The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

Chromatic #, Week 5, Making Progress

(April 7, 2015) We started today with child-produced function machines, then moved into our old standby, the Hadwiger-Nelson Problem. INTRODUCING DOMAINS OF FUNCTIONS M approached me before class with a slip of paper with her rule written on it: +10.  She explained that she had only practiced with numbers up to 1,000.  What to do if someone called out an…

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Chromatic #, Week 3, The Number Line

(March 24, 2015) “This is the last function machine I will ever lead in this course,” I announced at the start of class.  “After today, you will take turns leading them.”  My function machine of the day produced 7 from 3, 17 from 8, 6259 from 3129, and so on.  In other words, f(x) = 2x + 1. We never…

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Math Circle: A Matter of Perspective (Eye of Horus 5)

A Matter of Perspective (Eye of Horus 5) (October 15, 2013) Students arrived to see 7 arrays of blocks on the table, with the following numbers of blocks in the piles respectively:  1, 2, 4, 8, 16, 32, and 64.  Well, that was the numbers from one side of the table.  When we looked at the arrays from the other…

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Math Circle Blog: Plato, Codes, and Exploding Dots

Plato, Codes, and Exploding Dots “I must add how charming the science of arithmetic is and in how many ways it is a subtle and useful tool to achieve our purposes, if pursued in the spirit of a philosopher, and not of a shopkeeper!’” This was the last line of a dialogue my assistant R and I read at the…

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Math Circles: Two Weeks

No one had any clue what the rule might be.   We started last week’s Math Circle with 2 rounds of “Tens Concentration.” This arithmetic game is also a mindfulness practice, focusing and sharpening attention. You could have heard a pin drop as the kids tried to remember the location of that other card that would create a sum of…

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The Platonic Solids: Never Mind

Developing collaborative problem-solving through the joyful art of mathematics.   Since Euler codified the concept of functions, we started with a function machine. It was challenging to get past the design phase to play with the math, but after applying a chimney to a fish, we did. The first rule was quickly deduced: “It makes it half; it takes half…

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Collaboration via the Cupcake Function Machine

After the total silence that accompanies very hard thinking, the kids were thinking aloud and producing conjectures.   After we played with Polydrons and Schläfli symbols* for about 10 minutes, we created a function machine. The students dictated the machine’s parts (various polygons, a cupcake, and sprinkles) as I drew it. They specified that the “in” number should enter the…

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