# The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

### More Logic, More Factoring, and Sticking with Tough Problems

THE CRIMINALS OF THE WEEK (May 13, 2014) “It’s time talk about the criminals,” I announced to an exuberant group of kids who were not quite ready to settle into math circle.  The word criminals got their attention.  We tackled Smullyan’s Inspector Craig mystery puzzle #74.  I expected a huge struggle for 2 reasons: more clues to keep track of,…

### PROOFS #5: Debating the Merits of Proofs

THEOREM:          A cat has nine tails. PROOF:                1.  No cat has 8 tails.                                 2.  One cat has one more tail than no cats.  Therefore, a cat has nine tails.1 (May 14, 2013)  We began today’s Math Circle debating the merits of the cat-has-nine-tails “proof.”  N stood at the board diagramming “my” reasoning.  G came up to…

### PROOFS #2: Exponents, Roots, Pythagoras, Theorems, Proofs, and The Kaplans

PROOFS #2:  Exponents, Roots, Pythagoras, Theorems, Proofs, and The Kaplans [juicebox gallery_id=”25″] (April  23, 2013) Before continuing our TV problem, the students recapped last session for A, who had been absent last week.  This week’s problem solving once again presented rich opportunities for delving deeply into arithmetic; it has not been the algebra and geometry that is challenging for these…

### 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…

### Logic Session #5: The Jabberwock and the Converser

The Jabberwock and the Converser “’Twas brillig, and the slithy toves Did gyre and gimble in the wabe” So begins Dodgson/Carroll’s poem Jabberwocky.  I read it aloud without introduction as the students colored their own Jabberwock puppets.  The coloring focused students’ attention, as they were, as usual, excited about the impending puppet use.  They commented on the poem: “That doesn’t…

### Math Circle: Logic Session #3: Noise, Normals, and Negators

Noise, Normals, and Negators (January 29, 2013)  The kids bounded in, filled with curiosity about whether the new puppets, Wags and Rooney, were knights or liars.  Each child also wanted to hold a puppet.  We had 4 puppets and 8 kids.  Easy to manage, I thought:  each child could have a puppet for half the class.  Each child, though, wanted…

### Math Circle Blog: The Monty Hall Problem

The Monty Hall Problem You are a contestant on a game show.  The host shows you 3 doors.  He tells you that the prize behind one door is \$1,000,000 and behind each of the other doors is a goat.  He instructs you to choose a door; you will win whatever is behind it.  You choose a door.  “But wait,” he…

### Math Circle Blog: Aliens, Number Systems, and Contemplative Mathematics

Aliens, Number Systems, and Contemplative Mathematics “Some alien spies have been helping our captain.  It turns out that you were right: there are enemies hiding on the field behind the house.  The captain wants to know how many.  The alien photographer comes down and takes a picture of them, gives it to her captain, who writes it down and gives…