Compelling Questions with Desmos Activities

Starting in April, I decided to do a once-a-week Desmos Activity during the period where students were least willing to sit quietly and listen to me talk (even for a short period of time). I noticed that the medium of computers was often particularly engaging during this period and wanted to capitalize on it. I also wanted this to be a focused, valuable learning experience and not me just counting down the minutes until class was over, hoping they would stay on task on their computers.  Therefore, I decided I would experiment with this idea of a compelling, framing question. Since I was a student teacher, I have been in the habit of writing and having the students read a guiding question each day--things like "How do we solve equations with variables on both sides?" and "How do we create equivalent equations?" This was essentially me going through the motions of what was "good practice" without it having any substantive impact on my classroom. With these periods, I wanted to experiment with writing a question that was student-friendly, hopefully compelling, and that I could introduce at the beginning of class and use to summarize at the end of class.

With all this in mind, I came up with the following routine:

1. Students come in, take a chromebook, and log into the computer
2. The Do Now is to take a multiple choice polleverywhere survey. Both the link to the survey and the live results are projected on the board. This survey is designed like all of my other Do Nows—it either teaches/reviews necessary background information or previews what is to come.
3. I close the survey and have one student explain why they chose the most popular choice. We usually don’t discuss whether or not the most popular choice is the accurate choice--it is either obvious or they will figure out over the course of the activity.
4. I project and have a student read the question for the day and instruct them to keep this in mind as they are doing the Desmos Activity. I then give them their Desmos Code and they get started. I circulate the room, with the Activity dashboard on my iPad.
5. (Optional) About 15 minutes in, we have a 3-minute whole class check-in. I do this if there’s a particular idea that would be useful to discuss in order for them to continue with the activity. This might mean revisiting the Do Now prompt or a particular slide in the activity.
6. After giving them a 1 minute warning, I have everyone sign out and close their computers. I project the framing question again and we have a very brief (again, about 3 minutes) discussion where the kids answer the question.
7.  Exit Ticket. This is more of a management technique than a formative assessment. I have usually already gotten enough information about where kids are from circulating during the activity, looking at the work they are doing, and the final discussion. However, I need something for the kids to do while a couple of them are putting away the chromebooks.

Activity: Square Dance

Goal: Build on students’ understanding of the relationship between the side length and area of a square to introduce the concept of a square root. Have students approximate the value of some square roots.

Framing Question: Why is the \(\sqrt{16}\) not equal to 8?

Do Now Survey:

Other Details: For students who got to the stop signs in this activity, I had them come up and place various square root cards on the double number line clothesline. In our closing discussion, I set up the double number line again with some of the square roots accurately placed and others reflecting common misconceptions. I asked the kids to identify what the mistakes were, why people might make them, and had them fix them.

Reflection: This was a very successful framing question. Although kids had not made this mistake prior to the activity, they made it and corrected it during the activity and were able to figure out why someone would make that mistake and how to fix it in the closing. I’m not sure how compelling the question was, but it really made the whole lesson very coherent.

Activity: Water Line

Goal: Practice 8.F.5: “Sketch a graph that exhibits the qualitative features of a function that has been described verbally.”

Framing Question: What type of bottle makes a “bendy” line?

Do Now Survey:

Other details: We did a paper and pencil follow up the next day with the Filling Bottles task from the Shell Centre.

Activity: Marbleslides: Lines

Goal: Practice with writing equations of lines using how the slope and y-intercept manifest themselves in a graph.

Framing Question: How will the graphs of these two graphs look different?

y = 0.5x + 2                y = 4x + -2

Do Now Survey (intended to briefly introduce kids to the idea of domain and its notation):

Reflection: Engagement was incredibly high in this lesson, but neither the activity nor the framing question really serviced the goal. My kids loved the marbleslides, but were just quickly changing all of the possible options without really doing any thinking about slope and y-intercept. I think this could be fixed by having a still screen where they have to make a prediction and justify it before they get to change the equation(s) and by having the reflection questions sooner rather than 3 or 4 marbleslides all in a row at the beginning. The question was also something they should have been able to answer (we had spent time on this before) before we started, so it really was not interesting to think or talk about.

Activity: Nine Points, Three Lines

Goal: Practice with writing equations of lines using how the slope and y-intercept manifest themselves in a graph.  (Secondary focus: when is it possible/not possible to have 3 lines that go through 9 points)

Framing Question: How FEW equations can you try in order to get three lines through nine points? (Hint: Use a ruler to help you make a plan)

Do Now Survey:

Additional Comments: After the initial survey, I handed out rulers, asked them how they could use this tool to help them be more precise, and allowed them to re-vote if they wanted. It was my hope that the ruler could be a scaffold for kids during the activity to imagine what they wanted their line to look like, think about what that would mean about the slope and y-intercept, and then write their equation based on that. Also, in response to the lack of thinking in the previous week with Marble Slides, I also had them keep a written record of how many lines they tried, their final solution, and a “brag box” explaining how they figured out the correct equations.

Reflection: Kids were confused about the record keeping and thus the framing questions (designed to have kids think) fell a little bit flat. However, there was more strategic equation writing than the previous week.

Activity: Polygraph: Scatter Plots

Goal: Introduce students to scatterplots and draw upon our knowledge and vocabulary around linear relationships to describe them.

Framing Question: How can you and your partner get the right scatterplot in the fewest guesses?

Do Now Survey:

Additional Comments: In discussing the Do Now, I had students describe each of the scatterplots and we came up with the following word bank for students to use during polygraph: increasing, decreasing, linear, non-linear, close, and spread out. As they played, I walked around with the dashboard which allowed me to see all the questions kids were asking. I gave out tickets (our team’s positive behavior reward system) to kids who were using words from the word bank and encouraged kids who I saw struggling to formulate questions to use the word bank. I also wrote on the board the names of each of the successful pairs (who asked real questions), which they loved.

Reflection: My kids love polygraph. The format is so compelling that the question was basically unnecessary. However, unlike with marbleslides the compelling format was used to achieve the lesson goal, rather than distracting it.

Activity: Lego Prices

Goal: Introduce the idea of drawing a line of fit in order to make a more accurate prediction based on a limited data set

Framing Question: Why would someone draw a line through a scatterplot?

Do Now Survey:

Reflection: The goal, framing question, and activity fit really nicely together in this one. In our discussion at the end of the lesson, everyone was on board with their predictions being more accurate when they used a line of fit than when they didn’t.