Knots, Donuts, Surfaces, and Teacups (2000)
with Jim Belk, Maria (Sloughter) Belk, Cynthia (Bowers) Francisco, Leah Gold, and Kathryn Nyman
We worked with the girls using paper, playdough, and donuts to study properties of surfaces. The girls created mobius strips, and experimented by guessing how many twists and pieces would appear after cutting them. Some of the girls tried different methods of cutting and inadvertently started with extra twists which yielded results that were surprising to girls and grad students alike. We then made hexaflexagons before deforming playdough teacups into donuts. Afterwards, they took real donuts, wrapped string around them, and ate them, forming torus knots.

Origami ImagirO (2001)
with Angela Baldo, Maria (Sloughter) Belk, Leah Gold, and Debra Goldberg,
with additional help presenting by Kathryn Nyman, Suzanne Shontz, and Eileen Tan
We worked with the girls using kami, origami paper, to study symmetry. The girls created units which were the building blocks for the polyhedra. The units themselves had a symmetry, as many of us discovered; right-handed units would only fit with other right-handed units, and left-handed with other left-handed. The girls paired up and used these units to create a cube. Then, each pair of girls was challenged to create a cube that was a mirror image of the first cube. After playing with the two mirror image cubes for a while, we dicsovered that there was no way to rotate one to get the other. Angela Baldo presented a poster on this at the 3rd Origami in Math, Science, and Education conference in California.

The Secret of Nim (2002, 2003)
with Maria (Sloughter) Belk, Cynthia (Bowers) Francisco, Leah Gold, Evguenii Klebanov, Rajmohan Rajagopalan, and Treven Wall
We worked with a group of girls using M&Ms and pretzels to study the game of Nim. We started by having the girls pair up to play the 20 game: Starting at the number 20, each player takes turns subtracting an integer between 1 and 4 until zero remains; the player who ends at zero wins. After playing the game for a bit, the girls found the pattern and generalized it to similar games. Then the entire group challenged an "Expert" (one of the graduate students) to a game, and by correctly deciding whether or not to go first the girls defeated the Expert! From there the group moved on to two-pile Nim, where players take turns removing however many items they want from exactly one of two piles. The player who takes the last item wins. Some of the girls solved this and moved on to the three-pile case. After experimenting with different strategies for a while, the entire group challenged and defeated the Expert.

Fortune Telling for the 21st Century (2004)
with Maria (Sloughter) Belk, Evguenii Klebanov, Mia Minnes, Jonathan Needleman, and Treven Wall
We worked with a group of girls doing probability puzzles. At the beginning of the workshop we asked the girls, "What is mathematics?" Answers ranged from "numbers", "shapes", and "complicated" to "thinking", "learning", and "laughing". We also consulted an oracle, who told us, "You will change your mind about this." We then proceeded to try different puzzles. For each puzzle, the girls predicted what the most likely outcome would be, collected data on what happened during their experiment, and then compared the results to their predictions. After experimenting for a while, the girls developed an intuition for what was happening. They were able to come up with reasons why some outcomes were more likely than others. At the end of the workshop, we asked some of the more apprehensive girls whether they changed their minds about math. They had: "Math can be fun."

Smart Bubbles (2005)
created and presented with Maria Belk, David Biddle, Evguenii Klebanov, and Alex Meadows
and aided by the additional creative insights of Mia Minnes, Jonathan Needleman, and Treven Wall
We worked with a group of girls and approximately seven gallons of bubble solution in order to study minimal surfaces. We began by having the girls bend wire into different shapes and seeing what surfaces form when they are dipped into bubble solution. The bubble solution wants to find a way to connect the wire using the smallest amount of solution possible. The girls made interesting shapes, including circles, hearts, and spirals. We then used this idea along with transparent pieces of plastic held together with wooden pegs to find out how to connect three points in space (the pegs) using the smallest amount of material. The students guessed at the best way to connect them, measured their prediction with rulers, and then experimented by dipping the plastic into the bubble solution and shaking off the excess. The connections that the bubbles made showed the shortest pathway. After experimenting a couple of times with different arrangements of pegs, their predictions became quite accurate. Some even found experimental error in their measurements to account for the slight differences! All in all, a lot of good clean fun was had by everyone!

Note: many of these paragraphs were originally published in the Cornell math department's Math Matters newsletter.