Hi It’s Shelley here with A Math Circle Journey! I started an online math circle for kids about 6^th-8th grade back in September. This has been going remarkably well. My hope is to share what we did, what worked and what didn’t work so well each week. So you as you drop in you’ll be seeing my diary of sorts. I hope it helps others!

We have been using Mathematical Circle Diaries and have also incorporated some famous mathematicians from this book. To start, here is a link to my schedule for our online circle. Since I haven’t posted before, I’ll catch up in this post and then report in weekly.

Introduction

In this class we got to know each other and we talked about math and how it can be so different from what we usually think of for math. We watched bits of a TED Talk by Robert Lang on origami and math. The kids really enjoyed learning that math is more than doing worksheets.

I spent some time emphasizing that there were four different groups of people involved in Mr. Lang’s origami video: 1. those that used math to make patterns, 2. those that teach computers to use the patterns, 3. those that make stuff cooler or better from the computer and patterns, 4. Those that realize the cooler or better stuff can be used for “real life.”

I emphasized that not everyone likes all four parts of the process, but that all four parts are really important and that during this class hopefully they’ll find out which part they like more.

Then we tried a few challenging puzzles from James Tanton’s introduction to Arithmetic Gateway to All. Their homework was to work on the How Many Squares challenge.

All in all, a pretty good class for the first online math circle meeting!

Here are My Slides for our first meeting.

Problem Solver, week 1

This week in math circle, we started out discussing what it means to solve a problem in math. Then we tried out problems from this chapter in the Math Circle Diaries book. The kids did most of these pretty quickly. The challenge was explaining the problems to the others.

Our goal this week was to emphasize being able to explain our reasoning.

Next time, I’ll be using this list of heuristics from the Ohio Resource Center to help the students have more problem solving tools to work with. As the term has gone on, students have asked how to attack a problem and this would have helped.

The Ohio Resource Center also has Stella’s Stunners which is a great resource for problems and challenges based on all kinds of math subjects.

Here are my slides from this week’s circle.

Problem Solver, week 2

We went through the problem set from the book and worked on solving the problems and explaining them.

(No slides this week.)

Math History: A’hmose

This week we learned about A’hmose and the ancient Egyptian mathematicians. I had them google Rhind Papyrus and tell me what they found. Then we discussed it. The book Famous Problems and Their Mathematicians had some of the problems from the papyrus (you can probably google them too), so we attempted a few.

I actually expected this to be easier for my students than it was. They were rather confused and we ended up drawing lots of diagrams and building up their confidence in their math skills on this one!

The slide include some problems from Vardapet of Persia, but we didn’t get to those!

I also have my students reading Number Stories from Long Ago. This adds to our understanding of the history of math. We read chapters 1 and 2 and briefly discussed them. I plan to do a better job with this in the future weeks. I also plan to include the Question Box from each chapter as “homework.”

Here is a link to my slides for this week.

Knights & Liars

This was a fun week! We made truth tables and tackled the baffling challenges of Knights and Liars island. The students learned how to logically reason through responses based on the parameters set in the problems.

On Knights and Liars island knights must tell the truth and liars must lie. Tourists can do either. Here is a sample question from this class.

While visiting the Knights & Liars Island, you meet a boy who tells you that he is a liar. Does he live on the island or is he a tourist?

The kids loved trying to trip me up on these problems (which they did!) But we drew tables to show how things had to work out. I wouldn’t make any changes to this one. It worked well online and was fun for the kids.

Here are my slides for this week.

Knights & Liars, week 2

This week we went through the problem set with the students. This is always a great chance to review their problem solving strategies and help them explain their answers.

One student asked how to know what type of diagram to draw, so we spent some time drawing diagrams for a problem about koala bears. We drew it several different ways, and I tried to draw out of the students their methods of solving the problem. I really wanted to emphasize that there is more than one way to solve a problem and no “one right way.”

Math History: Meet Thales of Miletus

Since my internet went out one week I combined going through the problems for Knights and Liars and this history lesson. We had to go faster than I like and I talked to much!

We were learning about Thales and some of the stories of his life. We looked at his famous problem of measuring the distance of a ship to shore. Next time I’ll have the students look him up and share what they find out.

I like showing the students how math has practical applications and how ancient cultures thought. I’m not sure they appreciated it as much as me though! In a live setting, we would have done this with string and models. But, we are limited to online for now!

We also went through Chapter 3 and 4 from Number Stories and learned about the development of our writing of the Arabic numbers. It was a quick run through but it was interesting.

Here are my slides for this week.