# 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…

### 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…

### 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…