Exploring Fractions – Week One

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My third grade students started a new unit on fractions last week.  They started the unit by learning about part-to-whole fractions and how to identify them.  Student teams explored how fractions are represented in different situations.  One of the first activities asked students to create their own version of a part-to-whole model.  The scissors came out early this week while students cut out fraction area models.

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They compared the pieces within the area models to create equivalent fractions.  This gave students another way to compare and observe equivalencies.  This was time consuming activity, but so worth the time.  Students made connections and played around with the circles/pieces to compare the models.  The only negative was that some students didn’t cut the fractions exactly on the line so the pieces didn’t always line up.  The next day students compared the fraction pieces using <, >, or = signs.

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Students were making progress in comparing fraction area models.  The fraction circles were being used consistently and then the class moved to transitioning to identifying and placing fractions on number lines.  This was a challenge.  We started with a 0-1 line and then identified half.  From there students used benchmarks to compare fractions on line.  Students had some trouble when the number line was stretched from 0-2.  The class also explored how the fractions look on a vertical number line.  A different dynamic was at play there.  Students then practiced a bit more with an Open Middle activity.

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Students were given opportunities to discuss fractions with their peers through a few different fraction math talks earlier in the week.  The time spent today revolved around reviewing different fraction models. On Friday, the class participated in a fraction Desmos Polygraph activity.  Feel free to use the program here.  This was one of the learning highlights of the week.  Students were asked to pick one of the fraction models that they created early in the week, while other students asked questions to help determine the fraction.

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At first students asked questions related to the color of the fraction.  Then they moved to questions involving less than half and more than half.  Students found that clear questions revealed better answers.

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I was excited to see that students were using benchmarks and part-to-whole ideas to help uncover the mystery pick.  Students spent around 20-30 minutes exploring the polygraph with a few different partners.   I even snuck in as a participant.  I’ll be keeping this idea in my back pocket for next year’s plans.

Next week, students will start to add and subtraction fractions.  I’m looking forward to seeing how students will use the experiences this week.  There’s plenty more to this unit and we’re just getting started.

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An Elementary Desmos Journey

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During the past few months I’ve had a chance to explore Desmos.  I started seeing the platform on Twitter a while back through different educational chats.  It was prevalent in #msmathchat as well as in the EduTwitter math world.  I saw it across my screen, but didn’t really dig into how it could be used until NCTM.  During that time I attended a session titled “Which Comes First:  The Equation or the Functions?  Come Stack Cups and Use Demos to Find Out!” The session was presented by the University of California staff.

The session started out by having the participants sit in groups with a stack of styrofoam cups.  We were asked the question below.

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My table took the cups and started stacking them. They found the measurement of one of the cups and decided to use millimeters to be more accurate.  We came to a consensus and decided to extend the pattern and graph our pattern.  The presenters then asked us to head to a Desmos url where we could plug in our numbers.  The audience filled out this step-by-step sheet for the next 20-30 minutes.  Being a newbie to Desmos, I appreciated how the sheet guided us through the different components of Desmos and how it graphs the line as the numbers change.  The sheet also includes teacher directions that I found useful as I replicated this exact lesson a couple weeks after NCTM.

The second part of the session went in a different direction.

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Basically, we were asked to find out the option that would give us the most money during the next 14 months.  My table filled out this sheet and used this Desmos template to find a solution.  There was a lot of trial-and-error during this time and some perseverance, but it was a worthwhile journey.  Listening to others at my table was enlightening.  Hearing how other teachers, mostly at the middle and high school levels, gave me a different perspective.  Being able to find patterns and develop algebraic reasoning was at the forefront.  Using Desmos to create or check our predictions was helpful.  Moreover, I was able to learn more about the Desmos platform and how it could be used in my classroom.

Near the end of the session I started gathering all the links to save for later.  I started to think about how this could be used in my own classroom.  I began by using a few different tasks with my sixth grade standards.  The inequality activities were very helpful as I was becoming more familiar with the logistics of using Desmos in the classroom.  Desmos isn’t a math tool that’s used frequently in elementary schools.  The calculator included can be intimidating for elementary students as well the teachers.  Although, when my class first started using the platform my students were totally interested in wondering what all the symbols meant on the calculator.

During NCTM I was fortunate enough to come across Annie’s post on how to use Desmos in the elementary classroom.  I reviewed all of Annie’s examples and decided to graduate and move on to creating my own.  I started with copying a couple card sorts for a kindergarten and first grade group that I see four times a week.  The sort included having students put together base-ten blocks, written names, standard form, and expanded form statements.  The lesson went well and I had to intensely model how to login and ended up using a QR code for students to access the url on an iPad.

I then started getting used to how to create better questions using “what do you notice” or “what do you wonder” types of prompts.  About three weeks ago my third grade students needed to review polygons and relationships.  I decided to put together an original activity.

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Link

I ended up making the shapes in Illustrator and inserted them into the activity.   I used this task with a third grade group of students that were working on fourth grade standards.  Students worked in pairs as I didn’t have enough Chromebooks and iPads for everyone that day.  I used the pacing function and made sure all the students were on the first slide.  I love that Desmos includes that function as many of my students want to speed through an activity.  Stopping with “pause” to review all the different responses was also helpful.  This helped encourage a class discussion.

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At first I used the “anonymize” option, but soon found that students wanted to be identified.  Students used a similar prompt with a trapezoid and triangle.  I then went over a few different vocabulary terms before heading to the next slide.

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Students checked off the criteria that matched the shape.  I then displayed the correct solution and this led to additional questions and conversations.  When creating this I decided to look back at some of the most engaging Demos activities that I’ve used.  Most of them ended with some type of card sort.  I decided to do the same.

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I decided to have a “doesn’t have a match” column to increase students thinking.  It took a while for students to complete this as certain criteria worked with only one shape while other statements didn’t match any.  When I first created this I noticed that some of the statements that were created matched multiple shapes.  Ooops.  It was fixed before I gave it to my third graders, but that could’ve caused a few issues.  After around 10 minutes we review the answers as a class.

Screen Shot 2018-06-06 at 8.21.45 AM.pngStudents self-checked their work to see how accurate they were.  Some students didn’t actually match the statements completely.  They brought the statement to the column, but didn’t attach them.  I should’ve explained how to do this before completing the activity.  This happened with around three students.   The next time we completed an Desmos activity those students were fine and attached the statements.  There’s a small learning curve with these types of activities and this was one of those moments.

My next step is to learn how about the computation layer and possibly how to use it more effectively with my K-3 students.  I think it’d be great to be able to rotate or drag a shape on a coordinate grid.  Students could then use a digital protractor to measure the internal and external angles.   I’m also looking at how to use polygraphs more effectively next year.  My students had a blast using them during the last week of school. Maybe I’ll learn about that during the summer.  I’m looking forward to using this more with my elementary students next school year.

Investigating Inequalities

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This week one of my classes spent a good amount of time investigating inequalities and absolute value.  Both topics were brand new to students.  I looked around in my math files and decided that there might be a better way to introduce inequalities.  Students are familiar with number lines, math symbols and plotting points.  They weren’t familiar with extending points and graphing inequalities. So, while jumping around Twitter I came across a Tweet talking about a Desmos lesson related to this particular topic.

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I took a leap and decided to check it out.  You see, I’m a Desmos newbie.  I’ve heard many people within the #msmathchat and #mtbos talk about how it’s such an amazing tool.  I haven’t had a chance to try it out until this week. My school isn’t 1:1 and technology is used from time to time, but less frequently in math classes.  After reviewing the lesson and playing around I dived in and made a commitment to use the activity.  I borrowed Chromebooks from a couple other teachers and had a sample run before starting it up on Tuesday.

Students started off by plotting points on number lines.  They also made predictions of what their peers would place.  During the first day, students made it through almost all of the activity.  Students still had questions and they were answered as I paused the slides (I definitely like the pause function).  Near the end of the lesson I thought students were becoming better at being able to identify inequalities and match them to graphs.

The following day students finished up the activity with a WODB digital board.  It was interesting to hear their responses and reasoning behind them.

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On Thursday, students took their inequalities journey a step forward.  They were asked to complete an Illustrative Mathematics inequality task.  Students were given a situation where they needed to write two inequalities, graph them on separate number lines, and create a description.

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Students worked in stations, but completed each sheet on their own.  The students had some productive discussions during this time.  I have to remember to discuss the positive elements of this with the class after the weekend.  Students had to create a number line and then plot points where necessary.  They had to figure out if a close or open circle was needed and where the overlaps occur.  The only hiccup occurred when discussing the word between.

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Does the word between in this context include 37 and 61, or does it mean that it omits those numbers.  Students went back and forth on this issue and we had a class conversation about that particular topic.  Eventually, the class decided that 37 and 61 were included.  Students turned in the task on Thursday and I returned them back today.  Just a handful of students needed to retake the task, but it was mainly because the directions weren’t fully read or labels were missing.

Today the class explored absolute value and coordinate grids.  A test is scheduled for next Wednesday, but I could probably spend a lot more time on this topic.  The class will briefly investigate absolute deviation on Monday and complete a study guide on Tuesday.

I’ll end this post with a Tweet that made me think a bit about math instruction.

I believe “instructional agility” is necessary and teachers become more aware of this through experience.  Instructional agility can also lend itself to the resources and tools that are used in the classroom.


 

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.