Posted in Math II, Quadratics

My undying love for Desmos

For the past two years, I’ve been out of the classroom working as the high school math specialist for my district, so I’ve been totally jealous of everyone using Desmos classroom activities with students. I’ve presented trainings on how to use Desmos classroom activities and Activity Builder; I use the Desmos app on my phone every day; I bug my teachers to use Desmos at every opportunity; I am convinced it’s the most powerful math learning tool there is; I just haven’t gotten to use it with my own students … Until now. And it was every bit as glorious as I thought it would be.

First up: Marbleslides Parabolas. I have never seen students so intent on a problem in math class before. I mean, I know the students find me FASCINATING and everything, but seriously, the amount of learning going on in the room was amazing. I started taking pictures and they didn’t even notice! I set students up in pairs on chrome books and let them go. I was a little afraid that students would start changing numbers randomly without paying attention to the cause and effect, but from every pair I heard some version of “change that number so we can move it over to the left.”

Only a couple of sticking points: I know it shouldn’t, but it still surprises me that students weren’t willing to just hit the “Launch” button and watch what happened; they were trying to get each graph perfect before launching. I need to work on growth mindset with this group. This population struggles with the need to look “smart” in front of their classmates and aren’t willing to put themselves out there if it means being wrong. Additionally some groups got hung up on the domain; they wanted to “move the parabola to the right more” when they really meant that they wanted to change the domain. It took a lot of questioning to coach them to see how the domain restrictions were affecting the graph.

Next day, we followed up with another Desmos activity, Quadratic Transformations, that I borrowed generously from Mary Bourassa‘s Quadratic Transformations part 1 and part 2. Basically I loved her activities and wanted to condense them down to one day to solidify what we had learned from Marbleslides the day before. Students were engaged and thinking deeply, and they were able to apply what they learned to graphing and writing equations in vertex form the following day.

As a teacher, I never sit still while students are working (actually u have trouble sitting still no matter what… ADHD anyone?). I love hearing students’ conversations, seeing what they’re doing, and challenging their thinking (read: bothering them). So I walked around the classroom as they worked and didn’t really take advantage of the teacher dashboard. I think that’s going to take me some time to get used to. Maybe if I accessed the teacher dashboard on my iPad, I could still walk around the room and feel comfortable doing so. Does anyone have any tips for using the teacher dashboard effectively?

I’m looking forward to my next Desmos activities; I have two planned for next month: Building Polynomials #1 and Roots of Quadratic Functions: Looking for Special Cases.

I love my husband. I love my two daughters. I love my friends and my colleagues and my students. And I love Desmos.

Posted in Math II, Quadratics

My favorite lessons so far

Wow, I forgot how busy working both jobs is! Blogging every day has taken a backseat to grading homework, creating assessments, math placement, data analysis, meetings, answering emails, first weeks of school minutiae at the school site and district level… Oh yeah, and then actually having a life outside of work. I want to make a commitment to blogging, though, so that becomes a natural part of my reflective process.

So what have my students been up to? We’ve been learning about quadratic functions in multiple representations, key features of parabolas, and transformations of quadratics. Right now we’re wrapping up our first unit after doing some really great learning tasks.

Last week students worked on What are the connections, a task borrowed from CPM’s Core Connections Integrated II. The situation is a water balloon toss where different data is given: first an equation, then a graph; then (oh no!) the water balloon hits your computer and you only have time to scribble down some data points in a table before it fizzles out; then (since your computer is broken) you have to do the final measurements by hand, so you only get the launch point, the maximum height, and the point where the water balloon lands on the ground. They have to graph and compare the parabolas given the different representations. This task had students working in teams in a way they hadn’t before. They were asking questions, verifying their work, saying things like, “the function has the same values for x=8 and x=9, so the axis of symmetry must be x=8.5!” The follow-up questions had to do with the domain, range, intercepts, and vertex in context of the situation. They learned so much from this one task about the shape and key features of a parabola, not to mention the valuable skills of working together as a team. This is a must-do for all Math II (or Algebra 1) classes!

We spent a few days working on vocabulary, interval notation, and sketching parabolas given key features. Then we spent a day working on this application, Yearbook Sales, that I created. I ended up extending the task to two days because I loved how the students were working on it in teams. The situation: students have to find the best price of the yearbook, given that for every $5 increase in price, 20 fewer students would buy the yearbook. I was hoping for them to apply everything we had learned so far: connecting multiple representations (table, graph, equation), writing an equation for a quadratic equation given a situation, understanding the meaning of key features (intercepts, vertex).

What I loved most about this task was the arguing! I went to check on progress at one table, where two girls were really running the show, leaving their other teammate to his own devices. The girls explained their reasoning: they had written two linear functions (one for the price of the yearbook and one for the number of students purchasing the yearbook), and when they multiplied the two together to get the total profit, they thought that the two values should be as close together as possible to maximize their profit. Then their teammate asked, “so how much was the total amount of money?” and they responded confidently, “about $10,000.” Their teammate looked a little puzzled, then said, “but I found a way to get $15,000.” The girls’ heads snapped toward him, “Whaaaaaa…?” and I just backed away. It was perfect. I didn’t even have to challenge their thinking because their teammate did, and it got them working collaboratively toward an improved solution. After a successful day of work on this task, I gave students additional time the next day to complete a final draft of their solutions with questions to help guide their thinking.

We also spent a couple of fabulous days playing Marbleslides and transforming quadratics, but I’ll profess my undying love for Desmos classroom activities another day.