The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

OPEN Q’S #4: Total Stopping Time

(May 12, 2016) We spent almost the whole hour examining the “total stopping time” of sequences of Hailstone Numbers, those formed by the Collatz Conjecture.  (Pick a number.  If it’s even divide it by 2, if it’s odd triple it and add 1.)  Is there a starting number that doesn’t end up producing 1 as the final number of the…

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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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GARDNER #5: Life, Murder, and Box Tops

LIFE (October 21, 2014)  Last week’s boardwork was on display before the students arrived.  M, who was absent last week, was early for class today.  She saw the board and immediately asked, “Why does it say ‘die?’” “Ask them,” I told her, indicating J and L, who were also early for class.  J set the board up for Life1. Then…

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PROOFS #1: Aspect Ratios, the Golden Ratio, and Z’s TV

PROOFS #1:  Aspect Ratios, the Golden Ratio, and Z’s TV (April 16, 2013) Your cousin has just gotten a new job as an announcer on the Golf Channel, and is so excited for you to watch every broadcast.  While you may enjoy playing golf, you don’t really enjoy watching it.  So you decide to place a small flat-screen TV between…

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Logic for the Very Young

Logic for the Very Young (February 26 and March 5, 2013) “One afternoon, 2 children wander into a Kingdom unknown to them ….” So began our two-week Math Circle for children aged 6-7.  This story framed an exploration of logic games, questions, and strategies.  I had lost my voice, so my assistant Rachel led the Circle while I sat quietly…

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