For the lesson on distance formula, I start out by using Dan Meyer's Taco Cart to get students thinking about the Pythagorean Theorem. I always like to talk to them about why the Pythagorean Theorem works and show them at least one proof, because they rarely get that experience. My handout is here.
After we have some good discussion about the Pythagorean Theorem and they are amazed at the proof, I proceeded to show them the connection between the pythagorean theorem and the distance formula. We practiced a little bit and then we were ready for some fun.
This year, I decided to give them a taste of a STEM application and do the Barbie Zipline activity that @JStevens009 described in his blog. I gave the students the initial information that we would be zip-lining from the top of the bleachers (30 ft high). This was their starting point (0, 30). Our zipline would attach at the top of the bleachers and then down to the top of a yard stick. They had to then determine the ending point (?, 3) that would provide Barbie with a safe and fun journey. I required them to show their work using the distance formula.
Initial whiteboard brainstorming:
I had them finalize their work and hand it in. Then we went out to do the zipline. Unfortunately, only 4 groups out of 11 had a successful zipline experience. It was so cool for those groups. The other groups had designed ziplines that were too long and their Barbies got stuck in the middle. I think this had to do with the fact that we didn't spend enough time in class discussing what type of zipline might have the best design. I will definitely incorporate that into my initial discussions for next year and lead them into discussing the fact that they really need to pay attention to the steepness (or slope) of their zipline.
This prompted me to change the way that I wrapped up the lesson. Instead of calculating each group's speed and having a discussion about which group provided the best zipline experience as I had originally planned, we had a great discussion in class about what went wrong in the designs that didn't work and how to make this a better project for next year. I LOVED the insights that the class gave. They picked up very quickly on the fact that the zipline design needed to include a limit on the length of zipline (possible less than 100 ft), that the slope needed to be a certain "steepness", and that perhaps the location could have been a bit different (we had one barbie run into the rail at the bottom of the bleachers during her descent). We also talked a little about the physics application of G-Force that we could possibly calculate.
So, this didn't go as planned, but I think I met my goal overall of giving them a fun and exciting application of the distance formula while getting them to think about design flaws in the experiment.
