explain that they need to use the previous answer to get the next answer, so they cannot skip it.
Give it a try. I like it.