Friday, June 20, 2014

Culminating Project: Quadratics Toss!

While the Scavenger Hunt took up the majority of the time we had devoted to our culminating project this year, it wasn't a true culmination as it left out one of our units: Introduction to Quadratics (our partner class wasn't able to fully cover the unit, so it was omitted from the scavenger hunts we created for each other).

I was so incredibly fortunate to have an amazing peer teacher in class with us this semester. She was a tremendous help both in terms of helping the students with their work, as well as keeping the class organized (exit slips and the tracking board became her domain!). 

She made anchor charts, marked quizzes, organized hands-on activities (she was the only one who knew the answers to our What's in the Bag? activity, since she made up the bags!), and so much more, all while being there for the students by giving them feedback and keeping them on track. She is an incredible young woman, and I am grateful for all the time and effort she chose to put into our class. 

As we approached the end of the semester, she was tasked with the job of brainstorming an appropriate quadratics project. The resulting activity is pretty much her idea, with a couple of tweaks.


The Quadratics Toss!

As a 1-2 day activity, my MFM2P (grade 10 applied math class) was asked to model the trajectory of a bean bag as it was tossed from one side of a tennis court to the other. (Click here to see the project instruction sheet.)

In short, students had to:
  • sketch what the bean bag toss would look like;
  • after some practice, gently toss a bean bag over the tennis net to hit a target;
  • measure the range from bean bag launch to landing;
  • measure/calculate the height of the beanbag at its highest point;
  • model the trajectory using Desmos.

The idea of going outside and throwing bean bags was enough to get everyone excited! As a class, we brainstormed what the sketch would look like, and hung our parabola anchor charts from earlier in the school year back up. Students came up with a plan for taking their measurements, and then out we went.




Once we got to the tennis courts, we agreed upon a range for the launch: from centreline to centreline over the net. After a couple of trial runs, students started measuring what they needed before sitting off to the side in the shade (it was a perfect, sunny day!) to add the information to their sketches.


Added Bonus

While this activity was only designed to address topics from our quadratics unit, without anticipating it, students made use of a couple of other learning goals from different units. 

They found themselves taking measurements and making conversions (unit 5), as well as measuring height using trigonometric ratios (unit 6). It was great seeing the students comfortably manage these other topics without much review, and explain to each other how they could use these concepts to complete the project.


Technology?

I love that even though this was a very hands-on, kinaesthetic, get-out-and-run-around kind of activity, we were still able to make use of the BYOD technology at our disposal to model the pathway of the bean bag. To measure height of the bean bag, students used either the SmartMeasure app on the tablets, or a clinometer app to measure the angle of inclination and then later calculate the height.

Some students, who measured one distance in feet and another in metres, used a unit conversion app to make sure every measurement was either metric or imperial.

Back in the classroom, we used laptops and tablets to graph the bean bag's motion from one side of the net to the other on Desmos. The 2:1 ratio of students to device worked well with students naturally coaching each other while creating the graph. It was our first time using Desmos in this class, so there was a lot of trial and error, but the students quickly got the hang of it. They were meticulous when it came to getting the exact height, to the point of cheering aloud when they got it dead on! 




I really liked how this activity got the students up out of their seats, was exciting for them, and yet served as a great review of some of the quadratic concepts we had covered. They enjoyed the challenge, but never felt it was too hard or beyond them. 

This worked so well, that I would definitely do this activity again. With more time allocated, we could also take into consideration the height of the person throwing the bean bag (making our equation a little more accurate), and get the students to document the toss digitally (Skitch?). One of the students even suggested that they could build their own catapult, and then figure out the path of the bean bag! That's exactly the kind of engagement I'm looking for. :)

1 comment:

  1. Great! I just create an exercise for my students (at the bottom of this page http://www.matemticasparatodos.com/materiales.html). They needed to score a goal, making the ball pass over the first point and through the second. I utilized Desmos to visualize the trajectories. The link to all the graphs is at the end.

    Nice blog!

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