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I wanted to let you know about an upcoming free online course offered by the Park City Math Institute:
Online Course: Geometry Transformed!
Dates: November 7 – December 5
Description: A five-week course for teachers who want to deepen their understanding of transformations in plane geometry and who seek examples of how rigid motions and dilations and their combinations can be presented in the classroom.
For more information, please visit http://mathforum.org/pcmi/outreach/#two. Please contact Gabe Rosenberg at firstname.lastname@example.org with any questions.
Don’t forget to RSVP for our next Math Teachers’ Circle Meeting on Monday, October 16th 6pm-8:30pm at Trinity Christian College.
Please consider joining us for an evening of collaboration and hands-on problem-solving guided by college faculty members and fellow practicing mathematics teachers. Math Circle Meetings are designed to meet the requirements for Professional Development Hours and dinner is provided so please RSVP here: http://bit.ly/mathCircleOct2017
At the MTC meeting in September, we investigated the symmetry within certain shapes. We started with a discussion of the symmetry groups Dn and Zn and discovered many shapes which have these symmetry groups (using physical shapes). Then we were interested in finding out whether the angle between intersecting lines of reflection determine what the resulting symmetry groups are (whether it was Dn or Zn or neither).
We tried to investigate this by drawing two intersecting lines and trying to create images which were completely symmetric about both of those lines. This involved folding across those lines and drawing the reflected image across that line. Then doing the same across the second line. It turned out we had to keep reflecting across those two lines over and over, but eventually it seemed that the image got back to where it started (which left us with perfectly symmetric objects).
After some careful consideration, we found that two reflections (across the two lines) produced a rotation which was twice the angle between the lines of reflection. We also found that the number of reflections it took to get back to the start depended on the least common multiple between the angle between the lines of reflection and the angle of rotation.
Even more interesting, some participants found that the process ended early when their shape landed on a line of reflection, so we started to ask why that might happen. Finally, everyone was provided with some extensions on how this activity could relate to least common multiples, geometry (and proofs in geometry), discussions on error and cumulative error, and more.
Remember to join us for our next meeting, Monday, October 16th 6pm-8:30pm at Trinity Christian. Dr. Peter Tingley will be leading a topic called, “Frogs and Toads: An exploration of problem-solving.” RSVP Here:
Don’t forget to register for the upcoming Math Teachers’ Circle session to be held on 09/18 at Lewis University. We’ll be exploring symmetry in shapes!
We had great fun exploring rich mathematics during our August Workshop!!
We started the morning working on Freeing the Clones which led to a discussion about the concept of infinity and productive struggle!
Later we learned about using “Exploding Dots” to visualize and understand arithmetic in multiple bases and polynomial algebra!
After lunch, we introduced Hexaflexigons and made some of our own!
We had fun doing the Conway’s Rational Tangles dance as our last session which brought us back into discussions about infinity!
We ended the night with dinner and discussions about inquiry-based learning, promoting growth mindset, incorporating classroom activities, and facilitating group work!
We especially want to give special thanks to our sponsor Duane Walker, in memory of Mary Anne Walker, who made this workshop possible. Mary Anne Walker, who passed away in 2012, taught at Jefferson Junior High School for 10 years and Romeoville High School for 25 years. She shaped and influenced countless lives of young people, and those efforts continue through support of this workshop.
Happy summer everyone!
Remember to RSVP for our Free Math Teachers’ Circle Workshop on August 2nd 9am-7pm at the University of St. Francis in Joliet, IL! This is a great way to get ready for the next school year and earn lots of CPDU hours!
Interested in getting learning strategies to make courses more interactive through modeling activities? How about if we add CPDUs and a stipend to the deal? Check out this workshop at Lewis University. Space is limited so please register here: https://goo.gl/forms/Rmswyj8KEXHmMpqh1