**MSRI Mathematical Circles Library**

Volume: 20;
2018;
362 pp;
Softcover

MSC: Primary 97; 00;

**Print ISBN: 978-1-4704-3718-3
Product Code: MCL/20**

List Price: $55.00

AMS Member Price: $44.00

MAA Member Price: $49.50

**Electronic ISBN: 978-1-4704-4809-7
Product Code: MCL/20.E**

List Price: $55.00

AMS Member Price: $44.00

MAA Member Price: $49.50

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#### Supplemental Materials

# Mathematical Circle Diaries, Year 2: Complete Curriculum for Grades 6 to 8

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*Anna Burago*

A co-publication of the AMS and the Mathematical Sciences Research Institute

Mathematical circles, with their
question-driven approach and emphasis on problem solving, expose
students to the type of mathematics that stimulates the development of
logical thinking, creativity, analytical abilities, and mathematical
reasoning. These skills, while scarcely introduced at school, are in
high demand in the modern world.

This book, a sequel to Mathematical Circle Diaries, Year 1,
teaches how to think and solve problems in mathematics. The material,
distributed among twenty-nine weekly lessons, includes detailed
lectures and discussions, sets of problems with solutions, and
contests and games. In addition, the book shares some of the know-how
of running a mathematical circle. The book covers a broad range of
problem-solving strategies and proofing techniques, as well as some
more advanced topics that go beyond the limits of a school
curriculum. The topics include invariants, proofs by contradiction,
the Pigeonhole principle, proofs by coloring, double counting,
combinatorics, binary numbers, graph theory, divisibility and
remainders, logic, and many others. When students take science and
computing classes in high school and college, they will be better
prepared for both the foundations and advanced material. The book
contains everything that is needed to run a successful mathematical
circle for a full year.

This book, written by an author actively involved in teaching
mathematical circles for fifteen years, is intended for teachers, math
coaches, parents, and math enthusiasts who are interested in teaching
math that promotes critical thinking. Motivated students can work
through this book on their own.

In the interest of fostering a greater awareness and appreciation of
mathematics and its connections to other disciplines and everyday life, MSRI
and the AMS are publishing books in the Mathematical Circles Library series as
a service to young people, their parents and teachers, and the mathematics
profession.

Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

#### Readership

Teachers, parents, research mathematicians, and undergraduate and graduate students interested in teaching extracurricular math to middle and high school students.

#### Table of Contents

# Table of Contents

## Mathematical Circle Diaries, Year 2: Complete Curriculum for Grades 6 to 8

Table of Contents pages: 1 2

- Cover Cover11
- Title page iii4
- Contents v6
- Acknowledgments xiii14
- Preliminaries 116
- Part 1 . Session Plans 520
- Introduction 722
- Chapter 1. Session 1: Checkerboard Problems 924
- Chapter 2. Session 2: Review: Math Logic and Other Problem-Solving Strategies 1934
- Chapter 3. Session 3: Invariants 2540
- Chapter 4. Session 4: Proof by Contradiction 3348
- Chapter 5. Session 5: Decimal Number System and Problems on Digits 3954
- Chapter 6. Session 6: Binary Numbers I 4762
- Chapter 7. Session 7: Binary Numbers II 5974
- Chapter 8. Session 8: Mathematical Dominoes Tournament 6782
- Chapter 9. Session 9: Pigeonhole Principle 8196
- Chapter 10. Session 10: Geometric Pigeonhole Principle 89104
- Chapter 11. Session 11: Mathematical Olympiad I 95110
- Chapter 12. Session 12: Combinatorics I. Review 99114
- Chapter 13. Session 13: Combinatorics II. Combinations 109124
- Chapter 14. Session 14: Mathematical Auction 117132
- Chapter 15. Session 15: Combinatorics III. Complements. Snake Pit Game 121136
- Chapter 16. Session 16: Combinatorics IV. Combinatorial Conundrum 129144
- Chapter 17. Session 17: Magic Squares and Related Problems 139154
- Chapter 18. Session 18: Double Counting, or There Is More than One Way to Cut a Cake 147162
- Chapter 19. Session 19: Mathematical Olympiad II 157172
- Chapter 20. Session 20: Divisibility I. Review 161176
- Chapter 21. Session 21: Divisibility II. Relatively Prime Numbers; GCF and LCM 171186
- 21.1. Math Warm-up: Mysteries of Prime Numbers 171186
- 21.2. Discussion of the Day: Relatively Prime Numbers 173188
- 21.3. Greatest Common Factor (GCF) 174189
- 21.4. Least Common Multiple (LCM) 175190
- 21.5. How GCF and LCM Are Related 177192
- 21.6. GCF and LCM. In-Class Practice Problems 177192
- 21.7. Take-Home Problem Set 179194
- 21.8. Additional Problems 180195

- Chapter 22. Session 22: Divisibility III. Mathematical Race Game 181196
- Chapter 23. Session 23: Mathematical Auction 185200
- Chapter 24. Session 24: Divisibility IV. Divisibility by 3 and Remainders 189204
- Chapter 25. Session 25: Divisibility V. Divisibility and Remainders 199214
- Chapter 26. Session 26: Graph Theory I. Graphs and Their Applications 207222
- Chapter 27. Session 27: Graph Theory II. Handshaking Theorem 213228
- Chapter 28. Session 28: Graph Theory II. Solving Problems with Graphs 221236
- Chapter 29. Session 29: Mathematical Olympiad III 227242

- Part 2 . Mathematical Contests and Competitions 231246

Table of Contents pages: 1 2