Box Plots and Spreadsheets

One of my classes has been exploring box plots and data landmarks lately. Earlier in the year the class created histograms and found data landmarks on line plots. Box plots was not as easy as a transition as anticipated. There were a few roadblocks as students analyzed and created their own box plots while determining Q1 and Q3. Some students picked up on the concept quickly while others took more time. To help reinforce the concept I thought about bringing in a spreadsheet activity. I have been using spreadsheets quite a bit this year and it has been another medium in which students can experience statistics.

Students were first asked to create a question that they would be asking the class. The numbers could range between 1-51. I gave students free rein on what questions to ask and held my breath.. Here were a couple of the survey questions:

  • What is your favorite number between 1-51?
  • How many hours of sleep do you get per night?
  • On a scale of 1-50, what do you rate a cheese burger?
  • How many movies have you watched this year?
  • On a scales of 1-50, how well do you like dogs?
  • How many digits of pi can you recite?

Once students created questions they went around and surveyed everyone in the class. I gave each student a roster list so they could check-off who answered This took a good chuck on time – 10-15 minutes. Once the data was collected students grabbed a Chromebook and copied a spreadsheet that I had pre-populated.

Students took the data from the survey collection sheet and transferred it to column A. The data landmarks in row three were placeholders and awaiting formulas. Students then entered the minimum, median, maximum and mean formulas. They were familiar with those formulas as we explored them earlier in the year. I discussed with the class about quartiles and we put together a formulas for Q1 and Q3. We made predictions of what the vertical box plot might look like before finalizing. Students then entered the formulas for the quartiles and analyzed the box plot to see if it matched the data.

It was interesting to hear the conversations that students had as they compared the data to the box plot. The class had a discussion about interquartile range and variability. It was time well spent. From there, students shared their spreadsheets with me and I took a closer look to see how the data matched and if the correct formulas were in the appropriate places. Students seemed to grasp the concept fairly well. Feel free to use a copy of the spreadsheet by clicking here.

During the next day the class reviewed box plots and the spreadsheets that were created earlier. Students then complete the Desmos task Two Truths and a Lie. This is one of my favorite tasks for students to discuss box plots and use math vocabulary while doing so.

The spreadsheet and Desmos task took about 2-3 days to complete. The class took a unit assessment on Friday and I will be checking out how they did over the weekend. I put these two activities in a digital folder for next year.

Dividing Decimals and Spinners

My students have been exploring decimals for the past week and a half. The class identified place values, rounded and placed digits up to the thousandths on number lines. While looking for ideas I came came across Erick’s response to my Tweet about decimal division. After reading Erick’s post, I delved a bit deeper into how to connect the activity with my upcoming standards related to decimal addition/subtraction and long division. I did not have the connected blocks needed for the activity so I asked the kindergarten teachers. Fortunately they had a few boxes that I could borrow. Some of the already connected blocks were stuck together. Trying to pull them apart the first time took Hulk-like strength (as one of my students mentioned). I then put together a few questions for students to follow as they progressed through the task. The questions were placed in Canvas and formatted as a quiz with image uploads.

I randomly place students in groups of 2-3 . Each group was given a bag with 15-30 blocks.

The groups were given around 10-15 minutes to create a prototype. Groups used trial-and-error to figure out what helped the top spin more effectively.

I found out quickly that not all snap-cubes are created equal. The one on the left in the picture spun longer (I think it was 5x) than the right. Since this was not considered a competition I do not think it mattered to much, but this is something to consider moving forward. Students then went into the hall to find a flat surface and timed the spins and recorded it on their sheet.

Groups then added the trials together to find a total.

Students were then asked to find the average time for the trials using the long division algorithm. Based on the student responses, this seemed to be the the most challenging part of the task. Most groups estimated the quotient first and used that as a baseline. Students then used long division (they are used to using partial-quotients) to find the quotient and remainder in decimal form. They were required to round to the nearest hundredth during the process.

Some groups were required to round a repeating decimal, which was a new skill for them. Groups then shared their spinner with the class and the strategy that was used during the creation process. I was impressed with the different models and the teamwork that was demonstrated by most groups. This is a task I am planning on trying out again in the future.

Major kudos to Erick, Jen and Mike for the ideas!

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.

Four Weeks Down

Students finished their fourth week of school yesterday.  Routines are fairly established although there have been interruptions with students quarantining during the past two weeks.  Flashes from last year have been making appearances in classrooms as teacher navigate working with Zooming and in-person students at the same time.  I’m hoping this is temporary but no one has the confidence to say that’s the case.  When students remote into a classroom it changes routines and impacts more that what I can write here.  I’m moving forward and attempting to find lemonade in the situation. Looking back at the last month I’ve found ways to engage students differently this year compared to last school year.  This post highlights two of those instances.

Fortunately, this year my students have been able to work in groups. Words can’t express how big of a game changer this is and what a loss it was last year. Breakout rooms were a poor substitution. I’ve been utilizing whiteboards and math stations throughout the classroom.  While students work on tasks I bounce from one group to another to ask questions and to gain an understand of students’ thinking.  During the last few weeks I’ve been reading through Building Thinking Classrooms have been using some of the strategies found within. Being able to give feedback through questioning at the stations and hearing the students’ responses impacts my next steps as a teacher. I’d like to expand the time at stations a bit more as the year progresses and as social distance policies evolve.

Another strategy that seems to be working this year relates to how students interact during brief math conversations. Students are often given a daily math task or question that’s designed to encourage dialogue. Students take turns discussing the strategy or steps involved in attempting to solve a problem.  While one student is talking the other student is giving non-verbal cues that they’re actively listening.  Students are then brought back to the class as a whole group.  I visibly randomly pick students to share what their partner said during that time.  The student that is picked doesn’t offer their opinion about what the partner stated although the strategy is discussed as a class. I’ve used this at least twice every week since school has started and have noticed that students are listening better in their groups. Another bonus is that students are using the strategies that they hear from their partner/class.

I’m hoping to carry both of these strategies forward as the year progresses.  

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!

Considerations for the 21-22 school year

In about three weeks my school starts back up again. I have been told that this upcoming year will be different Last year many school started completely remote and then eased into hybrid as the year progressed. I am assuming there will still be some type of social distancing and masking involved for this year, but it depends on many factors. The next school board meeting along with ISBE guidance will most likely lay the groundwork for what will happen during 21-22.

As I think about August I am tempted to plan out the school year as if it everything is heading back to normal. We are still in a pandemic and our schools should keep that in mind when planning. There are a lot of vocal opinions about masking, vaccines and social distancing that may impact what happens. Instruction last year shifted towards a mostly digital model and my hope is that we do not give up on using instructional components for the new year. Some students experienced success with that model, while others did not. Other students struggled with remote learning and could not wait to get back into the classroom. I would like to believe that schools can and should blend what worked with elearning with the benefits of being back in the classroom. It is not a simple transition and requires additional thinking, but something to consider for August.

Summer Thoughts and Takeaways

This summer has been different compared to other years. Certainly different than last year when everything was shut down. I think the hectic pace of this past school year has many educators taking a break from school related work. Instead, they are focusing on other activities. Being outside, reading, cooking, gardening and other tasks have taken the place of planning for the new school year. I think this is a good thing. It is unfortunate but not shocking that many teachers left the profession last year. Teacher burnout is real and educators need time to decompress after the 20-21 year.

This summer I have taken a step back from working on creating /editing my Desmos decks and planning school tasks. I have not touched google slides and my school backpack remains closed – at least for now. I am taking a stats class this summer and learning something brand new. Feeling the struggle of learning something new is refreshing in a way and a good reminder of what students go through when new content is introduced. Even with the stats class on my plate, I am able to prioritize taking time for other activities. I have been able to read for enjoyment and work in the yard more this summer than I have in the past. My book list includes American Dirt by Jeanine Cummins (highly recommend this book!), A Promised Land by Barack Obama, and am taking recipes out of The All-purpose Baker’s Companion. I have not learned how to make sourdough like many of my colleagues, but my skills are improving.

The last few weeks have been refreshing. I have limited the amount of time on social media and have focused more on less tech-related activities. I still check-in, but am enjoying the outdoors when the weather cooperates. The last three weeks have me thinking about how teachers should have a work/life balance for the 21-22 school year. I don’t think happened last year. I feel like educators are more productive emotionally and physically when they are able to manage and balance their responsibilities.

Although it will be much different, there may be certain aspects of the 21-22 school year that will continue from last year. I am assuming that this upcoming school year will minimally resemble last year. We are still awaiting guidance from the state on social distancing requirements and masks. Will there be remote classes? Will social distancing still be required? What about sharing materials or the new variant? So many questions and not enough answers. It is still not going to be a typical school year, but that is okay. It is all about balance.

Let us grab a few self-care takeaways from the summer and use them when school starts back up in the fall.

New Learnings and Insights for Next Year

Back in May I decided to register for a college level statistics course. I decided this for a couple reasons: 1.) The credits could be used to receive a teaching math credential that will be useful in the future 2) I have always enjoyed analyzing school/student data as it relates to different types of assessments. I did not take the class in high school or college. A few of my graduate school classes required me to analyze data and set goals based on certain criteria but nothing was formally titled education statistics. I would characterize myself as a rookie in the stats knowledge department. With that being said I do not remember that last time that I took a non-education college level class. Near the end of May I confirmed my registration, purchased a textbook and found a used TI-83 calculator on marketplace.

The class is from a nearby community college but I opted for the “anytime” class as it work better with my summer schedule. The class started at the beginning of June and ends close to August. It is the first time experimenting with an “anytime” class so I was not sure what to expect. I was pleasantly surprised to see that the class was in Canvas (that’s what we used in school!) so I already knew my way around the platform.

The class opened up last week and I took a gander and what was inside the modules. The class has 11 multiple choice quizzes that you can retake up to three times. I am a fan of retakes, but you have to retake the entire quiz and not just the questions that you had incorrect. I am planning on giving feedback on this after the course has finished. There are lecture notes and power point slides for each chapter. Besides the quizzes, there are also Excel and TI calculator assignments, a mid-term and final exam. Old school are the two words that came to mind after reading the syllabus.

The assignments open and close on certain dates so you can only go ahead so far. This is not a self-paced course. Last week I read chapter one and completed the quiz. Many concepts were new to me and I had to retake the first quiz. Before the second attempt I took out the highlighter, reviewed the concepts online and found a few Desmos AP stats decks that were about the chapter. The second time was better but not by much. I decided to move on and not dwell on the need to chase a perfect score. As the class continued I took an additional quiz and performed better but still did not feel like I was was thriving in this “anytime” class. I am learning new concepts and feel like I grasp certain skills better than others. I think part of this is due to the format of the course and most classes that I have taken are more structured with some type of in-person requirement.

After reading through another chapter today I decided to reach out to coach at the college. The college offers help through Zoom. I clicked on a Zoom link and was paired up with a tutor to help talk through some of the problems. We discussed the skills that I had questions about and some of the concepts started to make more sense. In more than a few cases I had a conceptual understanding of what the problem was asking and was able to estimate correctly, but I was not using the the formulas correctly. Go figure. It is usually the other way around in the classroom! I felt much better after the session and things started to click much easier. It was time well spent.

After the Zoom session I started to think of a few takeaways that might be applicable for next school year:

1.) Sometimes you need to talk with others to grasp a concept. Digital resources are pretty awesome for learning new things, but some topics that are much better in-person. In this class you get zero feedback with passive digital resources. For the quizzes I received a correct or incorrect. I had to debate with myself whether it was worth it to retake the quiz not knowing what was incorrect the first time around. With a human you can receive feedback and take action based on the communication. What is your retake policy?

2.) It can be frustrating when you do not understanding something after reviewing it multiple times. I wonder how our students feel in this same situation and what feedback/re-teaching opportunities exist?

3.) What type of support is given to students that have questions outside of class time? This happened quite a bit during remote learning.

4.) How do we normalize the struggle that occurs when a student does not show that they understand a concept after multiple attempts. Please do not say growth mindset.

5.) How comfortable are students when asking for help?

6.) How do students know what to expect when it comes to assignments and quizzes? What formats are you using? Communicating the format and showing students an example can help ease anxiety.

I am learning new skills and am finding the small wins during this journey eye opening. It has been a while since I felt the struggle of trying to learn something new that is not in my wheelhouse. I am looking forward to the journey telling my students about the process next school year.

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.

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