This book, inspired by the Julia Robinson Mathematics Festival, aims to engage students in mathematical discovery through fun and approachable problems that reveal deeper mathematical ideas. Each chapter starts with a gentle on-ramp, such as a game or puzzle requiring no more than simple arithmetic or intuitive concepts of symmetry. Follow-up problems and activities require intuitive logic and reveal more sophisticated notions of strategy and algorithms. Projects are designed so that progress is more important than any end goal, ensuring that students will learn something significant no matter how far they get. The process of understanding the questions and how they build on one another becomes an exhilarating ride, revealing serious mathematics before the reader is aware of the transition. This book can be used in classrooms, math clubs, after school activities, homeschooling, and parent/student gatherings and is appropriate for students of age 8 to 18, as well as for teachers wanting to hone their skills. 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.
Author(s): Alice Peters, Mark Saul
Series: MSRI Mathematical Circles Library
Edition: 28
Publisher: American Mathematical Society
Year: 2022
Language: English
Commentary: Publisher PDF
Pages: 208
Tags: Mathematics Study; Mathematics Teaching; Mathematics Teachers–Training; Mathematics Education; Mathematics Introductory Exposition; Mathematics Teaching Problem Solving; Mathematics Teaching Heuristic Strategies; Foundations of Mathematics; Logic; Problem Books; Mathematics Competitions; Mathematics Examinations; age 8 to 18
Cover
Foreword
Preface
Acknowledgements
Part 1. Activity Guides
Chapter 1. Color Triangle Challenge
Some Initial Explorations
Toward a Generalization
Further Generalizations
Applying Arithmetic
Connection to the Binomial Coefficients
Historical Notes
Chapter 2. Magic Squares and Algebra
Constructing a Magic Square
The Geometry of Magic Squares
Some Facts about Groups
Uniqueness of the Magic Square: Some Combinatoric Results
New Magic Squares from Old
The Vector Space of a Magic Square
Magic Squares and Tic-tac-toe
Historical Notes
Chapter 3. Nim
One-Row Nim
Nim Variants
Two-Row Nim
Historical Notes
Chapter 4. Palindrome Grab!
The Basic Game
The Greedy Game
The Patient Game
Historical Notes
Chapter 5. To Twos, Too! Two Twos? More?
SDP2 Representations
SP2 Representations
S2P2 Representations
Some Extensions
Historical Notes
Chapter 6. Prisoner Puzzle
Last Man Sitting
Lucky 7?
Changing of the Guard
Historical Notes
Chapter 7. Broken Calculators
Calculator 1
Calculator 2
Calculator 3
Calculator 4
Calculator 5
Historical Notes
Chapter 8. Dominoes and Checkerboards
Constructing Tilings
Counting Tilings
Historical Notes
Chapter 9. Fair Division
Rectangles, Triangles, Squares
Quadrilaterals and Squares
Historical Notes
Chapter 10. Jumping Julia
Mazes and Graph Theory
Make Your Own Maze
Historical Notes
Part 2. Activity Handouts
Chapter 1. Color Triangle Challenge
Some Initial Explorations
Toward a Generalization
Applying Arithmetic
Chapter 2. Magic Squares and Algebra
Constructing a Magic Square
The Geometry of Magic Squares
Uniqueness of the Magic Square: Some Combinatoric Results
New Magic Squares from Old
Chapter 3. Nim
One-Row Nim
Nim Variants
Two-Row Nim
Chapter 4. Palindrome Grab!
The Basic Game
The Greedy Game
The Patient Game
Chapter 5. To Twos, Too! Two Twos? More?
SDP2 Representations
SP2 Representations
S2P2 Representations
Some Extensions
Chapter 6. Prisoner Puzzle
Last Man Sitting
Lucky 7?
Changing of the Guard
Chapter 7. Broken Calculators
Calculator 1
Calculator 2
Calculator 3
Calculator 4
Calculator 5
Chapter 8. Dominoes and Checkerboards
Constructing Tilings
Counting Tilings
Chapter 9. Fair Division
Rectangles, Triangles, Squares
Quadrilaterals and Squares
Chapter 10. Jumping Julia
Mazes and Graph Theory
Make Your Own Maze
Back Cover
