Evolution of a Lesson

It started at our Department Chair meeting.  DCs had time to work together to plan a lesson together.  One group called me over because they were looking for ways to get students to understand two-variable inequalities.  Some of the specific difficulties were that students were having difficulty deciding what 0 < 2 implied about the graph and also trouble understanding WHY the graph of a inequality was shaded.  I suggested that a thin context may help students with reasoning through these two pieces, which quickly turned to assessing learning about the topic through Desmos.  My colleague Ellen took the reigns and said she would create an activity to send out.  The context was about buying canned juice ($0.75 each) and fries ($1.25 each) for a budget of $20.  Below is a screen shot from our first attempt (initial activity here; final product here):

I was pumped to have such amazing colleagues working together to create an engaging and thoughtful product for our kids...I also looooooove Desmos.  With the Desmos activity as a start, Chris Wright (@cwright4math) and I got to work.  We bounced a lot of ideas back and forth about what it was that we wanted the activity to do.  We decided that we wanted students to be able to pick points for the inequality and have them get feedback about whether their points were solutions or not.  Then, using the overlay feature, allows students to take a look at the pattern that was created.  We spent time learning how to code Desmos Computation Layer, eventually getting what we were looking for and sending it back out to our teachers. Here's the slide that took the most time learning, but created the most feedback from our teachers and students:

This is some of the feedback we got from the implementation:

"One of my GT 7 teachers did this lesson today. I had the opportunity to watch the students work through the Desmos activity. It was well received and worked well.

I would recommend having the class discuss some of the slides as a whole group before letting them move on to the next part.

One of the students also asked if we could change the colors. He didn’t like that the shaded area was red which showed correct answers and the points outside the shaded area were also red showing incorrect answers. He wanted all the correct answers to be the same color.

I LOVED the slide with the adjustable points. It was so cool when the message popped up to say if the point they selected was correct or not. I need to learn how to make this type of slide."

So back to work with some more CL.  We learned how to aggregate the student responses so that students could interact with their classmates' answers.  A big moment for us was defining what exactly the learning target was for our students.  This conversation had started with a desire to get students to graph linear inequalities, but as the activity evolved the purpose became clearer too.  We landed on "Students will make connections between individual solutions (ordered pairs) to a two variable inequality and the visual representation showing the solution set to the inequality by using a budget".  This new target was about creating an understanding about the connection between the symbolic and graphic representations, a fundamental precursor to graphing inequalities.  As a community we dove deep into the learning progression that takes place for the new learning of graphing 2-variable inequalities.

With this clearer conception of what we wanted students to know and be able to do, we got to the next step.  We want students to recognize that there is a line that divides the plane into solutions and non-solutions, so we put in this slide (this is the overlay, which reveals a lot of great student thinking - the conversations when students saw some of the solutions was great!):

We also wanted students to be able to tell if an ordered pair is a solution without substitution.  We changed to card sort so that instead of the symbolic inequality, we provided the graph so that students could build the connection between the solution set and the graph.

Collaboration and feedback (from students and teachers alike) was crucial to improving this activity.  Equally important was having a very clear learning goal for the task.  Thankfully, this goal became clear for us early in the process.  I'm grateful to have wonderful colleagues willing to try new things who have created cultures in their classrooms where their students are willing to provide honest feedback.  Here is a link to our final product.