## 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.

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.

## 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.

## Uncharted Waters

I’m expected to report back to school this Friday. I received an email last week indicating a packed full week of professional developing that’s divided into synchronous and asynchronous sessions. One part of me is glad that teachers have six (we usually have less) days to prepare, but there’s another part of me that knows that this year will be unlike any other. As I review the detailed agendas I’m starting to mentally put together how a schedule will look once my school starts to meet face-to-face. As of right now (and this could change), my school will start on 8/24 with elearning for everyone and then transition to a hybrid AM/PM model at some point in September. The hybrid model emphasizes the need for face-to-face instruction for language arts and math instruction. I was given a sample elementary plan and it’s in draft form. The sample plan indicates that there’s approximately 50 minutes designated for math daily and my classes will most likely be split ideally with around half the students in the morning and half in the pm. I feel like the stars will have to be aligned to get exactly half of the kids as I believe the plan for AM/PM depends on bus routes.

I’m trying to make the best of this unusual situation. My classes will be much smaller and it looks as though I’ll be teaching the same lesson to my AM and PM classes. I’ll also be responsible for teaching students that have opted for elearning. I’ll have less time with each class than I usually do. During a usual school year I teach my math students for 60 minutes daily. That time will be reduced so I’m wondering how that’ll impact the structure of my classroom.

Generally, I start all of my math classes with some type of math routine. That usually eats up a good 5-10 minutes of class time. It’s a high-quality math appetizer in my opinion so I’ll probably keep this structure or transform it into a digital activity. After the routine students are introduced to some type of math task where they work in groups or partners. The class then reviews the results and I work through a few guided problems with the document camera. By that time the class is just about finished and we have a closure activity that involves some form of an exit card.

I’m assuming significant changes as my school moves into a September hybrid model. I’ll most likely be using Nearpod for synchronous lessons so the elearning and face-to-face students can all be on the same page. I’ve been an avid Nearpod user for the past few years so I’m familiar and have already tinkered with a few of my lessons for the first couple days. I’ll also be incorporating more Desmos tasks this year. During elearning I was able to leverage Desmos as one of my main tools to help offer students ways to show their thinking and to review past concepts. This year I’d like to introduce concepts through this platform. I’m excited with the steps that Desmos has taken over the summer to help teachers prepare better math lessons with feedback and check-in options. I’m also planning on using Google Quizzes (also known as a Google Form) more this year. Near the end of elearning I was having weekly digital quizzes as a replacement for paper pencil assessments. The auto grade feature was a win and I was able to provide specific feedback to students.

There are also some platforms that I still need to learn more about. Most of my students will be using Canvas this year. This is a shift since my entire school used SeeSaw last year and I had mixed results with that platform. There’s scheduled PD for Canvas next week and I’m hoping to come away with better ideas of how to use it to organize my classes and give students a better picture of what’s expected. I also want to dive into Edpuzzle. The #Mtbos community has had nothing but great things to say about the platform. From what I’ve heard so far you’re able to take a video and place questions in specific parts to help with comprehension. You could even embed sample questions related to the topic being discussed in class. I’m assuming these will be completed asynchronously. I need to also explore Loom a bit more. Similar to last year’s emergency elearning, I’d like to create instructional videos. My students found the videos useful when I introduced a new skill. Loom allows a small circular picture in the corner where students can see my wonderful face as I create the video. I think this is beneficial and adds a bit more of human element into the video.

I have a big picture view of what’s going to happen at the beginning of the school year. I’m sure the details will be fleshed out in the next few days, but I still have questions. My questions are more related to how to safely come back into school to meet students face-to-face and how to engage students simultaneously online and in the classroom. This has caused some anxiety over the last couple weeks. This will be answered in time and may even be decided for us as the county health department directs. I’m looking forward to teaching students math, whether that means seeing them in a Zoom session or face-to-face. This Fall won’t be like emergency elearning in the Spring, but it’s still uncharted waters. Let’s set sail.

## A New Normal

Last week all of my classes spent their time at home.  They participated in “eLearning” by  visiting a district website, picking their grade level and choice board activities.  Most of the feedback from the community was very positive.  The kids were engaging in content and the choice element was a bonus.  This week we have spring break and I’ve spent a good amount of time outside and away from school work.  I went on a walk outside this morning and ran into many different chalk drawings.  The kids can’t wait to get outside and return to something normal.

As we’re mid-week now, I’m noticing a couple trends.  We still don’t know how long this pandemic is going to last.  Right now school is supposed to resume on April 8th, but that doesn’t seem feasible.  Some districts have closed their doors for the entire year and have gone straight to eLearning.  I’m looking at you Virginia and Kentucky! State testing has been abolished (okay, more like canceled just for this year). Some states have pushed their soft opening date later down the line even closer to the end of school. More will probably follow, but that’s the current status until we get more information from the state of department of education.  The stock market continues to wildly change and the ticker at the bottom of the televisions indicate the new pandemic numbers.  It’s stressful.

Looking forward there are some things that have become apparent.  I’m going to go out on a limb here and say that as a country, I don’t think we were prepared to teach solely online with eLearning (more like emergency eLearning). Many districts scrambled to get devices into students’ hands in order to send them home for a prolonged period to time to be determined later.  Immediate etrainings and putting together lessons/resources were quickly slotted on agendas and superintendents sent out mass communication emails indicating safety and learning.  For the most part and from what I’ve observed, administrators have done a stellar job in keeping staff and parents informed of what’s happening even though the news is changing so frequently. I’m finding that updates are pushed out and emails are read a bit more critically nowadays.  A “high importance” email has become more of the norm lately. Next week my district will begin it’s second week of eLearning.  It’s not all rainbows, but I believe the first week was a success and I believe we’ll build on that and offer more ways to transition instruction online.

Teachers are often expected to be flexible and pivot as needed.  Fire drills, assemblies, loud speaker interruptions, weather delays, and many other instances highlight the flexibility that teachers often exhibit as they pivot their instruction and make decisions  quickly.  The type of pivoting is now different.  Teachers are now sent into this online world where the expectations are different. Some teachers take to this better than others, but it’s different than what most are used to.  Instead of using educabulary like essential questions and mastery objective, teachers are figuring out how to use Zoom and SeeSaw. Teachers are relying on each other to figure out how to make this situation work. The learning curve is high and teacher are rising to the challenge. Right now differentiation and feedback look different and priority is given to issues regarding access and opportunity. We don’t know how long eLearning will last this year, but I’m fairly confident that it has added to our skill set and has made us better educators in the process.  Ideally, I’d rather be in the classroom and be with my students as we explore pre-algebra concepts together.  I want to be able to see them as we explore functions and algebraic expressions.  I’m a bit anxious even thinking that school might be online for the rest of the year (hoping that doesn’t happen) as I wasn’t able to say goodbye to the students that I’ve looped with over the years.  Regardless, the cards have been dealt and educators and school are working for the best outcomes. We need to make the best of it whether it’s online or in person.  I’m optimistic for the next transition as we reach students through a different medium.

## What’s My Rule?

My third grade class ended their unit on data analysis and computation last week.  We’re now onto our next adventure of exploring patterns and number rules.  This last week the class started to identify number patterns.  The class observed how they could develop rules to find the perimeter of connected squares.  This was a bit of a challenge because students had to combine two different operations to find the actual rule.

We used this activity that I discussed a bit more in detail last year.  They looked for consistency and investigated with trial-and-error what the “rule” might be.  The class used a Nearpod presentation to see how a function machine transforms numbers.

Eventually the class moved towards creating their own rules using dice and a whiteboard.  It was during this time period that students started to dig a bit deeper into how rules impact a table.

One issue came up with the consistency of the numbers on the “in” side of the table.  A few students were confused with the idea that numbers didn’t necessarily have to be in order on the “in” side of the table.  A few examples helped address the issue but I thought it was interesting as most students are so used to a specific 1:1 scale.  I wonder if this is something that’s emphasized more at the second grade level and it just continues with our third graders.

Later in the week I brought out a digital function machine.  The kids had a great time placing numbers in and watching at they transformed into something different.

I highly recommend the PheT simulations. Feel free to check out other simulations that they’ve developed.  Next week the class will be working on creating and identifying true or false number sentences.

## Data Landmarks and Spreadsheets

My fourth grade class reviewed data landmarks this week.  On Monday the class explored examples of the maximum, minimum, median, mean and mode.  I had to review the terms multiple times throughout all of Monday.  Kids kept on asking about the difference between median and mean.  During this process I was finding that students needed additional practice with the terms.  They seemed to need another way to remember the difference between the data landmarks.  After contemplating a few different review lessons I decided to check out my school’s laptops.  I vaguely remember reading about a teacher that used spreadsheets to reinforce math terms.  I decided to go that route for Tuesday.

So Tuesday arrived and students received their laptops.  I modeled the different components of Excel.  This took more time than I thought it would.  I reviewed the idea of a cell and the components of a spreadsheet.  During this time I had a lot of hands fly up in the air with questions.  The questions revolved around how to change the column/row size, what a cell is, where’s the formula bar and many others.  To get the ball rolling I had the students take some personal data and use it for this project.  The class formatted the spreadsheet and we were about ready to start putting in formulas and then … class ended.

We started back up on Wednesday and began the lesson by explaining how to use formulas in Excel.  I modeled the first formula of how to find the maximum of the data set =maximum(b2:b14).  Students followed the example with their own data.  We then moved on to minimum, which they easily constructed.  Median and mean were a bit more challenging but the students explored and found the formulas using the first example. The magic started when students were asked to manipulate the data in the non-formula cells.  Students started to observe how the data landmarks change when the data changes.  This sparked a classroom conversation on the difference between the mean and median and which indicator might represent the data better.

Afterwards, students were able to print out their creation and take it home.  The class will be discussing this in more detail next week.

## Minecraft and Math Strategies

A few weeks ago my students started using MinecraftEdu during math class.  You can read about our first experiences here.  I used a similar activity with my fourth grade students this Friday.  Students were expected to build a house in MinecraftEdu.  Students followed these instructions.  During the process students will be practicing measurement skills related to fourth grade  math standards.

Additional components were added to the project.  Instead of working in teams, students built their own houses.  I also added blanks for students to show their number models and other information.  What I found more interesting this time around was the strategies that students seemed to use.  Students started with the first direction:

Students tried a number of different strategies.  Some students started laying out blocks in a square pattern and decided to multiply that measurement by four.  Other students created a rectangle and then eliminated blocks to match the measurement.  I would say that the majority of students had to use trial and error to create a perimeter that matched the criteria.

Some students decided to create dimensions that met the area criteria first and then addressed the perimeter.  Almost all the students had to break blocks and change what they originally made.

Students then started to create the height of the house.  About half of the students started by creating pillars.  The pillars stopped at a height that students determined.  Students then filled in the pillars, added in windows, created a door and double-checked their measurements.  Students then started to work on designing the inside of their houses.

Next week students will revisit this project and continue to work on the interior.  At some point roads or paths will be created to connect this community.  Additional math skills will be added as the class continues to create this virtual math world.  I can see angles, volume

## Coordinate Grids – Part Two

Last week my students started to plot points on coordinate grids.  They were identifying different quadrants and becoming more confident with drawing shapes on the plane. While reflecting on last week’s activities I noticed a Tweet that was sent our replying to one of my blog posts.

I’m a rookie when it comes to Desmos.  Most of the stories I hear involve middle or high school students. I needed to find something that worked with my elementary kids.  So I started to research and did a little bit of exploring to see how this could be used with my third grade class.  I ended up looking up some of the templates but had a bit of trouble finding an extremely basic rookie-like coordinate plane activity for my students.  I decided to go the route of creating a template and having  students manipulate created points for a project.  Click here for the template.

I quickly found that students had no idea how to use Desmos.  I gave the students 5-10 minutes to orient themselves.  Students were asked to move the points to certain coordinates  on the grid.  As they moved the points students started noticing that the tables on the left side of the screen changed.  Students started connecting how the tables changed and this helped reinforce concepts learned last week.  After this introduction time, students were given a rubric that contained the following:

• Move the points on the grid to create two angles
• The angles need be located in two different quadrants
• The angles need to be acute and obtuse with arcs located in each one
• Indicate the measurement of each angle

Students were then given 15-20 minutes to create their projects.

Students created their angles by moving the points around the grid.  Students then shared their projects with the class.

Students took a screenshot and then added the degree measurements to the angles.  The class reviewed the projects and students explained how they plotted the points.  This project seemed to help students make the connection between points and the x and y-coordinates.  It also reinforced skills related to angle classification and measurements.  I’m looking forward to expanding on this project next week.

## Exploring Coordinate Grids

My third graders started to explore coordinate grids this week. For many, this was the first time that they’ve used them. Some of the students have played Battleship or some other game that involves a grids.  Playing off that background knowledge, I used a road map to show how people can find certain locations by using a coordinate grid. This made sense to some of the students but a few still were unsure of what axis was used first to determine where to plot a point.  This was a reoccurring theme throughout the lesson.

During this process I remembered a strategy that another colleague suggested a few years ago. She borrowed the idea from another teacher and it seemed to work well in her classroom. A colleague of mine used (3,2) as an example of the “go into the building” – first number (right 3) and then “go up or down the elevator” (up 2) method. I decided to use that strategy and a few more students started to grasp the process.  The next activity in the paragraphs below seemed to solidify a better understanding for the rest of the class.

Earlier in the day I created a very short Nearpod lesson involving mostly pictures of coordinate grids. I handed out a iPad to each student. Students logged in and given a picture of a grid and asked to draw and label points.

I then revealed the pictures to the class on the whiteboard. The names of the students were hidden so that we could analyze each response without throwing judgement lightning bolts towards a specific individual. As the class went through each picture they started to notice trends.

• Some were switching up the x and y-axis numbers
• Some were not creating a point
• Some were not creating a letter for the point
• Some were confused by the negative sign in front of the numbers

Students observed these issues from the first question and grid. After a decent discussion on the above trends, the class moved towards the second grid and question. I gave the students that same amount of time and the results seemed to initially improve.

Students started to become better at finding their own mistakes before submitting their creations. I used the same strategy as earlier and displayed the results to the class. There were a few that had some of the same misconceptions, but not as many. In fact, many students vocalized the class improvement since the last question. One of the evident misconceptions revolved around students having trouble plotting negative numbers on the coordinate grid. The class discussed this and completed the third question and grid. The student responses from this question were much better than the prior two. Students were starting to develop some true confidence in being able to correctly plot points on a coordinate grid. I kept a list of the trends that students noticed and will bring it out later in the unit as we’ll be revisiting coordinate grids next week.

After our Nearpod lesson (which was about 15-20 minutes) students played a Kahoot on identifying points on a coordinate grid. I felt like this was helpful as students identified the points and were able to gauge their own understanding compared to the goal.

## Minecraft and Math

Earlier in the school year a group of three teachers at my school wrote a grant expressing the need to incorporate Minecraft in the classroom. The idea actually started last summer when a colleague and I attended a professional development event in Downers Grove. During one of the sessions I met two teachers from nearby school districts that used MinecraftEdu in a school club. What they had to say caught my interest and two other teachers and I decided to start a school club in 2016. We wrote the grant and it was accepted. Last week the licenses were purchased and I’ve explored the potential of using the program in the classroom setting.

Before the school year started I knew very little about how to use Minecraft. I decided to purchase a copy and explore the Minecraft world over the summer. I quickly learned the controls and watched a number of YouTube videos to become a better rookie. I’m still a rookie. I found the MinecraftEdu community online and started posting questions to the forums. Moderators answered my questions and I started feeling more comfortable using the program on my own. The forum has been especially valuable in giving me ideas to use in the classroom.

I downloaded a few world templates and started brainstorming. I then bounced a few ideas off of colleagues and decided to start using the program for a math scavenger hunt. The goal was to have students get used to using the program in an education setting while reviewing fraction math concepts in the process.  Most students already understood the controls and the game but weren’t used to using it for a different purpose.  I wanted to start simple and I thought a scavenger hunt would be an easy way to start incorporating the program in my math class.

Math scavenger hunt – third grade

Students entered into the fraction world that I created.  Once they entered into the world I froze all of them. I explained the goal of the world and answered questions. The goal was to explore the world and find the signs that were posted. Students were using the MinecraftEdu version where they weren’t able to build or keep inventory of items. Trap doors, caverns and bridges were all part of this simple world. Each sign had a particular math problem on it and students were expected to solve the problem. I then passed out a sheet that went with the scavenger hunt. The sheet had spaces for students’ number models and solutions.

I then unfroze the students and they were off to the races. Students split up and started exploring the area. They soon found that working in teams seemed to be more efficient in finding the signs. All students were finished with the scavenger hunt in 30 minutes. Afterwards the class reviewed the answers.

House building – fifth grade

I created a completely flat Minecraft world for this activity. Students were grouped into teams and given a task related to concepts that we’ve been discussing. The fifth grade class has explored area and perimeter and will eventually be investigating volume in January. Each group was asked to create a building that met a certain criteria. It was stated that each Minecraft “block” was exactly 2 feet on each side. Those measurements were used to meet the criteria.

Students worked together and started building their houses. A few groups had to restart as they found out that the perimeter and area didn’t meet the criteria. After around 30 minutes students are about 50% complete with their houses.  I’m assuming that another 30-40 minutes and the students will be finished with their projects.  At some point after break the class will be presenting their buildings to the class.

In January my school will be offering a Minecraft club to around 25 elementary students. We’re planning on building our actual school from scratch using some type of scale model. The students are already excited to be using this program in school and I’m looking forward to what students create and the process involved in that creation.