PAST Meeting Archives
2019
The Light Bulb Went On
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
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 had 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
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
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
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, Here are some more links to resources:
Christmas Cracker Mystery Calculator Article
Christmas Cracker Challenge
Christmas Cracker Card Trick
2018
Gift Giving-Zip Code Crunch
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
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
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
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:
The 2003 N.Y. Times article
A page with a chronology and history of the puzzle
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!
https://filecabinet.eschoolview.com/DDBF1D9C-0BA1-443D-BC91-088493C49FB7/SomaCube_GoogleDocs.pdf
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.
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