Texas and Electricity Rates

One of my classes has been exploring rates and ratios. We started off the lesson sequence by using tiles and eventually moved towards rate tables. The class used simulations and the paint Desmos deck. The class progressed nicely through the different ratio/rate models and late last week we began our final task of the unit. This task was adapted from the Chicago Everyday Math resource and I thought it was a nice blend between current events and rates.


In 2021, Texas was hit with a record winter storm. The storm knocked out power supplies across the state causing a shortage of electricity. Electricity is measured in kilowatt-hours. Customers are charged according to how many kilowatt-hours they use. An average household uses just over 30 kilowatt-hours per day.

Before the storm hit, customers who had a variable rate were paying on average about 12 cents per kilowatt-hour. Because of the shortage caused by the storm, some customers had their variable rates go up as much as 9 dollars per kilowatt-hour.

How much would a typical household on a variable rate contract pay for electricity for five days without a storm?

How much would a typical household on a variable rate contract pay for electricity for five days at 9 dollars per kilowatt-hour?

Why might some customers claim their bills are not fair?  Make a mathematical argument to justly your claim.


This was a challenge for students. Students read through the directions at least a couple times and still had questions. The questions dealt more with the significant difference between $9 per kilowatt hour compared to $0.12. They asked how that could be possible? Is that even legal? Why was it so cold in Texas? Is it because of climate change? I appreciated their curiosity and willingness to think about this as a fairness issue. This discussion lasted around 15-20 minutes. We then dove into creating a rate table.

Students first found out how many kilowatt hours a typical family uses in five days.

Once students put together their rate tables they started to work on the written response.
The students were elaborate with their written responses. One of the more challenging aspects of this task was that students needed to create a mathematical argument. Students are not used to that type of questioning at fifth grade and the strategies involved in finding a solution.

I am looking forward to using more tasks like this throughout the school year.

Math Stations and Expectations

Last week I was paging through Building Thinking Classrooms in Mathematics by Peter Liljedahl and thought it was time to revisit math station norms. I’ve been using them more this year than ever and for the most part, the students have reaped benefits from being in them. Last week I walked through the classroom to find some groups on-task while others were talking about non-math topics. I really don’t mind the social aspect of the math stations, but I also want to make sure that time is being spent wisely seeing that I only see students for 50 – 60 minutes.. I find that the math conversations and strategies that that occur at these stations pay dividends later on throughout the school year. I remember briefly discussing the math stations back in August and I thought a refresh was needed. My intention was to start off the week discussing math stations and then have students work in partners keeping in mind the expectations that were discussed that day.

I ended up using Desmos to collect student information about the environment, attitudes and behaviors occurring during math station work. Students first started by self-reflecting on their beliefs during math stations and then rated their group’s actions.

The class then reviewed overall results. This helped spur on conversations about math stations and group work. This also reinforced the notion that math station groups are meaningful and intentionally used in the classroom.

The conversation was essential in my mind to get students to think more critically about what makes a great math station. Students were then given the following slide with a text box.

This was also followed-up by:

What does a great attitude for math station learning look/sound like?

What does great behavior for math station learning look/sound like?

Every student added their response to the list. The class reviewed the results together and we created a notable list of the highlights. Students agreed to what was written down and then we categorized them into groups.

The answers were put together into a document and printed out.

Students then went to math stations for a group task. I’m looking forward to referring back this day to reinforce what math station groups should look/sound like moving forward.

You can find the slide deck for this activity here.

Me in Numbers

The first day of school is in the books. Not similar to last year, students were in the classroom and masked today. Most teachers that I know are exhausted after the first day and are look for a short respite before heading back for day two tomorrow. Today I was able to see all of my classes and I tried out a couple different activities. This post will highlight a one of them.

I started off the day with a classroom discussion about our summers. We had a conversation about highlights of the last few months and what we’re looking forward to for the new school year. I then put up a “numbers about me” slide. Students worked in partners (it has been so long since they’ve been able to do this!) for a few minutes to match each number to a statement.

I borrowed this idea from Annie from the recent ICTM mini-conference and used it with a group of third grade students Kids especially had trouble with the numbers that were closer together. After the partners presented their responses I slowly revealed the numbers that matched each statement. Now it was the students turn.

I gave each student this sheet and they came up with three statements. We had a classroom discussion about what is considered a better question than others. They then filled out the numbers. I’m in the process of filling out each student’s sheet so they can grade them tomorrow. : ). Here are a few that I’ve come across so far.

I’m looking forward to seeing the students reactions when they grade my guesses tomorrow. Day two is tomorrow. Here we go!

Studying Women Mathematicians and Scientists

Rosalind Franklin and the two-strand model of DNA

This year my students have been learning about mathematicians and scientists. This exploration started back during Women’s history month in March. My 3rd-5th grade classes highlighted a different woman mathematician every week. We studied Ingrid Daubechies, Florence Nightingale, Ada Lovelace and Marie Curie during the month of March. Not surprising, the study of women mathematicians was new to most students in the classroom. That dynamic changed when I asked the students to explore Mathigon’s site on the history of math.

Students were tasked to review the different mathematicians on the timeline and their contributions to society. I also asked to students to review the posters on a class bulletin board.

By the beginning of April I felt like students were feeling confident with the four women mathematicians and students started to show interest in wanting to learning more. I decided to assign a women in mathematics (could have been titled women in STEM) project at the beginning of May. Students were asked to study a female mathematician from a list

The list was mainly created from the Mathigon site and the Women in STEM site. A google form was used for students to pick their mathematician. I used a Form add-on that eliminated a choice once a person was picked to ensure different mathematicians were chosen. I also asked students to email me if they would like to study another female mathematician that was not on the list. That is how Trachette Jackson and Shakuntala Devi were added.

Students were then asked to make a copy of a Google Slide presentation template. That template was used to help students organize their thinking about what a particular slide should contain. A rubric was also created in the process.

After that the students used a Nearpod collaboration board to brainstorm what a great presentation looks like. I gave the students time to write whatever came to mind. The document was saved and then shared with the students to keep them thinking about what might help improve their presentation moving forward.

Students were then given about 2-3 weeks to periodically work on the presentation. They used time in and outside of class. They used this resource site to gather information about the mathematician. I found early on that more resources were needed and that is why I eventually turned it into a Google Sheet. Feel free to make a copy if you would like to use a similar project in your classroom

After about two weeks students were asked to share what they have put together so far. Most had 3-4 slides completed. They shared via Zoom screen share (since there are elearners and in-person students in the same class) with a partner and gave constructive feedback. Students used the opinions shares to polish up their presentations.

After finalizing their projects in Slides students screen recorded the presentation. Students used iMove to add effects and some even added a voice over element to narrate the presentation.

I am proud of what the students created given the circumstances this year and am encouraged to see students learn more about women mathematicians. I am looking forward to next week when all of the projects will be shared.

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.

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 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.

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.