Reblog - PUHSD #MathChat 1: Quadratic Catapults

8:00 AM

Original Author - Jedidiah Butler:

Simple enough task;  make the ball land in the basket.

The task had to be simple so that we could get over 2000 students to participate.  We started small, and eventually involved all three of the comprehensive high schools in the Perris Union High School District, with a repeat visit to Perris High School.
This article is reposted with permission from Mr. Jedidiah Butler, the PUHSD Math Coach Teacher on Special Assignment. The original post can be found on his blog "Math Butler Blog"
Here's the summary of what happened.

Our STEM specialist Josh and I put together a single-period, hands-on activity that would engage students with mathematical modeling.

Attempt 1

When people think of quadratics, the hands on project that comes to mind seems to be projectile launching and falling.  With that in mind, Josh prepped the activity.

Josh did a first run with this activity in Princess Choi's classroom with Integrated Math 2 students. Ms. Choi has proven herself to be a teacher that takes chances and tries new things if they have promise to support and engage her students .  Without her, this activity would have probably never got past the planning stages.

Materials

The tools given to students  included:


Directions

First, students were shown how to use a catapult.  The catapults were made of expensive plastic, and used a program to launch it. The program was simple but not very intuitive for first time users.

Tasks


  1. Launch a ball on the floor and Find the typical distance and maximum height. 
  2. Launch off a table and make a basket.


Once the demo was finished, students gathered into groups and started running trials and taking measurements.  While students were running the activity, each group quickly realized that group work and collaboration were required to make this work.  It would take more than 1 student to launch the ball, measure the distance, measure the height, and retrieve the ball.  Some managed with just 3 in the group, but most were more comfortable with 4.
Ms. Choi, Josh, and myself facilitated the groups by asking questions on what they were doing, how well it was working, and if a more effective alternate method was possible.

Teacher: "What are you trying to do here?"
Student: "Measure the distance."
Teacher: "Which distance?"
Student: "The ground, to where it lands, oh and the height too."
Teacher: "So you're getting 2 measurements then?"

Conversations like this were abundant during the activity.  Pushing the students to articulate the process and reasoning to go with it was just as valuable as the typical math content.

Students were also given a worksheet to document their process.  I'd like to add that this worksheet was the first iteration and we improved significantly on it for the second round.

The shot for the basket

Time flew by and the bell crept up too quickly.  Students and facilitators were engaged to a point where time was merely an afterthought.  They saw that math can be more than just numbers. Students leaving didn't want to go and incoming students rushed to class once they  heard about the activity.

Even with this success of engaging the students, there were improvements to be made.  The directions needed simplifying and the supplemental worksheet needed more depth. Word spread quickly about this activity and more teachers and students wanted to try it out.  So we did.  In a really big way.

Amp It Up

Our first run had roughly 2-3 total classes with only 1 class at a time.  As interest grew, it looked like we would be doing the event for a full day with up to 3 classes running at the same time.  That was just the first round of follow up with Perris High.  The group was so big that we had to request use of the multi-purpose room for a full day.

We learned from the previous experience that the goal needed to be as simple as possible.  We focused on the second task only:

Make the ball go in the basket

There was a few conditions though.  The students had to launch it from the stage down to the floor and they only got 1 attempt at making the shot.  That's correct, only one shot for the basket.  As some felt immediately put off by a 1 shot deal, we clarified that there was more to it.  The students could have as many attempts as they wanted from the ground.  So practice was key.
Some questioned that shots from the ground were not going to be the same as shots from the platform.  This was the teachable moment.  The learning that an educator wants a student to realize from this experience is what happens when you change the height from which the ball is launched?  Does a projectile travel further, the same, or a shorter distance when launched higher?  It was odd to me that this was not intuitive for the students at first, only adding value and purpose to why we were doing such an activity.

Managing a room, maintaining Focus

The teachers for each of these classes were invaluable in managing a room with 100-120 students. To help keep the students on track with achieving the task of making the ball in the basket, I gave them 2 words to focus on: precise and consistent.

This gave us just enough structure to guide the actions and behaviors of the students as needed.  To be precise, the students needed to be particular with their measuring, not just guessing.  To be consistent, it wasn't enough to just do the practice once or even a few times. These words may be redundant, but for our students it proved as a valuable guide.

Students were given similar tools as before and had to apply some problem solving to figure out how to best use the tools.  For example, each group was only given 1 yard stick, yet they had to measure the height and distance for their trials.

Upgrades



 The worksheet was redone to match current standards, incorporate multiple representations of the experience, and extend the understanding to apply the concept in a new situation.

Our district has students working 1:1 with Chromebooks.  To capitalize on that opportunity we had the new worksheet available digitally and an interactive Desmos Graph.  Some used these options while others stuck to their physical resources.  However the students completed the task, they were engaged, happy, and maintained high standards in their work throughout.  They did all of this while learning and applying the math from their class.  All 2000+ of them.


Who knew that shooting a little ball into a little basket could mean so much.

As we finished with the last class during the last period on the last day of the activity, Josh and I were exhausted.  It was enlightening to think how we finished compared to how we started.  The experience of having to scale it up for the masses forced us to look at the core concepts in the exploration.  The evolution of the supplemental material was also honed down to the essentials.  There was enough for the students to develop an understanding of the model through a few different representations, but any unnecessary tasks/prompts were whittled away.  The conversations that students had with peers and with teachers were what made this activity successful.  This activity was more than just practice on paper.  It was ScholarPlus.