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2023

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.  

We then met with Shelley for a lively discussion of the book.  She shared with us many fantastic pictures and stories of how the book has impacted students over the years.  She also gave many ideas for using the book in our classrooms, including the One Book One Day school-wide event.


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
IN PERSON AGAIN!  It was great to be back at the Educational Service Center on a Thursday.  Paul Zachlin began with “Myles Garrett Mathematics”, a kid-friendly version of the Josephus Problem.  After we explored this problem for a while, we were happy to learn about this kid-friendly version of the Standards of Mathematical Practice.  After a quick break, Kate Lane led us in an exploration of Spirograph.  Who knew how much mathematics was waiting there to be discovered using this classic toy?  Kate concluded the evening by sharing with us a connection with the Prime Climb.

Sequential Fun
September 9, 2021
Michael Buescher led us (via Zoom) on an exploration of two very fun problems.  The first is the Collatz Conjecture, an easy-to-understand process which leads to some unsolved math problems.  After playing with this for a while, Michael introduced us to the Brussel’s Choice, which is similar to what we had been doing, only now there were decisions to be made at the intermediate steps.  We had so much fun that we encouraged Michael to duplicate this presentation at the October GCCTM meeting!

Summer Summary 2021
June 21-23, 2021
Summer Immersion Workshop

Day One
Sara Good began the Summer Immersion with “Ready, Set, Go!”, an activity where we thought about many mathematical questions concerning the card game Set.
Next, Michael Buescher brought back “The Candy Problem”, where candy is passed around the table and patterns are recorded.
After lunch, we had a virtual session with Raj Shah where we asked and answered some amazing questions regarding graph paper.
Day Two
In the morning, Paul Zachlin began with an introduction to Number Theory.  We learned some terminology for various “kinds'' of integers.  Then we tackled a number of problems in Chapter 1 of A Friendly Introduction to Number Theory by Joseph Silverman.   We also explored the Online Encyclopedia of Integer Sequences, www.oeis.org
After a short break, Kate Lane had us playing with ropes in the activity called Rational Tangles.  We created knots that we needed to untangle, and we needed to develop some mathematical ideas along the way in order to discover what was really going on.  We needed a lunch break (and a little time to “unwind”) before we finally got into some of the deeper questions.
In the afternoon, we had a virtual session with James Tanton on folding (neckties or strips of paper).  This led to discussions on fractions and also to some unsolved math problems.  Some of the special sets of integers we had discussed during our morning number theory session returned in their glory!
Day Three
We began with some discussions on the role of FUN in the math classroom.  Next, we began playing with SOMA cubes.  We decided to go big or go home as we created an enormous SOMA cube puzzle, and then used it to create a 3x3x3 cube.  We thought about and talked about the number of ways this might be done.
To wrap up the morning, we played Zip Code Crunch:  An Adding Game..  Once again, in this surprisingly simple activity there are ties to unsolved math problems.
 
 
Pushing the Boundaries with Dr. Amanda Serenevy
May 6, 2021
Dr. Serenevy led us in an exploration in minimizing distances that led us to taxicab geometry.  We pushed the boundaries of our minds with this activity!

Show Me the Money with Dr. Raj Shah
April 8, 2021
Dr. Raj Shah certainly made math irresistible during our “Show Me the Money” session.  Starting with something as simple of making money with only 3¢ and 7¢ coins, we explored and tested countless ideas. Who knew one could be so rich in curiosity with such little change!

Our first ever Julia Robinson Math Festival
March 14, 2021
On Pi Day we hosted our first (online) Julia Robinson Math Festival to over 40 families!  Kids enjoyed the joy of mathematics from such games as Ultimate Tic-Tac-Toe to logic puzzles such as Wolves and Sheep, Squaring Puzzles, Gerrymandering and more.  When asked if they would want to attend another festival, the young mathematicians responded with a resounding YES!  We look forward to next year’s celebration around the time of Pi Day.

Let’s Take a Vote with Dr. Melissa Dennison
February 11, 2021
Dr. Melissa Dennison of Baldwin Wallace University stirred mathematical thinking around voting theory.  “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
Dr. Curtis Bennett of the California State University Long Beach led us in an exploration of curious decimals.  We worked in teams using spreadsheet technology to discover surprising patterns that arise from dividing by certain numbers.   Here is a recording of the session.

2020

It’s Hip to be Square with Dr. Steve Phelps
December 10, 2020
Today we welcomed Ohio math and technology guru Steve Phelps of Hamilton County ESC.  He led us in an exploration utilizing virtual algebra tiles in Geogebra.   Suddenly we found ourselves doing more than just completing the square.  We did things visually and dynamically, finding tangents to parabolas and other curves and going beyond a traditional representation of completing the square.  In fact, at times we were “completing the rectangle”. 

Mathemagics! with Dr. Arthur Benjamin
November 12, 2020
Today we welcomed the Mathemagician, Dr. Arthur Benjamin.  We learned how to perform a variety of mental math calculations, including: squaring two digit numbers, squaring three digit numbers, performing computations from left to right, and cubing numbers.  We even learned a few cool facts about Fibonacci numbers.
 
 
Let’s Play a Game - LIFE of a Mathematician
September 17, 2020
Today we began a year of virtual meetings, as we resolved to continue the Crooked River Math Teacher Circle despite the COVID-19 pandemic and in spite of the loss of our dear friend, and one of the founding members of our leadership team, Lynn Awring.  In this session, we honored the life of British mathematician John Conway.  In April of this year, he developed symptoms from COVID-19 and passed at the age of 82.   We celebrated his legacy with 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
 
The theme for today was Wandering Around the World of Geometry.   Lynn Aring began with a game involving Random Walks.  Michael Buescher then had us explore Random Walks in more depth.
The afternoon session consisted of tasks led by Sara Good and Paul Zachlin on Billiard Table Geometry.  We even learned about the beautiful earrings and other artwork that mathematician Diana Davis created after years of studying this problem.

2019

The Light Bulb Went On
Dr. Paul Zachlin
November 19, 2019

The Crooked River Math Teachers’ Circle had their second meeting of the 2019-2020 academic school year on November 19, 2019 at the ESC.  The meeting began with pizza and conversation at 4:00.  At 4:30, Sara Good presented the appe-teaser which was some puzzles involving squares.   Paul Zachlin from Lakeland Community College followed with The Light Bulb Problem, which is a variant of the classic “Locker Problem”.  A lot of mathematics came to light!

Shuffling Around 
Dr. Paul Zachlin
September 19, 2019

CRMTC held the first session of the 2019-2020 year on Thursday, September 19th at the ESC of Cuyahoga County. Twenty-Seven (27) educators including university faculty, university students, and K-12 classroom teachers attended the meeting. All five (5) members of the Leadership Team (Lynn Aring, Michael Buescher, Sara Good, Kate Lane, and Paul Zachlin) also attended the meeting.
 
Participants warmed-up by organizing a single suit from a deck of cards so that the cards would be laid down in ascending order (A – 2 – 3 – etc.) using a down & under deal. That is, the first card is laid down, the next goes to the bottom of the deck, the next card down, the next to the bottom, etc. Kate Lane from Baldwin Wallace University led this activity. 
 
Following this activity, Sara Good and Paul Zachlin led the group in the Roommate Game – An Exploration of Stable Matchings. We were challenged to find a way to pair roommates so that nobody would leave their roommate for a different one. (If you are interested, you can find the problem here: https://www.mathteacherscircle.org/news/mtc-magazine/spring19/roommate/)
 
Many thanks to the Greater Cleveland Council of Teachers of Mathematics for providing the salad, pizza, and snacks.



Summer Summary 2019
June 17, 2019-June 19, 2019
Summer Immersion Workshop

Day One
Sara Good began the day with a variation of the popular game Guess Who?  Not only did participants get to know each other, but they also hat to use a little math to formulate a winning strategy.
 
Next, Michael Buescher had everyone explore some patterns that arise from simple arithmetic with consecutive integers.  It was fun, and now we were really starting to use our noggins.
 
In the afternoon, Steve Miller from the Rubber City MTC had everyone building skyscrapers, and a lot was learned from the experience.  Lynn Aring had everyone do some self-reflection at the end of the day.
 
Day Two
In the morning, Sara Good pulled out the classic game, Rack-O.  We played, we asked questions, and we found ourselves doing mathematics!  Lynne Pachnowski from the Rubber City MTC was the next presenter.
 
In the afternoon, Paul Zachlin led the group in studying Mathematics from Primary Historical Sources.  We explored an ancient tablet and the mathematical notation used on it.  The main activity was Generating Pythagorean Triples using the methods of Pythagoras and Plato.  Lynn Aring asked everyone to consider the “teacher moves” they had utilized on Day Two.
 
 Day Three
Michael Buescher started everyone off exploring Magic Squares.   Then Kate Lane followed that up with an exploration of Panda Squares.  In both cases, there were plenty of patterns to recognize and follow!


Covering and Tiling
Dr. Paul Zachlin
May 9, 2019

 CRMTC held the last session of the 2018-2019 year on May 9th at the ESC of Cuyahoga County. 
 
Kate Lane from Baldwin Wallace University began the evening with an “appeteaser” called “Grasshopper Numbers”.  Following this activity, her colleague Aaron Montgomery, also from Baldwin Wallace, explored the covering of different size checkerboards with different size pieces.  We began with rectangles of size 1x2.  Things got more complicated as we looked at boards with 'holes' and tried covering with different size pieces. 


Triple Fun
Dr. Paul Zachlin
March 7, 2019

The Crooked River Math Teacher’s Circle gathered on Thursday, March 7th 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 [email protected]

2018

Gift Giving-Zip Code Crunch
Dr. Paul Zachlin
November 8, 2018

The Crooked River Math Teachers’ Circle had their second meeting of the 2018-2019 academic school year on November 8, 2018 at the ESC.  The meeting began with pizza and conversation at 4:00.  At 4:30, Michael Buescher from Hathaway Brown presented the appe-teaser “How much is your name worth?”
For the main event, since gifts need to be mailed, Paul Zachlin from Lakeland Community College led participants in the activity: Zip Code Crunch:  An Adding Game.  Who knew that zip codes contained so much interesting mathematics in them?


Cornhole Math 
Dr. Paul Zachlin
 September 13, 2018

The Crooked River Math Teachers’ Circle had their first meeting of the 2018-2019 academic school year on September 13 at the ESC.  The meeting began with pizza and conversation at 4:00.  At 4:30, the group engaged in a few “appeteasers” – just a few interesting problems to get our mathematical minds up and running.  We even went outside for a little Cornhole!   Participants then explored Cornhole Math, which began with questions about the amount of paint needed to paint different size cornhole boards.  The initial challenge was to illustrate solutions with pictures rather than relying on computations.  In the end, the illustrations were used to help shed light on why we “multiply by the reciprocal” when we divide by fractions.




Summer Summary 2018
July 30 - August 1, 2018

Summer Immersion Workshop

Day One

After a quick introductory game of “24”, including enough “I wonder” questions to last a week or more, Chris Bolognese of the Columbus Math Teachers Circle led us in the main event: Rainbow Squares.  Given the whole numbers 1 through n, can you pair them up so that every pair adds to a perfect square?  We discovered that sometimes you can (1 through 8, for example); sometimes you can’t (1 through 10), and sometimes you can do it in more than one way (1 through 26). When connecting the pairs on a number line, the “rainbow” part of the title becomes obvious, but when you do it in a circle you get different patterns.  And what arranging the numbers 1 through 15 in a row so that every consecutive two numbers adds to a perfect square?  Very interesting things happen then …
 
In the afternoon, Kate Lane brought the game Radical Tic-Tac-Toe (available commercially as Gobblet Gobblers) and brought new life to the passtime that you gave up once you and your friends knew exactly how to play, and every game ended in a tie.  Well - now things don’t end in a tie, and young kids are often the ones to beat - Kate’s son, Noah, was the most feared player, and curiously enough, a side square was often the most effective opening move - far different from the Old Standby.
 
Day Two

In the morning, Lynn Aring and Sara Good began the session with Jo Boaler’s visual numbers.   Participants had to opportunity to share many creative ways that they visualized numbers.  This was followed by examining the Prime Climb board and noticing many different patterns and interesting questions such as “Why is 11 the first prime that is red?”.
 
In the afternoon, we started with playing several different variations of Prime Climb, and spent the rest of the day exploring several conjectures about the distributions of colors of Smarties candies and different ways to eat them, posed by YouTube mathematician Vi Hart.  We proved one conjecture by developing an algorithm for eating a pack of 15 Smarties as five three-candy “sandwiches” with two of the same color on the outside and a different color on the inside.  Try it yourself!
 
Day Three

We welcomed Lynne Pachnowski and Linda Saliga from the Rubber City Math Teachers Circle in Akron.  They brought lockboxes and clues to open each of the six different locks keeping them secure.   But it wasn’t easy!  Each lock had a puzzle involving at least four smaller puzzles; these smaller puzzles hit on a wide variety of topics, from geometry to counting to functions.  These were true challenges - it took the entire group working together to break each lock’s code and finally open the boxes to get at the tasty treats inside.




It’s Only Logical
Dr. Paul F. Zachlin
May 17, 2018
In our final evening session of the 2017-2018 school year, we explored logical reasoning.  The session began with a Math teaser where Dr. Kate Lane had participants work on a 5x5 and then a 10x10 Nonogram.  An endless supply of these brain teasers can be found at https://www.puzzle-nonograms.com/.
Next, we played a number-guessing game called Pico, Fermi, Bagel.  This game is similar to the popular board game from the 1970s called Mastermind, although repetition is not allowed. 
The question was raised whether allowing repetition makes the game more challenging, and so we transferred to an analysis of Mastermind. 
You can see our questions, observations, and strategies for these games by clicking here: Mastermindquestionsobservationstrategies 
After some discussion, we tackled a series of exercises designed to develop strategy for Mastermind, which were taken from Section 2 of the article by Tom Davis.
We then learned that back in 1976, Donald Knuth proved that the game of Mastermind can always be won in five moves or less, and we looked at the paper. 
We finished the evening by looking at a paper published in a Biology Journal entitled,
Using the Game of Mastermind to Teach, Practice, and Discuss Scientific Reasoning Skills
Thanks to everyone who participated – it was a very engaged group!


The IDEAS of March
Dr. Paul Zachlin
March 13, 2018

The Crooked River Math Teacher Circle had an enjoyable evening analyzing puzzles.  We began by playing around with SOMA cubes.  Nanette Reilly guided us through some of the history of the puzzle before asking us to each build our own set out of wooden blocks and glue.  It was amazing how much mathematical discussion was generated at the tables as we participated in her activity.
Next, we pondered where to find the “missing area” as we looked at The Missing Square Puzzle.
Then the rest of the evening was spent on The Stomachion, a 2200-year-old puzzle associated with Archimedes.  In our groups we worked through an activity published as part of the NCTM Illuminations series.
Before wrapping up the evening, we looked at a few links that detailed some of the fascinating story of this puzzle.  Our primary reference was a page at the Cornell website, since it was Cornell mathematician Bill Cutler who solved the problem posed by Archimedes to find the number of distinct ways to recreate the square from the pieces of the puzzle.
Other links referenced that evening were:
Here is another account of the history we did not use much
A website with more mathematical insights into Archimedes’ puzzle
Thanks to everyone who participated!

2017

A War of Codes: CLE vs. CBUS
On May 18th,
 The Crooked River Math Teachers’ Circle held their fifth and final meeting of the school year at the Educational Service Center of Cuyahoga County. This was our fourth evening meeting during which dinner was provided to all participants, yet it was our FIRST virtual meeting with another MTC! The session was titled “A War of Codes: CLE vs. CBUS.” Chris Bolognese of the Columbus Math Teachers’ Circle led the two MTCs in an investigation of cryptography and a race to crack each other’s code. It was “virtually” the most fun that two warring opponents could have.
 
 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 
    

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