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.

Asynchronous Math eLearning Days

Last weekend I planned for two days of non-live instruction for students exploring 4th-6th grade concepts. This planning sequence has been on my calendar for a few weeks and I’ve spent a good amount of time wrapping my brain around how to keep the lessons engaging without being there. I also had to figure that I wouldn’t be able to answer questions live. I discussed this dilema with another teacher and we came up with a couple options for students involving a choice menu. I decided to give students a small choice board for the two days the school deemed as asynchronous. My choices are below.


Grades 5-6

Fraction Escape Room by Patty Stephens – This activity is a robust review of fractions. It took my students around 30-45 minutes to finish the task and it was quite challenging for some. This fits in really well with a fraction computation unit that the class recently finished.

Equation Modeling – Mega Man by Kurt Salisbury– One of my classes has been introduced to equations and this activity is a fun way to review and play with variables before introducing a formal process. This is a class favorite and it also introduces students to Mega Man!

Pan-Balances – Solve me mobiles – Similar to the equation modeling, this was used specifically for students to help visualize equations. The questions are also found here.

Grade 5

Integer practice by Jay Chow – My fifth grade classes are starting to explore integer computation and this was one way to have the students practice adding/subtracting integers. The Pokemon evolution was a bonus and I guess it’s still fairly popular as students gravitated towards this option.

Coordinate Graphing Ice Climber Plotting Points by Lorri Sapp – My fourth grade crew has been studying coordinate grids and this was a perfect activity to reinforce those standards. The activity begins by reviewing the basics of a graph end simply moves through the process to graphing coordinates in all four quadrants. The students enjoyed the game with the last couple slides the most.

Grades 4-6

Math Art Challenge – Isometric Grids by Adrianne Burns This was a fun activity that helps students explore geometric patterns on an isometric grid. Students built patterns and submitted them via Canvas. This was a student fan favorite activity as it applied to multiple grade levels and students were able to combine art and math.

Decimal and Fraction Review – Students in my fourth grade class have been exploring conversions this unit. This Desmos deck was used to review multiples of 10 and to also practice recent skills.

Map-Accelerator – This options gave students an option to review and be exposed to skills related to the Map test that was taken in the fall. This is a new feature and students and teachers are still getting used to how this works. Not many students chose this option.


Students worked diligently on one task each day. Some tried their hands at two. They then submitted a screen shot of their work for attendance and completion purposes. I’ll need to remind a few to turn in the assignments after break but that’s par for the course this year. With a few tweaks, I’m planning on using a similar style for the next planned asynchronous day.

Digital Check-ins

During a normal school year (all in-person) I interpret non-verbals and try to check-in with students frequently. I stand by my classroom door and give eye contact to students as they walked in and ask how they were doing. Sometimes students stop and tell me about their adventures or something that happened over the weekend. One of my goals was to have students talk more than me. The same check-ins would happen as students leave the room to head out to their next class. I believe these small moments overtime helped students connect to the classroom. Soon, students would share with one another about their lives and the classroom community builds from the ground up. A feeling of familiarity develops and students are more willing to take mathematical risks in the classroom. This organic process is more challenging when some students in your class are remote and others are in-person.

This year my school has been switching back and forth between remote and elearning. Tomorrow marks the third time this year that everyone will be remote. As or right now it looks like everyone will be remote until January, but that could change. My check-ins have had to take a different form this year. I call them “meet and greets” but they have the same premise. Every class starts with a meet and greet question or activity. It takes around 5-10 minutes and most days if feels like it is worth every minute. Here are a couple options for digital check-ins.

1.) 100 Prompts. I tend to get the questions from this shared spreadsheet.

Some of the questions are real gems, while others do not quite fit yet. This year I have used questions from this sheet around 50% of the time.

2.) Images. My students tend to get a kick out of these images as they are dramatic and some are related to pop culture. Students tells me what number they are and why.

I have found students open up and I see them laughing a bit as we progress through this meet and greet. So far my class has completed a cat, squirrel and baby Yoda. Twitter seems like the place to find these images by typing “on a scale how are you feeling” in the search bar.

3.) Desmos. Desmos has an amazing array of starter screens. My kids enjoy the robot and create a pumpkin activity. I think they could have spent more than 10 minutes creating their own pumpkin.

I tell the students ahead of time that this will be shared with the class and I turn on the anonymize filter if one or more students want the info to be kept private. I have not had a chance to use the data collection decks but they look promising. I am planing on using the Silly Warm Ups at some point next week. I am anticipating some amazing responses for the giraffe slide.

4.) Zoom. This is probably used the least, but using the Zoom private chat function has its benefits. There are times where I ask students to tell me how they are doing and to send me a private message in the chat. This has worked well for issues that happen in the moment. For example, a student told me that a family pet passed away. That awareness changed how I interacted with that particular student and was helpful when I followed up with them later. Just make sure students (and the teacher!) uses the private chat and not public.

Digital Fractions

My third graders started to explore fraction concepts last week. It has been a challenge as usually fractions are introduced with physical area model manipulatives. I usually take out the fraction circles and general pattern blocks for the introduction. That’s out of the question this year so I’ve had to rely on digital means.

I started the unit by reviewing fraction area models with a Desmos task. Students identified parts of a square.

The deck gets more challenging as it progresses. I was able to get through slides 1-11 with students. Slides past that could certainly be used but I’ll probably revisit those later in the unit.

From there I introduced students to linear models of fractions on a number line. Students identified benchmarks of quarters and halves on number lines. Students discovered equivalent fractions in area models and then transitioned that to number lines. Enter Desmos task # 2.

Students first start the task with a WODB slide where students analyze fractional parts. There’s also a beneficial card sort where students sort groups of equivalent fractions. The challenge questions in this deck are no joke. My class spent a good 15 minutes on the last two slides. Those slides helped contribute to a great fraction conversation afterwards.

During the next morning my students completed a GimKit to review the learning so far. The class also reviewed the notation for fractions greater than one whole. Students observed how the numerator can increase when the denominator stays the same. We also investigated how fractions are division and the quotient can be used to determine where to place a number on a line.

During the next class students completed a PHET simulation on fractions and area models. Students started on level 1 and then moved upward. The simulation can easily be added to a Nearpod presentation.

Most students ended up around level 4 + before time ran out. Later in the day students completed a Khan Academy quiz on fraction models. This quick check-in was valuable as I was able to quickly gauge where students were in their understanding of equivalent fractions.

During the next day students work on placing fractions on a number lines – enter Desmos task 3.

Students placed the fractions on the line and checked to see how close their estimates were to the actual answers. This gem of an activity gives students an opportunity to self-check and this deck was used over two different days. Students reflected on their progress in class during a debrief process.

On Friday students finished up their week by completing a fraction polygraph with different partners.

Students asked questions, used math vocabulary and a bit of detective work to find the correct cards. This was challenging for some kids as it highlighted who had an adequate grasp of fraction benchmarks.

I’m looking forward to diving into fraction concepts even more next week.