Three top-notch Math Circle leaders have come together to share with the world their insight and wisdom — and most important — their exuberant joy in math by presenting lesson plans to five of their favorite mathematical wonders for novice and expert math circle leaders alike! Woohoo! Carefully laid out to be inviting and welcoming to all, and carefully and thoughtfully structured to nudge the facilitator deeper and deeper into the delight and awe of running a math circle session (with rest stops and side turns along the way, if desired), this book aptly portrays the beautiful human spirit of the Math Circle community and the genuine process of exploring mathematics. So, come! Play with math! Here are five truly fabulous ways.

This is an exciting book. It brings us the freshness of experience. The mathematics is not laid out in logical order, but in pedagogical order. The writers use stories of their work with students to guide us through the discoveries that a group is likely to make, as a game, puzzle, or activity elicits mathematical thought. The activities start very simply, then soar to the heights, in some cases linking to open research questions.

The authors use these activities to introduce specific mathematical techniques (counting techniques, concepts from number theory, methods of proof) and also strategies (generalizing, considering special cases, re-formulating the problem). The activities are carefully chosen and structured. The exposition is well thought out, both mathematically and pedagogically. And even emotionally. The writers, because they have worked directly with students, are able to recount their observations of the students. emotional, as well as mathematical experiences. Emotions — the frustration of puzzlement, the joy of discovery — are the key to motivating the student to learn. And this is the core task of the teacher.