### 2024

**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.

### 2023

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

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.

### 2022

__Crooked and NIMble__

__November 17, 2022__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

__Where Way Eye?__

__September 15, 2022__**We welcomed Dr. Anna Davis of Ohio Dominican University. She led us in a workshop exploring the connection between art and mathematics through interactive displays and activities. We learned fundamental principles behind creating realistic art, computer graphics and optical illusions. Our participants used some strong mathematical reasoning to determine how far the camera was above the ground that took a picture of some railroad tracks.**

__Weaving Together Mathematics and Community__

__March 10, 2022__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.

**Lego Linkages**

__February 10, 2022__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.

### 2021

**Spinning Wheels and Making Art**

__November 11, 2021__**Sequential Fun**

__September 9, 2021__**Summer Summary 2021**

**June 21-23, 2021**

__Summer Immersion Workshop__

__Day One__

__Day Two__

__Day Three__**Pushing the Boundaries with Dr. Amanda Serenevy**

__May 6, 2021__**Show Me the Money with Dr. Raj Shah**

__April 8, 2021__**Our first ever Julia Robinson Math Festival**

__March 14, 2021__**Let’s Take a Vote with Dr. Melissa Dennison**

__February 11, 2021__*“Are there different methods for voting? What methods seem most fair? How can voting theory impact or even manipulate a political outcome?”*were some questions we asked, to name a few.

**Curious Decimals with Dr. Curtis Bennett**

__January 14, 2021__### 2020

**It’s Hip to be Square with Dr. Steve Phelps**

__December 10, 2020__**Mathemagics! with Dr. Arthur Benjamin**

__November 12, 2020__**Let’s Play a Game - LIFE of a Mathematician**

__September 17, 2020__*The Game of Life*, a game of iterative arrays that he invented in 1970 and has since fascinated mathematicians among us all. Paul Zachlin of Lakeland Community College led the investigation. Special thanks goes to Scott Kim of Math Monday for organizing the slideshow that we used for our exploration.

**Wandering Around The World of Geometry**

**Dr. Paul Zachlin**

__January 25, 2020__**Saturday, January 25 – A Double Session**

**. Lynn Aring began with a game involving Random Walks. Michael Buescher then had us explore Random Walks in more depth.**

__Wandering Around the World of Geometry__### 2019

**The Light Bulb Went On**

**Dr. Paul Zachlin**

**November 19, 2019****Shuffling Around**

**Dr. Paul Zachlin**

__September 19, 2019__**Summer Summary 2019**

**June 17, 2019-June 19, 2019**

__Summer Immersion Workshop__

__Day One__

**Day Two**

__Day Three__**Covering and Tiling**

**Dr. Paul Zachlin**

__May 9, 2019__^{th}at the ESC of Cuyahoga County.

**Triple Fun**

**Dr. Paul Zachlin**

**March 7, 2019**^{th}for an evening of “Triple Fun.” The evening began with pizza, salad and an activity led by Kate Lane called “Three Numbers.” Given any three digit number, you may choose any digit, erase it, and replace it with the sum of the other two, minus 1. Quick and easy process, but it can lead down some delightful rabbit holes. Continuing with the theme of “triples”, Paul Zachlin led the group in a discussion of Pythagorean Triples which began by looking at Plimpton 322, an ancient Babylonian text that some conjecture to be some sort of trig table.

**Christmas Crackers**

**Dr. Paul Zachlin**

**January 12, 2019**Fellow math enthusiasts gathered at the Education Service Center of Northeast Ohio to explore mathematics at the recent Crooked River MathTeachers’ Circle. Kate Lane teased the group with a the popular dice game of Tenzi. Sara Good followed with the Mystery Calculator, a mathematical treasure found in many Christmas Crackers during the holidays.The group used deductive reasoning to uncover how and why the Mystery Calculator worked. In the afternoon, Lynn Aring challenged participants with an Estimathon after taking them through engaging tasks of estimation from Estimation180.com.

Join the Crooked River Math Teachers’ Circle on Thursday, March 7,2019 from 4:30-7:30 at the same location. Registration begins at 4:00pm. For more information and resources, visit crookedrivermtc.org and follow us onTwitter@crookedrivermtc.

### 2018

**Gift Giving-Zip Code Crunch**

**Dr. Paul Zachlin**

__November 8, 2018__**Cornhole Math**

**Dr. Paul Zachlin**

**September 13, 2018****Summer Summary 2018**

**July 30 - August 1, 2018**

__Summer Immersion Workshop__

**Day One**

__Day Two__

**Day Three****It’s Only Logical**

**Dr. Paul F. Zachlin**

**May 17, 2018**Using the Game of Mastermind to Teach, Practice, and Discuss Scientific Reasoning Skills

**The IDEAS of March**

**Dr. Paul Zachlin**

__March 13, 2018__### 2017

**A War of Codes: CLE vs. CBUS**

**On May 18th,**

**Folding Up the Fun**

**On March 16th**, The Crooked River Math Teachers’ Circle held their fourth meeting of the school year at the Educational Service Center of Cuyahoga County. This was our third evening meeting of the school year, and dinner was provided to all participants. The session was entitled “

*Folding Up the Fun.*” Steve Pelikan of the University of Cincinnati facilitated the session for our group of K-12 teachers and university faculty. He led us on an exploration of fractions, patterns, exponentials, and change of base activities.

**Enjoy some Golden Grahams - a Mathematical Treat**

**On Saturday, January 21st**, The Crooked River Math Teachers’ Circle held their third meeting of the school year at the Educational Service Center of Cuyahoga County. This was our first ever Saturday morning meeting, and a continental breakfast was provided to all participants. The session was entitled “

*Golden Grahams--a Mathematical Treat.*” Nick Pilewski of Ohio University facilitated the session for our group of K-12 teachers and university faculty, leading us in two intriguing explorations about the Graham Sequence and the Golden Ratio. Sequences were made tangible with Zometools, a cool learning toy worth checking out.

**Order in the Court**

**On November 17th**, The Crooked River Math Teachers’ Circle held its second meeting during the school year at the Cuyahoga Educational Service Center. A light dinner was provided in order to fuel our brains for the mathematical exploration that was to come! University faculty and K-12 teachers participated in the activities that were developed to show that math can be meaningful and fun at the same time. We participated in four activities: Gardner’s Puzzle by Paul Zachlin (Lakeland Community College), Krypto/24 Game, Does Order Really Matter? Find Flexibility in the Order of Operations by Sara Good, and It’s a Date! and Reverse Polish Notation by Lynn Aring.

**Gettin’ Dicey**

**On September 15th**, The Crooked River Math Teachers’ Circle held its first meeting during the school year at the Cuyahoga Educational Service Center. During the meeting, teachers were given the opportunity to collaborate and engage in meaningful mathematics while making connections to the mathematical practices. Participants and the MTC Leadership Team (Lynn Aring, Sara Good, Teresa Graham, Michelle Kocar, Kate Lane, Jennifer Ray, Paul Zachlin) explored a variety of mathematical tasks with dice. Paul Zachlin (Lakeland Community College) facilitated the game of Farkle and encouraged participants to develop mathematical questions. Kate Lane (Baldwin Wallace University) facilitated a variation of solitaire and “Dr. Lane’s Cool Dice Trick” in which participants rolled dice 40 times in order to look for a pattern. https://filecabinet.eschoolview.com/DDBF1D9C-0BA1-443D-BC91-088493C49FB7/September 15th flyer.docx