Middle School Math Circle Diary

Hi It’s Shelley here with A Math Circle Journey! I started an online math circle for kids about 6th-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.

knights

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.

thales

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.

 

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Love of Learning Math Circle Diary

It’s Shelley here again with A Math Circle Journey. I started an online math circle for kids about 3-5th grade back in September. It has been going better than I thought! My hope with blogging about it 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 inspired by Moebius Noodles and have used many of the ideas. 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 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 played Symmetry Mirrors (from Moebius Noodles) with lego guys and toys. It was fun to watch the kids try to get their figures symmetrical. We did learn that kids need small toys (lego guys or small action figures). Dolls and Barbies were too big to handle and manipulate for the kids.

I sent them home with the challenge to do a game of live mirrors with their families!

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

Here are My Slides for our first meeting.

Symmetry: Doodle Zoo

This week in math circle, we made doodles with folds. I wasn’t sure if this class would work at all online. I was pretty nervous about it. I shouldn’t have worried! This was one of the best classes all term! I showed them how to make a doodle on the fold of a paper. It took a few minutes of explaining and showing on my webcam, but then they got it and ran with it!

If I were doing this again, I would start by asking every child to fold their paper and cut out a heart. Almost all kids have done this before. Then they would have had a starting point for understanding why they were drawing off of the fold and that we were trying to create a finished shape from our fold.

 

But once they understood the concept, they were off and running! We tried folding the paper three times, four times, and more to see what happened. One student wanted to cut out hearts that were connected, but she kept getting multiple, unconnected hearts. I asked her to think about how to fold the paper to get them connected together.

I slipped in some discussions of symmetry and asked them to make something with radial symmetry. They started folding the paper in different ways to try to figure out how to do. We talked about how to fold the paper for a snowflake.

The best part for me, was that one dad was sitting by his son (just out of webcam view) and he was as interested as his son! It was fun to see the simple challenge engage even an adult. It was all I could do to keep up with the 4-headed cows, multiple hearts, and amazing rocket ships the kids were creating.

Parents told me that this activity translated into a lot of work at home.

Here are my slides from this week’s circle.

 

Symmetry: Mirror Books

I LOVE this activity. My kids and I had done this at home. We were in awe of the ability to draw a line and turn that line into a circle! We loved making connections between the angle of our mirrors and the number of lines in our reflection of a shape.

Mirror books are simply two plain mirrors taped together like a book. You can do some amazing things with them.

twomirrors

In class I can’t control supplies in an online environment. That is what made this class a disappointment to me. L Parent’s didn’t understand that we needed plain, unframed mirrors. I should have send a picture to the parents and asked them for very specific mirrors. The trouble is, in online classes, parents don’t know what the goal of an activity is, so they take shortcuts and don’t realize until later why the mirrors in the bathroom just don’t work as well.

So I’m still trying to figure out how to make this amazing activity work well online.

I challenged the kids to find out how to turn a piece of pizza into a whole pizza and how to use the mirror book as a paper snowflake designer. Can you?

(No slides this week, we just played with the mirrors.)

Number: Iconic Numbers

I wasn’t sure how this one would go actually. It went better than I thought. We started out with the story of Goldilocks and the Three Bears. I told the story briefly. I wish I’d told it more dramatically, just for fun and to grab their attention. I also would have told them to listen for numbers while I was telling the story. “Look for” before a story makes activities better and more powerful.

But, we went on a number hunt through the story for 1, 2, 3, 4, etc. Three was easy – three bears, three chairs, etc. For the number seven we had to get creative. I think we decided on three chairs and four legs on the table!

As we moved on to number nine it was so fun to see a student raise his hand like a bolt of lightning! He’d obviously been waiting for 9! I called on him and he was so excited to say that nine was the three chairs, the three bowls of porridge, and the three beds! Those moments when a student grasps the subject and revels in his answer are what make math circles a delight!

Then we found numbers in nature and we found numbers in shapes. I had a slide of different plane and solid shapes. I asked the students to use the annotation tool to “write” on my slide. We chose a shape and decided what number it represented to us. Students often wrote different numbers. There was some disagreement, but when the students realized that they could justify lots of different reasons for their number and that they were all “right.” It was a good chance to discuss that we think differently, we reason differently, and we can make our own math!

In the copy of my slide below, you can see some of the kids said three because a cube is the 3-d version of a square. They said it had 12 edges. (Wow!) They said 6 for the 6 sides (faces) and they said 4 because it is a square made 3-d.

shapes slide

Overall this was a great activity about numbers. The next week the kids brought books about numbers, and mobiles made of shapes. It was a really fun week.

Next time, I’ll be sharing these 25 cool numbers!

Here is a link to my slides for this week.

(Note: Iconic numbers wasn’t familiar to me. Icon is defined as “a person or thing regarded as a representative symbol of something.” (Google dictionary) Basically, it is finding numbers that are “famous” or common in stories. For example, the number three is iconic. Think how often it shows up in stories, folklore, mythology, etc. Threes.com talks about the number three in more ways than you ever imagined possible!)

 

Number: Fractals

We started this week off with a video from the site fractalfoundation.org. The kids really enjoyed the videos. They were quite in awe of how they fractals could go on and on forever. We even had a brief discussion of infinity.

Then we talked briefly about tree fractals and substitution fractals. I had them try drawing each kind of fractal as we talked about it. I wish I’d slowed down and guided this part a little bit more. Next time I’ll have them trace their hand and then draw a hand on each finger and so on for the tree fractal. Then I’ll turn them loose on their own creations.

sub fractal

For substitution fractals the image of the owls from this site was really helpful. Substitution seemed easier for them to understand. For fun we went to this site and made substitution fractals of their names. They were amazed by it.

I made a small connection to the first week of class and talked about how the computer does the work of creating the fractal from the math patterns. I wish I had emphasized that a little more though. The kids were dutifully making fractals before class even ended. This one was popular!

Here are my slides for this week.

 

 

 

Math History: Meet Thales of Miletus

This week the internet pulled a fast one on me and my ISP went out regionally. I got about half way through this lesson. 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.

thales

The kids enjoyed learning about how math can be useful and how it can solve problems. They also loved hearing how Thales fell in the well!

Here are my slides for this week.

 

 

 

Function: Function Fun

I wish I’d had this class before Algebra in high school! We had a lot of fun with our crazy machines and it would have made so much more sense in math class!

We started out by talking about household machines. We discussed washers and toasters. I asked what went in and what came out. It was so obvious it was great, because it laid a great foundation for their understanding later.

Next, I showed them a “machine” and told them to each give me a word. I gave them a rhyming word for each word they gave me. It was tougher than expected because they gave me words like “Orange” and “Ice Cream.” A little hard to rhyme impromptu! But they eventually figured out my machine.

Next we did one that added to to every number they gave me. I wrote the actual math notation on the blue box of the machine and told them that is what it looked like in “high school math.” They thought it was neat that they could understand that stuff!

Our last machine made houses for animals (see below).

function machine

Then we discussed what kind of function machine they could make. At one point the discussion got a little off track to any kind of invention and we discussed inputs and outputs and that a function machine transforms what goes into it and it transforms it consistently. This was a good thing to discuss for their future math studies of functions.

To say they are excited to build function machines and show them next week is an understatement! They are thrilled with this project, and I’m excited to see what they bring next week!

Here are my slides for this week.

 

So far running a math circle online has worked out better than I expected. I have had frustrating moments when I’ve really wished I could reach through the screen and help a student, but the exposure the children are getting to math topics is worth the challenge!

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Happy Math Storytelling Day! Newsletter September 25, 2015

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Our newsletter grew beyond 6,000 subscribers this month. That means even more parents, teachers, and math circle leaders will be sharing their ideas, models, art, and stories. Speaking of stories…

Happy Math Storytelling Day! September 25

On September 25, invite your children to celebrate Math Storytelling Day. What types of stories do people create and share on this day?

Math Storytelling Day Zeno

Picture from the Sequences activity in our Multiplication Explorers course

Classic math tales span centuries of tradition and history, and are still popular today. Invite friends and family to watch these 1-minute videos, find these stories as books or blogs, or best of all, act out your own versions with toys! There’s  Zeno’s paradoxes (ancient Greece); the tale of king, chessboard, and rice (10th century India and Persia); or Hotel Infinity (early 20th century Europe).

Some traditional stories aren’t as widely known, but more and more people learn about them, as more cultures now share their treasures online. Check out these traditional sand drawing stories from the Sona tribe, and more Ethnomathematics activity ideas from our Pinterest collection.

The good news is that math stories are growing very popular! People have probably created more child-friendly, accessible, fun math stories in the last ten years than in all the past history combined. Record a video or a podcast with your phone, or use computer storytelling tools like Scratch from MIT and see if your tale can become one of the viral hits online. Meanwhile, check out Vi Hart talking fast in Infinity Elephants (2.5 million views) or the visual tale of symmetry and fractals Cows & Cows & Cows by cyriak (33.5 million views).

Not all math stories are happy. When we hold meetings, many grown-ups share their math grief stories, telling of teaching disasters, crushed dreams, or quietly giving up on mathematics. If you have math grief, share your story with others. We need to hear what went wrong, to do better for the next generation. Natural Math “About” page has a short presentation by Maria Droujkova with several math grief stories – and ways to help children.

Math Grief Stories

Why is math storytelling good for you? Here is a feature article from San Jose Mercury News. You can find more Math Storytelling Day resources at our blog.

POSTPONED: Second annual Sculpture Scavenger Hunt with Cary Visual Art is on September 26

We are expecting very heavy rain tomorrow, so the sculpture tour is postponed. We’ll let you know when we have a new date!

 

Sculpture Tour-2015 Postponed

 

Dr. Maria Droujkova and the Natural Math crew

CC BY-NC-SA

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Origami=math, Hacking Math teen course, scavenger hunt Sept 26: Newsletter September 21, 2015

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In this newsletter:

  • All ages: Origami = math?
  • Teens: Questions and answers about the new Hacking Math course
  • All ages: Join us for a free math scavenger hunt on September 26

Fold cicadas and read 6 reasons why origami=math

Happy Origami Math

Parents and teachers often ask why we call this or that informal activity “mathematics.” Where is math in a puzzle, game, or craft? This year, we did origami at the annual BugFest, and got this question a lot. Why is origami good for your math?

Check out our new blog post with the pattern for origami cicadas, and 6 reasons why origami is good for your math!

Questions and Answers about the Hacking Math course

spirograph

There is a lot of interest in the new Hacking Math course that we are starting this Saturday. Here are some questions and answers:

  • Can I sign up if I will have to miss a meeting?
    • Yes. We will record meetings and the recordings will be available to course participants.
  • Can you help me with the price?
    • We’d like to encourage you to share the course with a friend (using one computer during the meetings). It will help you split the cost, and improve your learning experience. Most people learn better when they program and discuss math with someone in person. Professionals call this approach “pair programming.” In the future, we will make courses more affordable by running multiple groups at once.
  • What times are the meetings?
    • 4 PM Eastern (New York) time on Saturdays, starting the 26th. Sorry we didn’t post the time before.
  • Can my serious and interested 11-year-old take this course?
    • Yes. Especially with friend or family help. Ages are always just guidelines. This will be at about formal algebra level.
  • What number of hours per week do I need outside of the meetings?
    • Probably 2-3 hours.
  • Can I have a certificate of completion?
    • Yes! We’ll even include course participant computer-generated art on it.

See more info and sign up!

Second annual Sculpture Scavenger Hunt with Cary Visual Art is on September 26

On Saturday, September 26, 10 AM to noon, visit downtown Cary, NC! We will be on the main lawn by the Town Hall, near the sculptures. Cary Visual Art and Natural Math welcome families with children of all ages for a fun and thoughtful scavenger hunt, appreciating the sculptures on exhibit as part of the Cary Outdoor Sculpture Exhibition.

Do you live too far? We’ll post the scavenger hunt materials after the event, so you can run it at your own town!

Sculpture Tour

RSVP to reach.out@naturalmath.com to participate in the event, or just show up.


Do you want to volunteer at Natural Math events (online or in the Research Triangle, North Carolina) and work with us to make math adventures happen? Write us at reach.out@naturalmath.com to talk! Children and grown-ups are welcome.

Dr. Maria Droujkova and the Natural Math crew

CC BY-NC-SA

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