Fall 2015 Math Circle

1. Overview

We had a great time with this Fall 2015 Math Circle. We really liked seeing studentscollaborating and working with college students and parents to learn new things. We hopeeveryone saw that math has all sorts of interesting questions to explore. The number one keyto successful problem solving? A positive attitude! For more information about the Ship-pensburg Area Math Circle visit us at http://webspace.ship.edu/lebryant/mathcircle

Below we include some notes about the activities we did along with some links to learnmore.

2. Activities

Problem Solving In our introduction les-son, we talked about problem solving tech-niques. These include working backwards,starting with an easier problem, being pa-tient, and trying lots of different approaches.We put together a problem-solving packetthat you can access on the Math Circle web-page, if you did not already bring one home.

Candy Sharing Game On our first day, wealso tried a candy sharing game. In this gamethe leader distributed “candy” among play-ers. When the leader said “Share!” each per-son who had two or more pieces of candy gaveone piece to the person on their right andone to the person on their left. After thatround of sharing was done, the leader wouldsay “Share!” again and the process would re-peat until the group saw a pattern. This wasan easy collaborative game that allowed ev-eryone to try different strategies for produc-ing patterns (like terminator, fixed point,and cycles). These are patterns mathemati-cians are interested in when examining anyrepeating process.

1

2

Mobius Strips In this lesson we started witha bit of “magic.” Dr. Bryant was able tocut out just the middle of an index card andshe passed a basketball through it! Have youtried this at home yet? This was an intro-duction to the idea of topology: the study ofwhat properties of a shape remain unchangedafter certain changes. The index card wasdefinitely changed and so a topologist wouldsay that the regular and cut index card aredifferent objects entirely. But a donut anda coffee cup? The same! One of the moreinteresting objects to study when thinkingabout changes is the Mobius strip, because itdoes some very wild and unpredictable thingswhen changed (cut). Everyone in the mathcircle tried to guess what would happen be-fore we did one of our cutting experimentsand then we would try to understand whyour guess was right or wrong. To try ourexperiments again at home, follow the link atthe end of this handout.

Figure 1. “O” wins with old rules

Figure 2. “X” wins with new rules

Tic Tac Toe Sure, everybody has played tictac toe before. But Dr. Galluzzo showed usthat the normal tic tac toe is “unfair” to someof the spots on the board- they cannot be in awinning line as often as the middle spot can!By changing the rules a bit we were able tomake a tic tac toe game where every singlespot on the board is as useful as every otherspot. Then we tried playing games to learnthese new rules. This activity started witha mini Sudoku discussion because there wasa connection between the new rules we madeand Sudoku on a small board. We learned wehave some really great Sudoku and tic tac toeplayers in our Math Circle!

3

Codes Spies are not the only ones who needto know about codes. In everyday life, codesare used to send information around the in-ternet and keep important information safe.We learned about Caesar ciphers, Masonic(pigpen) ciphers, scytales, and morse code.Then we used those codes to complete a scav-enger hunt around the math building. Every-one worked together to finish and earn theirMath-O-Ween treats. Good teamwork, MathCircle!!

Math Kangaroo On our last day we took apractice Math Kangaroo exam. The MathKangaroo competitions are geared at get-ting kids in grades 1-12 interested in math-ematics. Enrollment for the “MathKangaroo” International Competitionin Mathematics is in progress onwww.mathkangaroo.org until the end ofDecember while space is available.Thereis a “Certificate of Participation,” a t-shirt,and a toy on the test day, Thursday,March 17, 2016, for each participant. Thequestions are prepared by the InternationalCommittee and are the same in over 50 coun-tries on the same day. All enrolled studentsenjoy free access to Video Solutions of earlierMath Kangaroo Questions in the Media Li-brary from the time of registration until theend of August. Parents can register their chil-dren for any public Math Kangaroo Centerthey find on the Math Kangaroo webpage.The participation fee is $20 for each stu-dent. Families of three and more participat-ing children, parents in hardship, and Title-2- schools can apply for discounts. Informa-tion is available at www.mathkangaroo.org orat info@mathkangaroo.org and at 1-630-624-6284 after 6 P.M. CST.

4

3. Some Recommendations

There are many games and books out there that promote mathematical and logical think-ing. Here are a few of our favorites. Tell us about yours and we can add them to the list!

4. Internet References for Some Activities

• Candy Sharinghttps://riverbendmath.org/modules/Candy_Sharing_Game

• Wolf and Sheep Puzzlehttp://jrmf.org/problems/WolvesAndSheep.pdf

• Mobius Stripshttp://celebrationofmind.org/assets/martin-gardners-mobius-surprise.pdf

• Cryptographyhttp://www.cryptoclub.org

• Math Kangaroohttp://www.mathkangaroo.org