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.

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What’s the perimeter for three connected squares?

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.

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Click for presentation

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.

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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.

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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

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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.

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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

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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.

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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:

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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.

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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.

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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.

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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

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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.

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

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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

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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.

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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.

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  • 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.

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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.

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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

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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

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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

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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.

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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.

Students and E-portfolios

Student E-porfolios
Digital Portfolios

Last week my math students wrote in their math journals about their experience in math class so far.  Their entries were fascinating and many students documented their learning that took place since the beginning of the school year.  Some students drew pictures and wrote lengthy paragraphs indicating skills learned.  At the end of the class the journals were put back in their designated place in the classroom.  I looked over the journals and made comments.  Afterwards, I starting to think about what happens to these types of journals after they’re sent home at the end of the year.

What happens after a student receives back their classwork? The work is often presented in a number of ways: hanging up the assignment, placing it on bulletin boards, showcasing it around the school, or sending it home for refrigerator placement.  I’m not sure what happens after the assignment heads home. Optimistically, I assume that they’re kept forever, but most likely the assignment moves towards a recycling bin at some point.

I’m finding that the work that students complete is becoming increasingly digital. Regardless of how the work is created, it’s often captured and presented in a digital form. Student work that’s completed and presented digitally lives on.  Not only does it live on, but it can be seen by people outside of the school, state, or even nation.  For example, students might use base-ten blocks to show their understanding of how to add numbers together.  The end product, although it may be a physical representation, has an opportunity to be captured digitally and communicated to stakeholders.  Some school districts are finding that they can help showcase student understanding through digital means.

I’ve found that some of these same school districts have moved towards a student e-portfolio model.  This is much more prevalent at the middle and high school level, but exists in small pockets at the elementary level. In some cases, students have access to their own e-portfolio and they submit their work digitally. Over the past couple of years I’ve seen elementary teachers use Weebly, Google, Seesaw, and Showbie to have students submit their work digitally.  In turn, student receive feedback and document their learning experiences in the process.

A few teachers in my school are currently using Seesaw to have students’ submit their assignments.  Teachers need to approve the submissions and parents are notified that items are located in their child’s portfolio.  Teachers and parents can provide feedback to the students.  Students can even take that feedback and resubmit their projects as needed.

Silicon Valley has also paid close attention to how this is playing out. Learning management systems (LMS) are starting to become more of the norm as students and teachers become more familiar with how they work. As districts become more familiar with LMS, questions about student privacy and data collection should be addressed. Having an online student portfolio gives teachers, students, and parents opportunities to be transparent in communicating what’s happening in class. This type of student work evidence goes far beyond a classroom newsletter.  Being able to submit assignments and receive feedback digitally encourages learning beyond the school walls.  Submitting projects digitally also allows teachers to give feedback a bit differently.  Instead of writing feedback on papers, teachers can record comments verbally or record a brief video with examples.  Although I prefer to give feedback 1:1 in person, giving feedback digitally has its advantages. Ideally, the student e-portfolio would follow the student throughout a school district.

Back to my students’ math journals … so the next day I had students submit their work to their e-portfolios.  Through this action, students were taking their physical work and making a digital copy.  Parents were able to immediately check out their child’s work and make comments.  Some parents made comments, while others just view the work.  I’m not looking for interaction on everything submitted, but I feel like having that opportunity to communicate and the transparency involved is important.  It also can help initiate the “how was school” talk that happens when children come home from school.  Through the years the physical journals may stay intact, but the digital copy will always be accessible.  Having access to past entries can help students see the growth that they’ve experienced during their journey.

How do your students document their learning journey?