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Mathematical Circle Diaries
Problem Sets and supporting materials for the "Math Circle Diaries, Year 2" book.
"Mathematical Circle Diaries, Year 2: Complete Curriculum for Grades 6 to 8" is a sequel to the "Year 1" book. It shares the same presentational approach, and it continues where the first book ended.
The book offers a curriculum that can be used in the second year of a middle-school mathematical circle. As in the first book, the curriculum is organized as a collection of lessons: every lesson includes the materials to be presented in class, the sets of problems to work on, and all other bells and whistles required to make this lesson easy to prepare and fun to teach.
This book covers a broad range of topics that belong to the "core" of a math circle education. These are proofing techniques and problem-solving strategies, as well as useful and exciting topics that are typically not well-covered in school. These topics include invariants, proofs by contradiction, the Pigeonhole principle, proofs by coloring, double counting, combinatorics, graph theory, binary numbers, divisibility and remainders, and many others. Yet, there are also plenty of challenges (problems, puzzles, riddles) that require nothing but common sense to solve them. The book includes problem-solving sessions, Olympiads, games, and tournaments as well.
As in the "Mathematical Circle Diaries, Year 1," the goal is to present topics that are both interesting and useful for children, balancing mathematical rigor with the scope of material and level of presentation that are accessible for middle school students.
Another goal of the book is to ease the challenge of preparing for a circle session. The material of the book is distributed among 29 easy-to-use lessons. Most of the lessons are organized as theoretical discussions followed by sets of relevant problems. These discussions and problems provide enough challenge for a broad range of students, from a rookie to a seasoned problem-solver. Some lessons are structured like mathematical entertainment sessions, problem-solving contests, and tournaments (Mathematical Dominoes, Mathematical Auctions, Olympiads). Besides, the book contains many pointers and useful “know-how” of teaching in a circle, such as advice on presenting the material and avoiding typical mistakes.
Follow this link if you want to leave feedback on the book or get notified when new materials are added to the site.
Problem sets and selected chapters from “Mathematical Circle Diaries, Year 2”.
Problem sets and selected chapters from “Mathematical Circle Diaries, Year 2”.
Use this resource to make your lessons easier to prepare and more fun to teach. Included is the entire collection of problem sets except for Olympiads and other competitions.
Also, to give you a better idea of what this book is about, several lessons from the book are included as well. (Click on the underlined chapters.)
Session 1: Checkerboard Problems. Problem Set. Extra Problems.
Session 2: Review: Math Logic and Other Problem-Solving Strategies. Problem Set.
Session 3: Invariants. Problem Set.
Session 4: Proof by Contradiction. Problem Set.
Session 5: Decimal Number System and Problems on Digits. Problem Set. Extra Problems.
Session 6: Binary Numbers I. Problem Set.
Session 7: Binary Numbers II. Problem Set.
Session 8: Mathematical Dominoes Tournament. Problem Set.
Session 9: Pigeonhole Principle. Problem Set. Extra Problems.
Session 10: Geometric Pigeonhole Principle. Problem Set.
Session 11: Mathematical Olympiad I. Math Olympiad Problems.
Session 12: Combinatorics I. Review. Problem Set. Extra Problems.
Session 13: Combinatorics II. Combinations. Problem Set.
Session 14: Mathematical Auction. Problem Set.
Session 15: Combinatorics III. Complements. Snake Pit Game. Problem Set.
Session 16: Combinatorics IV. Combinatorial Conundrum. Problem Set. Extra Problems.
Session 17: Magic Squares and Related Problems. Problem Set.
Session 18: Double Counting or There Is More Than One Way to Cut a Cake. Problem Set.
Session 19: Mathematical Olympiad II. Math Olympiad Problems.
Session 20: Divisibility I. Review. Exercises 1. Problem Set. Extra Problems.
Session 21: Divisibility II. Relatively Prime Numbers; GCF and LCM. Exercises 1. Problem Set.
Session 22: Divisibility III. Mathematical Race Game. Math Race Problems.
Session 23: Mathematical Auction. Problem Set.
Session 24 Divisibility IV. Divisibility by 3 and Remainders. Problem Set.
Session 25: Divisibility V. Divisibility and Remainders. Problem Set.
Session 26: Graph Theory I. Graphs and their Applications. Problem Set.
Session 27: Graph Theory II. Handshaking Theorem. Exercises. Problem Set.
Session 28: Graph Theory III. Solving Problems with Graphs. Problem Set.
Session 29: Mathematical Olympiad III. Math Olympiad Problems.
Math contests and games.
Math contests and games.
In our Circles, we have a few favorite team competitions. This book uses Mathematical Auction, Mathematical Dominoes, Mathematical Snake Pit, and Mathematical Olympiads. Read the rules of the contests here.
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