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.

Desmos

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.


 

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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.