# The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

### CANTOR #1: Let’s Say I’m a Millipede

(January 5, 2016)  “Are there more books or bookcases in this room?” This question thus began our first math circle of the new year. “Do you mean bookshelves or bookcases, not that it would make a difference?” asked W.  Everyone agreed immediately that there are more books.   ONE TO ONE CORRESPONDENCE “How could you tell without counting?” I asked….

### 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 #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…

### OPPOSITES: Mathematical Thinking for Five-Year-Olds, 2.0

COUNTING STRATEGIES   (March 25, 2014)  We started out on the floor counting pennies.  “I want to buy a piece of candy – a Swedish fish.  It costs 10 cents. Do I have enough?”  The pennies were arranged in a particular way.1 The students counted, with various results.  “Is there more than one way to count them?” “No!” announced everyone…

### Getting Emotional about Pi

(February 25, 2014)  Kids arrived to see some yarn and 3 different-sized cans on the table:  salt, coffee, and espresso.  I asked the kids to point out the key parts of a circle on the cans – the circumference, the area, the (invisible) center, and the rope/radius,1  and the diameter.  We hadn’t worked with diameter before, so we talked about…

### Math Circle: Questioning Everything (Eye of Horus 2)

MATH CIRCLE: Questioning Everything (Eye of Horus 2) EXCITEMENT AND ENTHUSIASM (September 29, 2013)  Many students arrived feeling very enthusiastic about today’s session.  Several parents had emailed me about how excited they and their kids were after the last (first) one.  K and her mom told me about their own investigations of interesting numbers they had been doing at home. …

### PROOFS #7: We Want to Think

(May 28, 2013)  Seventy-five minutes.  No future sessions.  Four kids.  Five proofs.  What to do? This was the dilemma facing our Math Circle today.  I’d been deliberating all week over how best to use our last session.  So many proofs.  So little time. I gave the decision to the kids in attendance, R, P, N, and G.  Our options:  a…