This week, Paula Torres (@lohstorres1) and I were asked by Chris Duran (@chrduran) to work with his team on developing a Lesson Study. The idea of a Lesson Study has been floated around at our sites for a while and has always been pushed to the side for a number of reasons. Because of that, I was happy to see us get the chance to meet and work through the process.

One of the first tasks was to set an objective for the lesson, which became a conversation about the Standards for Mathematical Practice (SMPs). This is a far cry from our normal planning days, especially because the norm is to plan lessonS and not spend an entire day honing in on the learning of a singular lesson.

​As we were trying to determine which SMP we should use as the focus for the lesson, I put it out to Twitter because, you know, I like the Twitter-ers. If you had to pick one SMP to focus on, which would you choose and why?

For me, to nobody's surprise, SMP 3 is the one I would like to direct my focus. If I can construct a viable argument and critique the reasoning of others, I am in a better position to have a discussion about mathematics and can navigate the other SMPs easier. Sure, each have their unique value, but I'm a huge fan of #3.

This is the one that we decided on as a team as well.

Coming to an agreement on the focus SMP was only the first piece of the Lesson Study, but it was an important one. Using that as a launching point, we picked a date that would work and agreed to build a lesson around quadratic functions for an Integrated II class. Paula led a thoughtful conversation about the transition and relationship between standard form, vertex form, and the graph of a quadratic. No surprise there; she's been in the classroom for over thirty years and always finds ways to improve. Speaking for myself and implying for others, the surprise was that we hadn't thought of it before. 

We teach each of those concepts in isolation, but Paula really found a way to tie everything together. That is a big benefit of the Lesson Study model: getting the chance to discuss why and how we teach, not only the what.

Even though we worked around the mental map a little, building the entree first, it was good to see where we wanted the students to go and the conversations we expected them to have. When one of the team members offered up a two-problem set as a warm-up, I tossed out the idea of showing a quadratic on a Desmos graph and having the students discuss it. Or, another person mentioned, we could do a Which One Doesn't Belong with them.

Wait, what's that?

Hook: set.

We talked about WODB for a bit and the value in beginning class with a discussion versus a problem set. A week prior, I was sharing the idea of starting class with a conversation at CUE, and now the Lesson Study group was doing the same thing. SCORE.

Because I wanted to be useful (my role was primarily to share resources), I built a thing:

Link to the GIF. Feel free to use it.

Although the team wound up choosing a static WODB from the site, I was happy to see that they were interested in what I had created and ideas sprouted from it. To them, there is too much going on with the GIF, especially as a first time seeing quadratics in this sort of relationship.

Copious conversations will naturally lead to the day flying by, and that's exactly what happened. We didn't get the chance to complete the fine details of the lesson, but we got really close. More importantly, admissions were made about room for growth, strategies were shared about engaging students, and doors were opened to collaboration within the team. 

You can teach by yourself, or you can build a movement as a team. This group chose the latter and I think it will prove successful.

Oh, and Paula and I built an extension activity with quadratics in Desmos Activity Builder. Check it out and let me know what you would like to see changed. Overall, this was one of the best days of preparing a lesson I have ever been a part of.

I'll update this (or write a new post) when we get to the lesson, along with sharing the student conversations, the engagement level, and the curiosity that is drawn out. This should be fun.

Happy "Amazing Lesson Prep" Fishing

Folder with all planning documents and handouts that I used.
Desmos Activity Builder (thanks to Andrew Stadel for helping to make it better)
Reflections from the previous year.
Reflections from my first year.
Collection of all reflections.

As I watched Ms. Burt's students fly kites and determine angles of elevation, the itch started to return. It had been nearly a year since anyone had asked, and I had no way of doing it unless someone did. But then... it happened.

"Would you want to come and do Barbie Zipline with my students?"

Why yes, yes I would. 

"Hey, could Ms. Miller and my class do it, too?" asked Mr. Flores. 

​Yes. Ohhhhhhhhh yes.

A week before I came in, all three teachers started to build hype within their classes. Things like "next week, you're going to go Barbie Ziplining" came up and students were asked to bring in dolls or small objects that they could send ziplining. 

"Why?!"

"You'll see. Just trust me; it'll be worth it."

On the logistics side, Ms. Burt had already taught Pythagorean Theorem and Angle of Elevation in her Integrated Math-II class and the Miller-Flores combo had already taught Pythagorean Theorem in their Integrated Math I Tutorial classes. Academically, the students were prepped.

Ms. Burt checked with the football coach to make sure we could use the football field for the day, and outside of a strange look when the request to "use the field for Barbie Zipline" came through, there were no issues. After all, he was just as curious as the students.

This year, I wanted to bring in a bit more technology and flow to the lesson, so the entire story of Barbie Zipline was put into a Desmos Activity Builder, which you are free to take and make a copy of to make it work for your students. Because of how wild it was, I had to use this video as the appetizer:

The appetizer rolled right into the entree, which is another smooth positive of using Desmos Activity Builder.

On a programming note, I chose to use the Teacher Pacing feature of Activity Builder, just so I could control a bit more of the narrative. This lesson relies on the story just as much as the mathematics, so I wanted to make sure the students all understood the entirety of what was happening.

First, we had to make my mom and wife happy before I went ziplining, so the students drew a "really safe" line.

Next, we had to make my dad, the thrill-seeking adventurer, happy before I went ziplining on this Vegas Slot Machine Insanity, so the students drew a "really fun" line.

Some silliness ensued, but there were a lot of really good conversations. OK, now that we know it has to make both parties happy, what would be a safe and​ fun line?

Once students had their parameters, it was time to do the graphing and the math behind it. I had given them some boundaries for their numbers, but let them explore the best set of data to use for their trial run. 

To help you understand this, the top of the bleachers is 26 feet off the ground and the bleachers extend out 60 feet horizontally. Therefore, I gave the students bounds of 26 to 34 feet of starting height, 60 to 150 feet of horizontal distance, and 0 to 8 feet of ending height. 

They graphed the desired path, then found the amount of line that would be needed (Pythagorean Theorem or Distance Formula) and the Angle of Elevation.

Mixed in all of this math were some very good commentary:

The students completed the Day 1 activity in class, finished up any loose ends at home, and had their pink paper ready to go for Day 2... Ziplining Day.

While I was doing the instruction for Day 1, Ms. Burt, Ms. Miller, and Mr. Flores went around and had each student who needed a job write down what they were responsible for doing. They also numbered off each group, something I hadn't done the first few times through this lesson. But today was ziplining day.

When students arrived, I checked with each person who had a job to make sure they knew what they were doing and that they were ready:

• Runners had comfy shoes on
• Photographers and videographers were taking their pictures and video in landscape mode--NO VERTICAL VIDEO!
• Timers had a smart phone and knew how to use the stopwatch
• Deckhand knew how to work the pulley and carabiner 
• Finish line anchor knew how to hold the bat and the line
• Line holder knew that the job was pretty lame, but that he/she would be holding the line tight when we needed it and let it sag when we didn't
• Documentarians knew what they were writing down

Once everyone was briefed, each group had their representative tied up with a lanyard. My only request/requirement was that they didn't tie the lanyard around the object's throat. Even if it's a stuffed animal, I don't like seeing something hanging by its neck, so I joked about keeping their object safe by designing a harness.

We good? Let's GO OUTSIDE!!!

As nature would have it, the day we go outside was the hottest out of this whole 2017, up to that day; go figure. I had applied sunscreen and wore comfortable clothing, but nothing changes the fact that I was standing on metal bleachers all day.

We tested each group's parameters, one at a time, for a total of 10-12 trials per class period. Everyone did their job the way they were supposed to, nobody got hurt, and some Barbies had fun, while others died.

We made our way back to the classroom where the final question was posed:

Let's say this company in Las Vegas approached you and said they wanted a 3,000 foot zipline. You can't hand them a cute drawing and expect a contract, so based on your data, what would be a good starting and ending height? Why?

This is a piece of closure I hadn't done in years past, so I'm happy to know that there was something the students were doing with the data, rather than ending the lesson and moving on.

Even though this is not the first time, or second time, doing the lesson, I keep finding ways to improve what we are doing. If students are going to truly enjoy the experience of Barbie Zipline, it needs to be airtight. Here is what I would like to change for next year:

• Find a new variable for the horizontal distance. "Kids these days" went and ruined the variable D for everything in math. No longer can I ask a class full of teenagers to "find the D" in the problem or tell them that "a longer D is not necessarily going to be more fun"... GAH!
• Re-visit the Activity Builder lesson. It was good, but I want it to be GREAT. Not sure how I can do that right now, but it'll get adjusted before the next time I do this.
• Bring in my own dolls. I'm hesitant on this because I want students to have ownership of the object that gets flung down 170 feet of fishing line, but some students were bringing in objects that were just too light. If I can control that and keep it consistent, I think we would get better data.
• Put a smaller cap on the maximum distance the zipline can travel. Students naturally think that the longer the line, the more fun it will be. The truth is that fishing line is very elastic, and having that much of it out there means that there is a lot of stretch. Keeping the upper bound to 120 feet instead of 150 would mean more students seeing their representative have fun and not just play it safe.
• Check with all parties to ensure the space we are using is clear. As I had mentioned, the football coach was made aware, but we forgot to ask the PE teachers and the track coach if the track was going to be used. Oops. We had to change a couple of the dimensions to make sure PE students didn't get tripped up by nearly-invisible fishing line and that's no fun.

Overall, it was an amazing two days. I'm exhausted, my feet hurt, and my voice is almost gone, and I wouldn't have it any other way.

Happy "Zipline" Fishing