Des-blog

The Des-Blog is home to the Friday Fave, which is a weekly post about some of the favorite activities amongst the Desmos Teaching Faculty. This week we asked the Desmos Fellows to share some of their favorite activities, and to tell how these activities help students learn math.

Which One Doesn’t Belong?

First off, if you’ve never heard of the WODB puzzles, head here for a brief introduction. Two of our Fellows Fave submissions this week included a WODB task.

Shelley Carranza found her most recent favorite after a visit to Paul Jorgen’s class, where he displayed the above Desmos graph and asked students to find a reason why each of the parabolas didn’t belong. Students argued their positions using graphs and expressions, and built off of each others’ thinking as they reviewed concepts and vocabulary from the unit.

Allison Krasnow also shared a WODB activity that she recently used with 4th grade students. Allison used the dashboard to chose slides where the majority of the class had chosen 1 image and no one had chosen 2 or 3 of the images. She then challenged students to come up with a mathematical reason for why the other images didn’t belong. Allison also supported students in developing academic language by having them discuss and then rewrite their explanation using sentence frames.

A Day on the Town with the Bugs

Bob Lochel shared this delightful introduction to parametric functions where students explore whether or not bugs traveling along intersecting paths will ever meet, and consider why this is so.

A Leaky Cup

Anna Scholl’s students collected data about the water level in a A Leaky Cup and used Desmos to build a model to predict when the cup would be empty. Anna’s goal was to have students build a model using regression. Before students reached that part of the lesson Anna found that they were applying their knowledge of function transformations (a theme of the course) to try to fit a model. Groups then compared models and strategies using the dashboard before learning about regression.

Land the Plane and Game, Set, Flat were also mentioned as recent favorites.

If you’ve been following along with our work in the fellowship program you know that Marbleslides has been a recurring favorite, not to be left out of this Fellows’ Fave edition. We’ll leave you with this recent lunchtime conversation between Paul Jorgens and a student of his who had recently been introduced to Marbleslides:

“Mr. Jorgens. You have to tell me how to stop them!”

“Stop who?”

“I need to know how to stop lines.”

“Huh?”

“Let me show you.”

When others are giddy about an activity, the Friday Fave cannot help but get a little excited, too.

Land the Plane is one of a suite of new activities we recently released.

The structure should be familiar. We get you started with an estimation task, then we get you to use algebra to increase precision and efficiency.

We ask students to imagine lines in their minds, and we ask them to write equations for the lines they picture. But we don’t tell them how to do it. Maybe slope-intercept form works best for you on screen 4, and standard form makes sense on screen 8, or vice versa. Maybe one student attends to the direction the airplane is pointing, and another notices the slope of the edges of the runway.

This is all fine, all supported, and is fodder for classroom conversations about equations of lines. Students practice, but not in a do it this way because I said so kind of way; they practice in a how can I get better at this fun task? kind of way. When students are wrong, the runway lights signal the plane to turn around, and their plane doesn’t land. Of course they get to try again.

Land the Plane is a brand new activity, but it has already been well received. Excerpts from a Twitter conversation:

“Runway lights” are genius! Making my son do this during breakfast in the AM.

Brilliant concept. Executed well

Real math and real delight. A giddy combination. Go ahead and land the plane.

This week the Desmos Fellows shared ways in which they “go over” or review a Desmos Activity to help students summarize and reflect on learning. We shared a variety of strategies, some of which take place during the activity and others that take place at the end or even the next day.

Leveraging Partial Understanding to Reflect on Learning

• Tony Riehl monitors student work on an iPad as he circulates the classroom. This allows him to check in with individuals or groups and help them as needed.
  
• Paul Jorgens is flexible in how he helps students reflect on their learning. He shares that reviewing an activity starts with the learning target and continues with the formative assessment. “Sometimes it makes sense that the formative assessment is within the activity and sometimes it might be outside or both. Perhaps there is a screen at some point that gets at the heart of that target. In that case, I will use teacher pacing and we will look at that screen together considering misconceptions and variety of approaches to close the lesson.”
  
• Allison Krasnow, Dave Sabol, and Shelley Carranza all shared next day strategies for helping students to reflect.
• Allison builds a new 1-2 slide activity that incorporates some of her favorite mistakes and asks students to collaboratively improve or correct the work. This strategy was inspired by My Favorite No from the Teaching Channel.
• Dave has reviewed homework using partially correct responses from a Desmos homework assignment. He had students discuss the slide below in groups and share out with the class.

• Shelley linked to an NCTM article by Martin Joyce in which he shares his strategy for extending a Desmos lesson. Martin printed out anonymized responses to a Marbleslides screen and had students provide peer feedback on the responses.
• Jenn Vadnais acknowledges that theses strategies help develop a culture of inquiry, conversation and sense-making, and she is hoping to share such strategies in workshops in her district.
  

Accessing Prior Knowledge and Connecting to New Learning

• Bob Lochel recently used a Desmos activity to unlock previous student understanding. He paused the class a few screens in to lead a guided discussion that would help students access material in a new unit.
  
• Lisa Bejarano uses Desmos activities as a visual starting point to introduce a topic, providing a graphical representation of a concept. After the activity students add notes to a composition book to determine what the concept looks like analytically, and then relate back to the graphical representation.
  
• Scott Miller helps students reflect by selecting and sequencing responses from less sophisticated to more sophisticated. He strategically displays the responses in that order so the class can discuss and build on each other’s reasoning.
  
• Anna Scholl has helped students build connections and summarize learning by exploring special quadratics using Desmos and a worksheet. Some students commented that completing the Desmos Activity first helped them understand the problems on the worksheet better because they understood the connections between representations.
  

Exit Tickets to Reflect on Learning and Plan Next Steps

Ayanna Ramsey, Heather Bolur, and Nerissa Gerodias have all used exit tickets at the end of a Desmos activity to help students reflect on their learning.

• Ayanna uses the results to help her go over misconceptions in small groups or with individuals.
  
• Heather Bolur uses pause during the activity to go over common errors, highlight student responses, or show the overlay. She then uses exit slips on paper that align with concepts in the activity.
  
• Nerissa projects her dashboard and switches between Responses and Graph Overlay to see if anyone needs help. She ends with a class discussion followed by a reflection screen where students write what they learned from the exploration.

What are some other ways in which we can review a Desmos activity? Let us know on Twitter @desmos.