The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

ESCHER #6: Exploration

(February 24, 2015)  Our last session.  One parent asked – as everyone was walking out at the end – “Did you come to a conclusion in your math circle?”  The answer was a resounding no.  This course was more of an exploration.  We often begin a math circle course with an overarching question.  This time, we had nothing other than…

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ESCHER #5: All About Assumptions

ESCHER #5:  All About Assumptions (February 10, 2015)  I brought in some soccer balls to continue our discussion about which regular polygons can be tessellated.  The kids discovered that the balls were a pattern of both pentagons and hexagons.  The question became “Why?”  Conjectures:  Roundness?  Size? Of course, since soccer balls are 3-D, they weren’t going to answer our question…

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ESCHER #4: Can Any Regular Polygon be Tesselated?

ESCHER #4:  Can Any Regular Polygon be Tesselated? (February 3, 2015)  The story of today’s session can be told by a list of questions the participants asked in response to one question I had written on the board at the beginning of class: Can any regular polygon be tessellated? Resulting questions: >What is a polygon? >Can a line be a…

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ESCHER #3: Things Get Emotional

(January 20, 2013)  “What’s this for?” asked the kids as I handed everyone a piece of triangular graph paper.  I explained that you can make fancy tessellations on this kind of paper. “What’s wrong with squares?” asked A, referring to traditional graph paper.  I then handed out square grid paper for anyone who wanted to try it on squares.  M…

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Symmetry: The Questions (ESCHER #2)

(January 13, 2015)  For the most part, I’m going to let the pictures do the talking this week.  They tell the mathematical story of our session via the students’ work and question. We continue to wrangle over the definition/types of symmetry.  I posed 2 new questions this week: 1)  Can you get a mirror image of an object using rotation…

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ESCHER #1: What is Symmetry?

(January 6, 2015)  How do you define symmetry?   This question became the crux of our first Math Circle on Escher.  Our 11-13 year-olds debated this question for well over an hour. It all started when I passed a bunch of images around: >beehives and other natural patterns, >examples of Moorish architecture, >various Escher works, and >a guy staring at his…

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