Nim is an ancient game in which players take turns picking up stones from distinct piles. (The word “nim” means “take” in old English.) There are variations of the game depending on how many piles of stones there are at the beginning of the game, how many stones a player may take in a turn, and what constitutes a “win.” The game is simple, and students need no background knowledge to play the game, yet it serves as a medium for discussing important mathematical ideas: the notion of strategy, division with remainder, modular arithmetic, representing patterns with variables, and mathematical induction.

These are two mathematically related games that are best played one after the other so that students can see their relationship. Like one-row Nim, they are both simple, two-person, perfect-knowledge games of strategy.

This is a set of activities to be used over a few periods. It includes "Fifteen," an arithmetic card game, and "Magic Squares," a classic topic in recreational mathematics, and a three-dimensional version of tic tac toe. The activities are each rich in their own right. Students gain practice with mental arithmetic and spatial thinking, while they are piecing together strategies and making deep and surprising connections.

This activity is played either on graph paper on a large floor with square tiles. Put three counters on three vertices of one of the tiles. These counters are frogs, and they move by playing 'leapfrog.' To take a turn, a student moves his counter to another vertex by “reflecting” his frog over another frog. The job of the group is to get any one of the three frogs to land on the fourth vertex of the original square. This is a nice problem-solving activity which also gives students experience with coordinate graphs and the idea of parity.

This is a classic card game in which players combine four integers to make the number 24. The game is engaging for students of different levels and requires nothing more than a deck of cards.

This is a series of activities in which students construct polyhedra using toothpicks and gumdrops, as the instructor guides them through various investigations. The activity also has a fun extension in which students explore the polyhedra by dipping them in soap-bubble solution.

In this series of activities, students investigate knots, gaining practice with spatial reasoning and learning a little about an important branch of mathematics not normally studied at this level.

The following activities are meant to give students an introduction to a topic in topology, classifying surfaces. The introductory lesson and activities use a story about a vicious dog and a fence to encourage students to think about the properties of different surfaces, such as whether a closed loop on the surface divides it into different regions. Students then practice classifying surfaces according to their genus (or how many "holes" the surface has). The activities are followed by a "museum trail" to be used in New York's American Museum of Natural History. Students walk through the Hall of Mexico and Central America and answer questions about the clay statues and figures on display. Students examine the figures through the lens of topology, analyzing the surfaces and classifying them according to their genus.