Silver Linings

It is hard to believe that this school year closes out in three weeks and it is challenging to describe this year in a brief statement. While the school year end is near it has also been a good time to reflect on a few positive changes that have happened.  Before turning our backs on this year it might be beneficial to see if there is a silver lining.  That potential silver lining has nuggets that will help with planning for a more usual 21-22 school year.

Here are a few ideas to ponder:

  • I am still planning on using digital platforms like Desmos and Nearpod to engage learners in review and math exploration.  Although screen time will be minimized compared to this year, I have found that teacher-paced digital decks have potential and the data that is collected in the process pays dividends for planning.  On multiple occasions I have found myself taking screenshots of student work or quickly writing a note in the chat about a certain element of a student’s response. 
  • Every year I find myself thinking about how to curate a more organized library of resources.  This year has encouraged me to be more critical in how I organize my Desmos decks.  I have been using mainly Sheets for this and am hoping to be able to quickly retrieve this resource for certain skill next school year.
  • Along with the curation of materials, I believe local assessment practices have improved this year.  Since all assignments are online many resources moved from paper-based to digital.  A large chuck of time has been dedicated to that this school year.  My math unit tests have decreased in overall length which I think is a good thing and are more constructive in evaluating students’ understanding of the material.  Questions that were not clearly aligned to a particular standard were eliminated in favor of tasks that were more robust. I cannot remember the last time the tests were re-evaluated and I am glad that my team analyzed them with a more critical eye before digitizing them.
  • I have said this before and I continue to see the importance of having a brief “meet and greet” time as part of the daily schedule.  Checking in with students and allowing them an opportunity to discuss what is important in their lives helps create a better learning environment.  This year most classes have started with morning meetings or something like that to offer a listening ear to students as they traversed this long school year.  This has become even more important as students came back to school for in-person learning
  • One of the highlights his year was being able to meet with students’ parents over Zoom.  The limited time on video has increased the effectiveness of these meetings and has also provided an opportunity to meet where transportation/timing was not ideal.  I am hoping this is still offered next year along with professional development opportunities.

As I write this, boxes are sitting in my room ready to be filled up as I am moving classrooms again. I have to decide if items are worth putting in a box for reuse.  While doing this I should keep in mind that there are a few silver linings that I would like to keep for next fall.

Graphing with Context

This week one of my classes has been studying coordinate grids and graphing. They’ve learned about coordinates, using a table, identifying rules and created ordered pairs during the last part of March. On Monday the class reviewed line graphs and change over time. At this point in time the class is identifying the informal slope (without a formulas) of a graph and describe events that are taking place by analyzing the relationship between the x and y-axis. Earlier this week my students worked through Kurt’s Retro Desmos solving systems by graphing task.

I selected specific slides to complete as the class hasn’t been introduced to the y-intercept yet. The class spent a good chunk of time on slide four – a class favorite. Students tried out different strategies to see what happens as the lines cross or increase in steepness. This led to a class discussion about the slope of the line and what the x and y-axis means in context. A number of students experimented with what happens when you make multiple lines on the graph. This slide caused students to think about the context first and then how the lines look second. Near the end of the class students mentioned that they’d be interested in the process of finding the rate or speed of each character as time progresses.

During the next class I used Kurt’s slides and idea to create an assignment. I added a few criteria pieces related to the 100 meter dash. Some of ideas were taken straight out of the original activity. Click here for the Desmos assignment slide.

Criteria: Mario starts 30 meters ahead, Sonic and Mario are tied at 4 seconds, Sonic takes a 3 second break, and Sonic wins at 9 seconds.

Students worked on this assignment in class and checked their work by pressing play. I was impressed with how students made multiple attempts in trying to meet the criteria. The video playback of the race was used as a self-checking mechanism.

Students then answered a question related to Sonic’s line.

Tomorrow the class will review the graphs in more detail. I’m looking forward to diving into more graphing fun tomorrow.

Changing Models

Arrows indicating direction of student traffic flow

For most of the year my school has been following a hybrid AM/PM model.  Half of my classes attend in the morning and the other half in the afternoon. Some student are in-person and others (about 25%) are elearners, but all attend the same class Zoom session together. In the morning I have three math classes that are about 40 minutes each and then I repeat the process with a new group in the afternoon.  My largest class is about 14 students since it’s split in half.  While not ideal, this model has led to some positive outcomes and I’m glad that district moved in that direction. A few observations:

Since there are less students in the sessions I find it much easier to discuss topics as an entire class.  Guided group discussions take on more meaning as students have more opportunities to ask/answer impromptu questions. Students are able to social distance at an optimal levels because there are less students in the school. There isn’t a lunch period so families and staff feel safer regarding virus transmission opportunities.  

I’ve also noticed that the class has had a community element, but is not the actual entire class.  Since half is in the morning and the other half in the afternoon, students aren’t able to get to know their classmates as well as before the pandemic  Some of their friends that they saw last year aren’t in their session.  Also, math time is limited to 40 minutes, which means something has to unfortunately be cut. This year that cut is taking the form of students working together in groups

Starting tomorrow the model will shift. Boom. Instead of having an AM/PM class, I’ll see my entire class for a full 60 minutes – that’s 20 additional bonus minutes. Approximately 25% of my students are still elearners so they’ll join-in along with the rest of the class in Zoom.  You heard it right, all of my classes and students will be in Zoom.  I’ll be modifying the model from earlier in the year. I’m planning on incorporating more student group work with that present of time. I feel that component has been one of many important elements that have been missing with the hybrid model.  Along with the extra students comes a re-emphasis on social distancing and routines as students will be in school for the entire day.  This is a significant change as lunch, recess and hallway congestion all become more of an issue. The thing that will be immediately noticeable for students is the increase in the number of desks in the classroom and probably the amount of tables/desks needed to eat lunch with social distancing.

New protocols related to recess, social distancing, shared materials, and lunch will need to be communicated to students. Technology and chargers will need to be brought to class and students will have music, art, and PE in-person in the classroom and outside if weather permits. Just writing the last few sentences brought a slight smile to my face.

Even though the last few days have been used for planning, I’m finding that there’s a sense of anxiety that’s permeating the air. Usually that’s reserved for the first day of school. In a certain context it’s like teachers are starting a new school year.  Norms and community building will be forefront as students start getting used being in-person again, although a change in expectations may be needed as school is much different compared to what we left last March.

I’m looking forward to this seven week adventure. After that we can close out the infamous 2020-21 school year.

Solving Equations – Progressions

For the past few weeks my students have been exploring equations. The current unit of study introduces equations by showing different visual models end eventually ending with an inverse operations strategy. Students initially see equations through solving for ? or x by using trial-and-error. Up to this point in time that’s how they’ve solved equations. There hasn’t really been a formal procedure until this particular unit. As the unit progresses the class uses bar models, pan-balances, hanger models and inverse operations. This post is designed to review the different models that are introduced.

Bar-Model

Using a bar model is fairly new for most of the students that I teach. Students separate a box with a line. The left side of the equation goes on the top and the right on the bottom . Students use logical and spatial reasoning to solve for x. This was a jump in challenge for students. The spatial piece of being able to visualize how much space the variable will take has the potential to be confusing. My class ended up spending about two sessions reviewing this strategy.

Hanger Model

Students have already been introduced to Solve Me mobiles so this wasn’t as much of a stretch as a bar model strategy. This was the first time that students started to “balance” terms with a hanger. Another two lessons were spent here. Students enjoyed working on this although it was quite challenging when students reached the mastery level on the solve me mobiles site

Pan-balances

The next strategy involved pan-balances. This model involves more operations and steps. Students tended to thrive with this and it was great to use in breakout rooms. Students took items away from both sides of the equations and strategy played a role. As students discussed their strategy they found not all methods to solve them were efficient.

Inverse operations

Near the end the unit students were introduced to the inverse operations strategy. This is generally what students come to class knowing, but they’re unsure of why it works. Up to this point students have relied on visual models and are continuing to make sense of equations. They also reviewed how to combine like terms and integers during this process.

The progressions of how students see equations starts to really shine through between the pan-balances and inverse operations strategy. After reviewing all of the different strategies I surveyed my students and most are now more favorable to using the inverse operations strategy. I even had a few students comment that the strategy actually depends on the equation. Bingo!

I’m looking forward to reviewing the solving equations unit after spring break.

Here are a number of Desmos activities that I used throughout and to review the solving equation strategies:

Reviewing all the strategies

Combining like terms

Solving one-step equations

Kindness Calendar

One my school’s themes during the past few years has revolved around acts of kindness. There has been an intentional effort to reinforce what kindness looks like and sounds like in elementary classrooms. It is part of the community culture and I believe the school even purchased a banner or two that students see as they enter the school.

It was much easier to reinforce the idea of kindness when students were all in-person. Quick acts could be mentioned in the moment and then used as reference points throughout the year. Fast forward to today and the instructional setting has dramatically changed. Many schools now have at least a certain amount of their population online and some are present in a socially distant classroom. This has made it more challenging this year and I am finding the new emphasis on social/emotional needs ties nicely with the kindness theme.

Earlier in the year I came across a tweet from Megan about an optional kindness calendar. I have seen similar calendar but I was digging the idea that her students came up with daily acts of kindness.

I took Megan’s idea and had my students come up with a list of how they could be kind for the next month. They had a number of ideas and many were built from the original calendar that was shared. I was able to collect around 60 different responses.

The ideas were then put into a calendar for the next month. Students online and in-person were able to view it as a Google Slide and it was part of my agenda presentation. Each day the class briefly reviewed the ways in which they could be kind. I made sure to indicate that this was optional and just an idea to consider for the day. As the weeks went on students expected to see the daily kindness act of the day as part of our routine.

This week I tried something different to see the calendar’s relevancy and if it was something that I would like to keep for the remainder of the year. I used Desmos and asked students how they were kind for that week.

Students reviewed the past week and picked one day. I did not want to guilt anyone into having to pick one so I added the did not participate option. Here are the results for students in grades 3-5.

The results were fun to look at but the real gem was in the open response sections. It was great to see the different acts of kindness and how deliberate people were in completing them.

Based on the responses I will most likely keep the calendar for the last couple months of the school year. Feel free to use the Desmos template by clicking here.

Math Breakout Rooms

I was introduced to Zoom breakout rooms last March when my district went remote. Breakout rooms were novel and many teachers started to use them during the last couple months of school. It was one way to get students into smaller groups where they felt more comfortable sharing. They were awkward at first for students and staff but most were able to get their breakout room sea legs by May.

Fast forward to the 20-21 school year. Like many around the nation, my school started the year off completely remote. Having a head start in March helped most teachers get into a routine quickly. Most teachers started to use breakout rooms immediately and were able to see the benefits. The social interaction that usually occurs in-person can’t be exactly replicated, but a form of it can in a breakout room. I’ve been part of some amazing student math discussions in breakout rooms this year. I’ve also been in other rooms that were full radio silence. Some this year have had detailed agendas that students follow while others are more student-directed.

Most of my elementary math breakout rooms consist of 2-5 students. Since we are using a hybrid model I try to match students in-person with those at home. I found early on that partnering up kids in the classroom over Zoom causes major audio issues. Less students participate in the breakout room when there are more than five participants. Generally, students in the breakout room have a specific task or activity. Sometimes the assignment comes from their consumable journal and other times it might be a prompt. Students are usually in the their breakout rooms for 5-15 minutes. We have a 45 minutes block for math. While students are working I pop in and out of the rooms with my camera and sound off. I observe the conversation and ask questions if needed. Most of the time, I visit a room and listen to what’s happening, add something in the chat for that room and then move to the next room. After the breakout rooms close the class has a debrief sessions and I try to have each team discuss their solutions. This strategy has worked out well this year, but I’ve had inconsistent success.

I still have questions.

  • What makes a good breakout room?
  • What’s the ideal room size and time?
  • Does camera on/off matter?
  • How do you manage breakout rooms while teaching in-person and elearners at the same time?
  • Should students share their iPad screen?
  • Do you find annotation through Zoom helpful?

I don’t believe there’s a perfect formula for a breakout room, but there are better practices. Feel free to let me know what has worked in your classroom.

Math Schedule and Hybrid Routines

I’ve been teaching in a hybrid model setting for most of the school year. My school started remotely and proceeded with an in-person staggered start. The classes are divided so I have half of the students in the morning and the other have in the afternoon. I appreciate that the school has made social distancing a priority and is limiting the amount of kids in a physical classroom at one time. The overall schedule has also changed and my math block has decreased to 40 minutes instead of 60.

Long story short, I teach kids at home and in the classroom at the same time. My instruction is mostly digital. I do that for a number of different reasons. While the digital model hasn’t been ideal, it allows everyone to participate and I can gauge engagement by looking at a teacher dashboard. My agenda and routines for each class have changed over time. Currently this is how I’ve been managing my quick 40 minute block.

11:00 – 11:05


Students come into the classroom and login to Zoom. Students at home do the same. Once everyone is logged in we start the meet and greet session. Usually there’s a prompt that students answer. This is whole group and students talk to each other about the responses. This time is dedicated to help build classroom community and connect with students. You can find many of the pictures for the meet and greet here.

11:05 – 11:10

Students log on to Nearpod for a brief review of past concepts. I use Nearpod for this time slot around three days a week or so. It’s a quick 2-3 slide presentation. Sometimes I’ll replace the Nearpod with a Quizzes or Desmos task. This time is purposefully used for students to review past concepts and I can see if additional practice is needed for specific skills.

11:10 – 11:25

Students take a look at the agenda slide and then review the goal for the day. The class completes a consumable journal page under the document camera. This is generally the time that is used to introduce new concepts/skills. Questions are asked the most during this slot. This time slot can be a challenge to manage as far as engagement is concerned. Still tweaking.

11:25 – 11:40

During this time students are either working in breakout rooms, on a set of problems from the consumable journal or independently working through a teacher-paced Desmos task. During this time I’m working in Zoom breakout rooms with students or sending feedback through the Zoom chat. I’ll often turn off my mic and video so I can hear the students and so the conversation doesn’t slow when I enter a breakout room. At times I might ask a question or two to check for understanding. The class then comes back together before the end of the session to review the group work/Desmos task results. There’s a quick closure statement about what we explored that day. I then say goodbye and a new group of students start populating the Zoom waiting room.

This routine will probably change, but it has been working so far. Ask me in a week and I might have a different answer.

Digital Weekly Math Reviews

This school year has been a bumpy ride. Many teachers have been asked to teach students in-person and online at the same time. Along with the hybrid model, time with students has been limited, which can cause retrieval issues. I’ve noticed that students need more retrieval opportunities with more feedback this year compared to years past. More check-ins and reviewing has been necessary. Out of necessity comes a different approach. For the last couple months I’ve been using a digital math review practice at the beginning of each week. I’ve been finding different ways to use Desmos to help students think about their own mathematical thinking. I have created a few original decks in the process, but have had the most success with copy –> edit with other decks. There are so many brilliant Desmos users (I’m looking at you  RCS Desmos Team!) that’ve already put together amazing decks with CL self-checking abilities.

The Desmos activity in this post was primarily used to review math concepts. My rookie level CL skills gives the students a higher, lower, or just right designation. The small written feedback has been helpful so far. The deck begins by reviewing math concepts explored during the unit.

The next slides offer students an opportunity to review the results and go back to change them.

Students take around 5-10 minutes to complete the task. From the teacher dashboard I can tell how each student is doing and if additional review is necessary. I’m hoping as I learn more CL that I can make these types of practices better. Feel free to use the activity by clicking here. I’m looking forward to seeing what you create!

Thoughts on a “normal” return

The last time I saw a full class of students in-person was March 2020. I’ve been teaching in a remote/hybrid model since then. Along with many educators, I’ve had to change my approach, learn new skills and find ways to reach students in a different way. My platform has drastically changed to a digital model. Schools have also had to change the way in which they provide support for the community. 2020 was a rough year. It also provided us with a different perspective on how schools can address needs of students and staff.

My hope is that August 2021 will look different than August 2020. With that being said, I also hope education changes because of what has happened. Let’s analyze what worked well during remote/hybrid learning and what didn’t. I’d like to continue some of the processes that have been used this year and possibly discard/replace others. This post is meant to reflect a bit on some positive shifts that might be beneficial moving forward.

1.) Online meetings and professional development Part of me wonders why we haven’t been doing this all along. In my experience, staff meets are generally used to communicate information to staff. Many times this can be written up in an email. I think having virtual staff meetings encourages the organizers to parse down the content to what’s important and to give time for staff the ask questions as needed. It also helps that specific questions for individuals can be addressed by the presenter as they stay on the Zoom session while others exit the meeting. I’m going on a limb here and say this could also apply to district meetings, professional development, and school-wide assemblies. I feel like this year the professional development has been more applicable than any other year. It helps that the presents are in-house.

2.) Emphasis on social and emotional needs Ever since the pandemic began I’ve noticed an increased emphasis on addressing SEL needs. Districts have tried to implement SEL programs to encourage students to talk and to work with one another. Some districts are even trying to create opportunities for students to come back into the school so they’re able to receive in-person time with staff. Breakout rooms and meet-ups have taken place to encourage this type of collaboration. Teachers have also been part of this initiative as many administrators recognize that self-care should be required.

3.) Hybrid/Remote models Now, don’t get me wrong here. I think in-person instruction is the best bet for most students, but I think having a form of a blended model works better for others. I’ve seen some students shine with a hybrid and remote models and others that would certainly benefit from being in a classroom. Let’s not think of going back to “normal” school as the best option. I’m wondering how this will play-out during the 2021-22 school year. Time will tell.

4.) Digital resources and a learning management systems Going completely remote last March required teachers to make a hard transition. Most paper-based resources had to be converted. I initially used SeeSaw with my students and Canvas became available this school year. It was a steep learning curve but most teachers in the district are now more comfortable in creating digital assignments for their classes. Transferring non-digital curriculum resources to digital has been very time time consuming this year. I’m hoping that the resources created this year will be used next year. The lonely copy machine hasn’t been getting much love lately.


This year has required teachers and administrators to stretch like that haven’t before. It has been a stressful year. There have been some positive pieces that I’d like to see continued even as we move to a sense of normalcy next school year. It’ll be great when classrooms will once again be filled with students being able to work closely together, share/use math manipulatives, use vertical whiteboards, participate in school clubs, attend recess, have pe/music/art in a classroom, and attend field trips. I’m looking forward to the day, but until then let’s think about how education structures could potentially change moving forward.

Digital Math Tasks, Predictions and Reflections

Student feedback and goal setting have been different this school year. The students that I teach have been learning from home and in the classroom. The district has moved back and forth between remote and hybrid models since August. Students have recently been back in the classroom and and it’s not possible to use shared paper materials. This has been one of the most challenging problems this year. Therefore I’ve needed to rely on digital means for instruction and manipulatives. This has impacted how students receive feedback and set goals.

I’ve been using Desmos more than ever since my lessons are digital. It has pushed me to find ways to use the platform so students think more critically about math. Through the process I’ve learned more about how to create better tasks that enable students to reflect on their math work. I’ve found so much support from the Twitter Desmos community. I’ve slowly been learning more about Desmos CL and how to incorporate it into my decks so students are able to process the concepts they discover and receive feedback. I started using CL more frequently after reading Julie’s fantastic post. For the past month or so I’ve been working on creating self-checking tasks with small wins here and there. Last week I found a recipe that has been somewhat successful for formative checkpoints. I used it with a few different classrooms last week with multiple choice questions.

Here’s how it goes. Students synchronously complete a list of multiple choice questions related to a specific skill. I added the sketch pad for students to show their work and used teacher pacing to make sure students only have access to the question slides.

Once students finish the questions they visit a slide where they’re asked to reflect on the questions. They also draw on the sketch pad how they think they performed. During this time students revisit the questions in order to make an accurate prediction.

Then the final slide opens indicating correct/incorrect answers. The prior slide is copied over and students reflect on their performance compared to the estimate.

The student responses comparing their results to the prediction were stellar. Afterwards, the class had a conversation about the questions that were more challenging than others and why those stood out. I’m hoping to expand on this idea in January.

Feel free to use/copy/change the activity. It can be found here.