Another updated lesson from yesteryear enriched by Desmos and years of me tinkering around figuring out what I'm doing. This time, polynomials.

When I taught Algebra II, we spent some time with polynomials: identifying real roots and coming up with possible expressions. It was pretty scripted. I came up with the pictures, distributed a set, had the students pick a couple, copy a paragraph and fill in the blanks for their picture. It looked like this (circa 2012):

Being smarter about this sort of thing now, I removed the script and put the design requirements in the hands of the students. Using Desmos, they were to create a series of 4 polynomials (3rd+ degree with at least one 5th degree) and tell me about them. Two went in their notebook and two went on the wall.

Great products and great discussion along the way. Students also got to play around with scale factors, the secret sauce for making any polynomial graph remotely useful. Prior to this activity we talked about hand sketching the graphs and tried a few. Later on the relevant assessment, I reversed the idea to see if they could work backwards:

Questions like this teach me to trust the students more. Previously I'd fret about asking this sort of thing without explicitly talking about it (the point of the old version of my activity). But if you really want an assessment to do its job, you see what a student can do on the fly with the introductory pieces you have provided.