Our Second-ever Julia Robinson Math Festival

Saturday, January 18, 2025

Over 80 families registered for our Saturday morning event, and a great time was had by all.  Here are my photos and videos of the event.  Thanks to all the Crooked River regulars who helped out with our event, including the Test Run we did on Thursday, January 16.  We hope we can do this again in the near future!

Think about Math until it Cliques

Thursday, November 14, 2024

Paul began the meeting by asking how many line segments can be drawn from 1 point to another if we have a set of n points, where n is an integer between 4 and 8.  A set of n points along with every possible line segment (edge) drawn between them is called a “complete graph on n vertices”.  We needed to know about complete graphs for the main activity later.  Here is one answer.  

Next, Michael introduced us to a game called Sprouts, originally developed by mathematician John Conway.  We enjoyed playing and figuring out if there was an advantage to going first or second.

For the main activity with Paul, we played a game where the board was a “complete graph on n vertices”.  Two players alternated coloring a line segment, and if they formed a triangle of their color, they would win.  This was an introduction to what is known as Ramsey Theory.  Many of the ideas we discussed can be found at this website:
 Ramsey Graph Games - great questions and fun activities

Here are some other links that were shared during the evening:

GeoGebra:  Coloring a Complete Graph of 7 Vertices

GeoGebra:  Coloring Complete Graphs of 4,5, or 6 Vertices

Bounds for Ramsey numbers

The Quanta Magazine article that inspired today’s Math Teacher Circle

The Math Problem That Took Nearly a Century to Solve

K-12 Unsolved

Thursday, September 12, 2024

Sara and Kate combined to give us a fantastic kickoff to the 2024-25 school year.  As an appeteaser, Sara had us play a die rolling game called “101 and Done”.  Here is a link to her slides for the evening - the first slide has instructions for this game, and the remaining slides have other links referenced throughout the evening.

The inspiration for the “main event” was this document from mathpickle.com, which documents the following story.  In November 2013, mathematicians and educators gathered at the Banff Research Station near Calgary to select one unsolved math problem for each grade K-12.  They did so, and Sara and Kate each took us through one of the winning unsolved problems.

Sara captured our interest with Creature Curiosities, her version of the winning problem for Grade 3 which explores what is known as the Graceful Tree Conjecture.  We could have played all night with this problem, but then Kate guided us through another great activity, which did not win in Banff, but we all loved.  Her Mutant Fibonacci Bunny Sequence was very fun to explore - we all worked hard to try to get to 13 in as few moves as possible.  It took Paul the rest of the evening to brute force it in Excel, but here is his spreadsheet if you are interested.

Splitting to Mars

Thursday, March 21, 2024

Sara hosted this fun event where we left at the end with as many questions as we had answers.  When we entered the room we added our names to various Venn diagrams that appeared around the room.  These diagrams would be needed later as we tried to send crews to the two moons of Mars, Phobos and Diemos, such that each would be staffed with the same number of specialists.  The three types of specialists we considered were Geologists, Biologists, and Engineers.

Sometimes it was not possible to do so evenly, so we changed the rules to allow the split to be off by one.  Ideas explored this evening included the Inclusion/Exclusion principle, Parity, and the Pigeonhole Principle.

Solitaire Refinement

Thursday, January 18, 2024

Paul began the session by giving everyone a deck of cards and teaching them how to play “Double Solitaire” (or Triple or Quadruple, etc.).  Many mathematical questions came to mind, including some that were answered only very recently.  Here is a recent Bachelor’s Thesis which gives nice information on the probability of winning Klondike solitaire.  Also, here is an even more recent paper showing the probability of winning a number of different solitaire games.

Matrix Magic

Thursday, November 16, 2023
Michael kicked off the event by showing us some examples of magic squares.  Next he gave us some partially completed 3x3 magic squares, where three numbers were known, and we needed to determine the other six. This led to the question of when three numbers is enough to determine a magic square, which we explored for some time.  Here is a link to Michael’s slides.

Next, Paul gave us a 5x5 matrix which he called “The Game of 57”.  Three Crooked Mathematicians played in front of the crowd, and sure enough, all three were winners (selecting numbers that added up to 57).  It was quickly believed that this game was impossible to lose, and much of the evening was spent exploring how and why.  This game was taken from Chapter 2 of  Martin Gardner’s 1959 book, Hexaflexagons and Other Mathematical Diversions.

We finished the evening by exploring how matrices are also used to solve systems of equations, and how free software like Octave can be run on a SageMathCell to solve a linear system.

Tell Me More

Thursday, September 21, 2023
The Crooked River Teachers Math Circle met for the first time this school year on Thursday,  September 21st.  Our evening began with the ‘Smileys’ puzzle from the Julia Robinson Mathematics Festivals.  In this puzzle one tries to turn all the frowns turned upside down. ??  Puzzles includes squares, hexagons, and triangles of frowns and smileys. 

After our introductory game of ‘Smileys’, Michael led us in a exercise of ‘slow reveals’.  He began by projecting a graph, but all of the important information was missing.  We had fun trying to guess what data the graph represented.  As Michael would slowly begin revealing parts of the graph, we modified our guesses.  (Hilarity ensued.)  He then taught us how to make our own slow reveal graphs and provided the some websites for sets of slow reveal graphs.

Slow Reveal Graphs: https://slowrevealgraphs.com/ 

Slow Reveal at Math With Bad Drawings:  https://mathwithbaddrawings.com/2020/06/03/what-graphs-reveal-if-you-give-them-the-time/

NYTimes: What's Going On in This Graph?

Our Julia Robinson Math Festival

Saturday, June 17, 2023
In our first ever Julia Robinson Math Festival, we welcomed over thirty young Crooked mathematicians to the Educational Service Center for a morning of fun mathematics games and activities.  They asked us to please do this again!

A Festival of Math

Thursday, May 18, 2023
We engaged in two activities that are part of our upcoming Julia Robinson Math Festival, which will take place on Saturday, June 17, at the conclusion of our summer immersion.

Sara Good started our evening by passing out Geometiles to each group.  We explored these puzzles for well over an hour, and each group explored our own questions that were raised as we worked on these.

Next, Paul Zachlin led us in a game where we try to place Wolves and Sheep onto an n by n “chess board”.  In addition to the pdf version of this puzzle, you can click here for a jamboard version.

We are excited to engage in these and other similar activities this June!

This is Probably a Good Meeting

Thursday, March 16, 2023
Dr. Edwin Meyer of Baldwin Wallace University, who specializes in helping students become critical thinkers lead us in our main activities.  After sharing a bit about his background and what lead him to teach problem solving, he shared a problem he gives his students on the first day of class.  After allowing us to grapple with the problem he lead the group in an exploration designed to answer the questions:  if a deck of cards is random dealt to four people, what are the odds that 1) each person will have an ace, 2) two people will have an ace and one person will have 2 aces, 3) two people will have 2 aces each, 4) one person will have three aces and one person will have 1, and finally 4) one person will have all four aces.

Numbers Have Personality!

January 19, 2023

These activities were a team effort, courtesy of your Crooked River Math Teacher Circle leadership team!  Here is the Google Slides doc that we used.  Slides 2, 16, and 17 include links to other wonderful resources.

Sara Good started our evening by having participants take their chosen number through a personality test.  We used adjectives to describe numbers where tests for the numbers were available at different stations.  We saw examples of numbers that are abundant, deficient, or perfect, aspiring or sociable, practical, weird, untouchable, or amicable.

Next, Kate Lane had us working to find happy and sad numbers.  Paul Zachlin wrapped things up with a search for vampire numbers.

It was certainly a great way to kick off the year, as we know different groups have different personalities, too!  This group of teachers was full of energy for the entire meeting.

Dr. Melissa Dennison of Baldwin Wallace University introduced us to a two-player game called NIM.  We played a lot, discussed strategy, and then played a number of variations. Here are the slides that she used.

We concluded the evening by viewing and discussing the video Learning and Behavior Characteristics of Gifted students

We read All of the Above in advance of this meeting, in anticipation of our video conference with the author, northeast Ohio native Shelley Pearsall.  We began by building tetrahedrons and other geometric figures using paper plates in the way that artist Bradford Hansen-Smith showed to Paul Zachlin two decades ago.  

We spent the session playing with Lego Mindstorms pieces.  We began by making static geometric shapes before proceeding to dynamic linkages.  Here is a great resource for how to make triangles using Legos.

Paul Zachlin then presented his slides on Lego Linkages, which came from a longer set of slides by Zoltan Kovacs.  Both Paul and Zoltan had been inspired by the book, How Round is Your Circle?   The slides began by showing why linkages are: :important, interesting, useful, beautiful, modern, and challenging.  We viewed a video of the amazing enormous kinetic sculptures called strandbeests (“beach animals” in Dutch) by Theo Jansen.  We ended up using our legos to construct 2-bar, 4-bar, and 6-bar linkages, and we traced algebraic curves corresponding to each.  We learned What Watt sent to Watt (his son) to explain the linkage in his steam engine.  Here is a Desmos simulator for 4-bar linkages.  Here is the Geogebra model of Hart’s Inversor.

In the end, we straightened out which lines were straight, and which were close, but not quite.