Day 35: What’s Your Sign?

Using a sign chart is a visual way to pull together a lot of the concepts and processes related to polynomial and rational function!!  I love how my students are like fish to water when we get to this topic.  We have discussed, dissected and clarified the ideas so much that when we use them in a more abstract way, they rarely have difficulties.

Opener: For which intervals is the graph of   positive?  Increasing?  How is finding the answer to each of these questions similar and different?  How could you answer these questions without using your calculator to look at the graph?  Or without looking at a graph?

I used the opener to introduce the idea of a sign chart. First of all, it was a nice review of factoring a cubic function.  It was also really interesting to compare the words positive vs. increasing…typically confused when students haven’t been given the time to really think about what each word means.

The one question: “Did anybody do it differently” opens up so much conversation, and regrettably, I don’t ask it every day because of the constraints of the curriculum.  But when I do, I end up with great insights into the variety of ways problems can be solved.  My classes continue to amaze me with the different ways they think about problems and I leave class with a big goofy grin on my face!!