Algebra 1 is really a class of insane growth for students, if you think about it. Most of them come into the class still pretty uncomfortable with the thought of ‘x’ and what it means, unable to solve a one or two step equation consistently.
They leave knowing how to solve quadratics and convert them to other forms. It’s crazy.
This year, I assigned my Algebra 1 students an end of year project to review and mesh together everything they learned about quadratics in the last quarter and a half of the year. This included:
- Solving by factoring
- Solving by completing the square
- Solving using the Quadratic Formula
- Rewriting functions in factored form
- Rewriting functions in vertex form
- Rewriting functions in standard form
- Graphing quadratics using key features like zeros, y-intercept, axis of symmetry, and the vertex
Each of them was assigned a different quadratic equation and directed to do that entire list of things with it. It was a very hard task for some of them, but it also helped them realize how much they’d learned this year. Working on the projects was a really good review for their final exams next week, since it reminded them of some things we hadn’t done in awhile. They also ended up working with quadratics that didn’t necessarily have “nice looking” (I hate that term) solutions which always makes them slightly uncomfortable.
The finished products look really great on the bulletin board outside my classroom! (Along with my “ways to be mathematically smart” poster that I stole from someone on twitter that I can’t remember!)
The one that’s a different color from everyone else’s was my example so they could figure out which work they were supposed to show on the poster.
After everyone finished, I had them complete a scavenger hunt to find quadratics that had certain features: a negative axis of symmetry, for example. This ended up generating a TON of really awesome math conversation. I stood there listening to them have this discussion on the last Friday of the school year, during a shortened schedule, using vocabulary terms and pointing out examples to each other, and kind of got a little choked up. A group of them even were trying to see if they could all get different examples for each task from each other! It was pretty amazing to listen to them and think back to when they couldn’t solve a one step equation in August.
Files for the project prompt and a rubric for grading that I used are here. Also, files for cards for each quadratic that the students chose are here. I cut these out and had them draw one out of a bag. I completely randomized level of difficulty but you could separate them into levels of difficulty and have certain students draw from separate bags.