# 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…

### 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…

### 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…

### 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…