Quadratic Functions project

Thanks to @SweenWSweens and his M&M Catapult Project (explained here and here and updated here), we are ending the quadratic functions unit in my 10th grade class with a bang. Well, a whooooosh, but you know what I mean. Kids had a ton of fun with this activity and it gave great practice for writing and solving quadratic equations. The basic idea (but really, you should check out Sean's posts) is that groups launch an M&M and measure the horizontal distance traveled and approximate the vertical distance traveled by using the time, putting this together to create a quadratic function that models this relationship. Then, they apply this model when the launcher is placed a given height above the ground to figure out where to place a target.

First of all, Sean was super helpful, walking me through the lab and giving me great tips on how to adapt it for my students. Love that #MTBoS. My project description and follow-up questions are here.

Here are the changes that I made to Sean's awesome plans and why:

1. I let kids build their own launchers. I shared Sean's basic design (pictured at right), but let them tweak it or do their own thing altogether. It actually took kids only about 20 minutes using our engineering lab, which had all of the supplies already, except for clothespins, as opposed to the few hours I would have spent making all of them and then dealing with kid complaints that their launcher wasn't good. Next time, I will do this again, but will also share Sean's updated design, which I did not see in time (below).

Here is what my kids built (most just did the basic design, a few went nuts and did their own thing):







2. Little direction was provided about lab technique or how to find the equation relating the height vs. horizontal distance. We did discuss the equation relating vertical distance traveled and falling time, but next year, I will do a better job of integrating this concept into earlier problems so that students can generate this idea themselves. What I liked as a result of giving less structure:
• Students incorporated other topics, which I did not anticipate. A few groups did statistical analysis to look for outlier data, which was awesome since that was a concept learned way back in September. Others compared lab protocols from different science classes and their applicability to this project.
• There was much more variety in approaches, which allowed for richer discussions within and between groups and more connections made. Some groups used the vertex, some used intercepts, and others used quadratic regression on desmos to generate equations. There was likewise diversity in how to change the model to incorporate the new starting height for the final launch. 
• The intellectual rigor was higher - students had to figure out what to do and then for their write-up, remember and reflect on their approach.
3. I used some class time after the activity for groups to whiteboard their approaches and then share out with the class and get feedback on their thinking. I also used 15 minutes the day that the write-ups were due for students to peer edit each other's work. The goal was to have more cross-pollination of ideas and connections made, as well as a chance to justify their own and critique each other's reasoning. I'm hoping that this also helped to produce higher quality final products and deeper understanding. Next year, I hope to run a more structured peer-editing process with specific questions for students to address.
4. More individual accountability - students were asked to divvy up points to their group members and describe each person's contributions as well as complete individual follow-up questions. I need to think about this more to see if I think this overall contributed to students' learning and experience with this project and helped or hurt their collaboration.

And now, more pictures!!

Building the launchers:

Gathering data:

Final launch day:

A few student whiteboards:

Once again, huge thanks and shoutout to Sean for creating this!! it ended up being a great project for this unit. Students had a blast, but were also appropriately challenged. 

Feedback from students: