# The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

### Human Trafficking, COVID, and Graph Theory

“Aw, are we talking about human trafficking again? I don’t want to feel sad,” said F at the beginning of the session following the human-trafficking discussion. I was grateful to F since I wasn’t sure whether to continue that topic or move to something else. Thanks to his comment, I knew what to do.

### Reducing Human Trafficking through Math

Middle-school Math Circle students use graph theory to examine the problem of human trafficking.

### Data Interpretation and Analysis

(February 5, 2020) “Suppose there was an election for Official Ice Cream Flavor of the USA, and the choices were ravioli, mint chocolate chip, butter pecan, mango, vanilla, and chocolate. Which voting methods could be used?” So began our class, which was filled with debate, questions, and conjectures as I posed more questions. “Suppose the country votes state by state…

### Gerrymandering via IBL

(January 23, 2020) Is it possible to teach students about gerrymandering and the Four-Color Theorem by asking questions and not lecturing students about anything?* My plan was to ask the students just four questions: 1) What’s the difference between the House and the Senate? 2) If your state has a population of 50 people, 30 affiliated with the blue party…

### Intro to Voting Theory

(1/16/2020) Our overarching Math Circle goal is for students to invent and discover math for themselves. In this course, the plan/hope is that I’ll ask a bunch of questions and the students will invent their own voting methods before discovering what voting methods people have created throughout history. Pet of the World  “What would happen if you got to vote…

### OPEN Q’s #6: Liar’s Dice

(May 26, 2016)  Split into 3 teams.  Each team gets 5 dice.  Roll them all, look at them, but don’t let the other team see them.  The first team makes a 2-digit bid.  The first digit of the bid is your prediction of the total number of dice of a certain value every team combined has.  The second digit is…

### OPEN Q’s #5: Graceful Tree Conjecture

(May 19, 2016)  This is a graph-theory story best told with pictures, so feel free to go straight to the photo gallery below.  But I’ll try to explain it in the words I used with the students: Draw a tree.  Any Tree.  Sequentially number both ends of each branch or branch segment, starting with 1.  You have created a “graph”…

### OPEN Qs #1 and 2: Graph Theory and Number Theory

(April 21 and 28)  So far, the questions I’m giving the kids to work on in Math Circle are leading them to ask very interesting questions on their own.  The bullet points below are all questions and conjectures posited by the students, not me.  The problems themselves are unanswered, or open, questions in mathematics.  I used presentations similar to those…