The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

CANTOR #4: Diagonal Proof

(January 26, 2016) “COUNTING” THE RATIONALS We began where we left off last week:  how can one list the set of rational (fractions and integers) numbers in a one-to-one correspondence with the naturals (counting) numbers? I gave the students some time to work on it, and everyone came up with a way to do it. (See photos for variations.)1  Everyone…

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TAKEAWAY GAME (December 9, 2014)  We began our final session in this course with a few rounds of The Takeaway Game.  My goal was to focus attention for deep mathematical thinking, and to plant seeds of a solution strategy for The Very Clever Prince.  (We never did get time to return to the logic puzzle about the Prince; some of…

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Thinking Like Mathematicians

The kind of real mathematical thinking that a math circle encourages.   Photos of a Julia Set crop circle and a Cissbury Ring crop circle whetted our appetites for circles this week. Everyone had many questions about how the crop circles got there, particularly how they got to be “so perfect.” Then the kids wanted to continue the process of…

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