Des-blog

In our most recent fellow’s prompt, we asked the fellows to compare Lego Prices and Are People Waiting to Get Married?. Our discussion highlighted values and unique perspectives, helping us to develop common ideas around what makes a good Desmos activity. Many of the fellows highlighted elements of the Desmos guide for building activities as they compared the activities, while others focused on the objective and how their students would relate to each context.

Incorporates a Variety of Nouns and Verbs

• Heather Kohn, Linda Saeta, and Paul Jorgens noticed that both activities incorporate a variety of nouns and verbs. Over the course of each activity students are asked to predict, sketch, build a model, use an equation or graph to answer questions about the context, interpret parameters, and to reflect on their thinking.
  

Create Problematic Activities

• Bob Lochel acknowledges that both activities allow students to connect representations effectively, but thinks that Lego Prices does a better job of developing need to connect the data and graph to an algebraic expression. Using the computation layer then personalizes the experience for students, builds informal practice, and allows students to take ownership of next steps.
  
• Nathan Kraft also comments on the way that Lego Prices connects student thinking throughout the activity with a central problem, and notices the absence of this in Are People Waiting to Get Married?. “We really did something with those initial guesses [in Lego Prices] thanks to the computation layer. With Marriage, we’re asked to guess a median age in 2010, but then that never really comes up again, unless the student remembered this question from slide 1 and feels like checking the graphs. As I was going through the activity, I wasn’t sure what the focus was (slope? intercepts? systems? linear vs. non-linear?)”
  
• Anna Scholl and Paul Jorgens also note the lack of a clear problem in Are People Waiting to Get Married?, with Paul offering some ideas for how to improve the frame for the activity. “I don’t feel connected to the prediction in the opening screen. Maybe I need to be asked how old I think I will be when I get married. Maybe we can see a median of our class data and then look at some trends of real data. Perhaps a better opening question might be to ask about the speculate on the typical age for someone to get married.” Thanks Paul!
  
• Michael Fenton offers his perspective on how Lego Prices does a better job with creating problematic activities.
  

Create Cognitive Conflict

Though Lego Prices may do a better job of framing a central problem, we still have lots of love for Are People Waiting to Get Married?, which ends with this particularly compelling screen.

• Nick Corley and Linda Saeta notice that extrapolation on the last screen of Are People Waiting to Get Married? drives home lots of cognitive conflict.
  
• Dan Anderson notes that “I liked how the Marriage activity talked about the danger of extrapolation while the Lego activity extrapolation NAILED the prediction for the Death Star. Both are valuable lessons. The Lego extrapolation is nice because it works, and the Marriage extrapolation is nice because it doesn’t work.”
  

Instructional Goals

• Anna Scholl points to the differences in prequisite knowledge for both activities, and that they each seem to have different instructional goals. Knowing the standards for the courses that you teach as well as how those standards progress throughout courses can help in determining such subtleties.
  
• Heather Kohn reminds us that choosing between these activities depends on what we want students to do mathematically. In Lego Prices students will build a model with draggable points. They’ll use an automatically generated graph and equation to answer questions about the context. Are People Waiting to Get Married? asks students to build a model by hand, and use that model to answer questions. Both models are linear, but the skill involved is quite different.
  
• Nick Corley, Linda Saeta, and Dan Anderson find that Lego Prices might be suitable for students in middle school both due to the y-intercept being zero and the model being built by a draggable line.

What do you consider when choosing activities? Let us know on Twitter @desmos.

When the Friday Fave was a child, truck driving was the coolest possible job. CB radios, convoys, a life on the road; it seemed everyone aspired to long-haul trucking. It’s unclear whether the nature of the work has changed, or whether society has just developed new romantic notions about other lines of work. Whatever the case, the Friday Fave will always harbor a nostalgic fondness for trucks and the open road.

Which brings us to this week’s Friday Fave—Slanty Hills—your chance to be in the driver’s seat. Pick your tunnel, observe the consequences, and figure out how to warn the others in your convoy.

The mathematics of slopes, angles, the tangent function, and percent grade are all brought to bear on this problem of multiple representations. Students come at these representations from many different angles (heh)—they measure; they do a card sort; they put things in order.

So if you’re a person responsible for teaching angles and tangents, get your students to truck on over to Slanty Hills. Maybe it’ll be your new Friday Fave?

We asked the Desmos Fellows this week to pick an upcoming or completed activity and tell how they would use the teacher dashboard during the activity. Responses fell on a spectrum, with many of the fellows describing how they use the dashboard during the launch, explore, or summarize part of a lesson. We also got ideas for using the dashboard to analyze student work and to extend an activity.

Launch

• Dave Sabol recently used teacher pacing in Charge for screens 1-4. This encouraged participation from all students and allowed Dave to select students to share their thinking.
  
• Scott Miller also used teacher pacing for the first three slides of an activity to enable an informal introduction to a task that would later be completed algebraically. This allowed students to ask clarifying questions about the context before they got to more challenging parts.
  
• Jenn Vadnais used teacher pacing at the beginning of an activity to model the use of and give students practice with a tool that would later be useful in solving fraction challenges.
  
• Paul Jorgens recently did an activity with his class on transformations that started with a “which one doesn’t belong” prompt where the students had to pick a cow. He used teacher pacing on screen 1 to give students a chance to argue for their selection. The histogram and responses for this screen were both valuable, showing that each cow had been chosen by at least one student and allowing strategic selection of students to share justifications.
  

Explore

• Bob Lochel found that adding a couple of “yes/no” multiple choices questions to an activity gave a natural spot to pause for discussion and sharing out.
  
• Anna Scholl has been intentional about designing activities with natural stopping points for discussion. She’s found that creating 2-3 slides for students to work and think through followed by pause makes for a nice balance. She’s also found that a card sort with extra answers that are wrong, or multiple correct answers based on unknown information helps generate discussion in her class.
  
• Adam Poetzel designed an activity for students to represent multiplication problems as arrays that is intended to be entirely teacher paced. For screens 3-5 Adam lists a series of questions in the teacher tips that teachers can pose to probe and extend students thinking. On Screen 5, when teachers ask questions such as “Make a parade that has 24 faces, and write the matching math sentence”, there may be several possible parades made by students. When ready, the teacher can pause the class and display several different student screens. The class can decide if the parade does have the correct number of faces and if the math sentence is correct.
  
• Nolan Doyle shared two activities with us this week that he used for an informal exploration of domain and range as well as increasing and decreasing intervals of quadratics. Nolan used teacher pacing after the initial exploration to build on student thinking as he introduced interval notation. He shared that “it worked really well to allow students to explore the concepts through Desmos and use those exact graphs for their notes as we came together as a class to formalize their thoughts and discoveries.”
  
• Nick Corley uses a tablet while circulating the class to see if any students are struggling and to guide them in the correct direction. He also projects the dashboard during a card sort screen so that students can identify when they are correct.
  

Summarize

• Tony Riehl also uses a tablet to monitor student progress as he walks around the room. This helps him check in with students as well as pause and pace for class discussions as needed. Students in Tony’s class work in groups and provide each other support throughout the activity. Tony further supports student learning by using pause and pace at the end of the activity to help summarize the activity and ensure that students leave with the same information.
  
• Sarah Blick Vandivort paused her class after slide 12 of Systems of Two Linear Equations to drive home the idea that the point of intersection is the solution and it makes both equations true.
  

Extension

• Paul Jorgens designed Translations and Reflections so that students that finished early had a chance to created their own challenge. He chose a few of the student created challenges at the end of the activity and had students discuss in groups how they might solve the challenge from their peers.
  

Analyze Student Work

• Teachers in Patty Stephen’s district used Desmos for an assessment, and used the teacher dashboard to look at student responses and analyze student work together. Patty notes that the ability to share a dashboard with another teacher in her district would have been helpful to the collaboration process.
  

How have you used the Teacher Dashboard to monitor student learning and increase classroom conversation? Let us know on Twitter @desmos.