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The Southwest Math Circle had the privilege of having Dr. Peter Tingley of Loyola University Chicago lead our October 16th Meeting at Trinity Christian College.
Peter first had us do a warm-up problem to start a conversation about strategies for problem-solving.
When faced with a problem, Peter gave these problem-solving tips:
1) Do something.
2) Do something else.
3) Learn from what goes wrong.
4) Do an easier problem first.
We then started our session with a problem with frogs and toads. The question was proposed as follows: A 5 by 5 grid is arranged as in the picture below. The frogs can move to the right or down or jump over toads in the same direction. Toads can move to the left or up or jump over frogs. The goal of the game is to have the frogs and toads switch sides on the board.
We had a great time solving this problem and found that the strategies to problem-solving we had discussed earlier really came into play.
In working on the problem, we decided that we needed to add one more thing to our problem-solving list:
5) Don’t stop just because you solved the question!
We hope you will join us for our next session on November 20th at Saint Xavier University. Please RSVP here: http://bit.ly/MTCNov2017
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.
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.