Mathematics can be exciting and fun for all students, especially when exploring the myriad activities and problems found in this book…Designed to capture students' attention and creativity, each problem-based activity promotes exploration and interesting discoveries, often with a hands-on approach using everyday objects…The extensive list of complementary resources provides additional opportunities for enrichment and challenges…Get the book, use it, and help students have fun doing interesting mathematics.
Sophisticated mathematics is accessible to all. This book proves it! Solve This is a collection of intriguing mathematical problems and activities linked by common themes that involve working with objects from our everyday experience. Learn about the mathematical mysteries of a bagel, a checkerboard, and a pile of laundry, for example. Discover for yourself that wheels need not be round, that braids need not have free ends, that it is always best to turn around twice—and more! Mathematics is all around us. We all do mathematics every day.
The book irresistibly tempts the reader to embark on a journey of investigation and discovery. All the activities are immediate, catchy, and fun, but upon investigation begin to unfold into surprising layers of depth and new perspectives. The necessary mathematics in increasing levels of sophistication is fully explained along the way, but readers may amend the journey in any way to match their mathematical abilities. Elementary, middle, and high school students, college students and mathematics majors, faculty from all departments and professional mathematicians, as well as self-described math phobics have all enjoyed these activities and have all attained a sense of satisfaction and accomplishment from them. Mathematics educators will find this an invaluable source of fresh and innovative approaches to topics in mathematics.
This book is for everyone. No preparatory learning is needed to dive right in! You will enjoy doing these activities even more as a group event. Whether you are a student or an instructor, anxious about or comfortable with math, or just curious about mathematics, you will be challenged and delighted by the activities described herein.
Part I: Activities and Problem Statements
1. Distribution Dilemmas
2. Weird Shapes
3. Counting the Odds…and Evens
4. Dicing, Slicing and Avoiding the Bad Bits
5. "Impossible" Paper Tricks
6. Tiling Challenges
7. Things that Won't Fall Down
8. Mobius Madness: Tortuous Twists on a Classic Theme
9. The Infamous Bicycle Problem
10. Making Surfaces in 3- and 4-Dimensional Space
11. Paradoxes in Probability Theory
12. Don't Turn Around Just Once!
13. It's All in a Square
14. Bagel Math
15. Capturing Chaos
16. Who Has the Advantage?
17. Laundry Math
18. Get Knotted!
19. Tiling and Walking
20. Automata Antics
21. Bubble Trouble
22. Halves and Doubles
23. Playing with Playing Cards
24. Map Mechanics
25. Weird Lotteries
26. Flipped Out
27. Parts That Do Not Add to Their Whole
28. Making the Sacrifice
29. Problems in Parity
30. Chessboard Maneuvers
Part II: Hints, Solutions and Further Thoughts
Part III: Solutions and Discussions
Believing that mathematics really is accessible to all, James Tanton (Ph.D., Mathematics, Princeton University 1994) is committed to sharing the delight and the beauty of the subject. In 2004 James founded the St. Mark's Institute of Mathematics, an outreach program promoting joyful and effective mathematics education. He worked (2004-2012) as a full-time high school teacher at St. Mark's School in Southborough, MA, and he conducted, and continues to conduct, mathematics graduate courses for teachers through Northeastern University and American University. He also gives professional development workshops across the nation and Canada.
James recently relocated to Washington, DC and is currently the Mathematical Association of America Mathematician in Residence. He also conducts the professional development program for the Math for America program in DC.
James is the author of The Encyclopedia of Mathematics (Facts on File, 2005), Mathematics Galore! (MAA, 2012) and twelve self-published texts. He is the 2005 recipient of the Beckenbach Book Prize, the 2006 recipient of the Kidder Faculty Prize at St. Mark's School, and a 2010 recipient of a Raytheon Math Hero Award for excellence in school teaching.
He also publishes research and expository articles, and through his extracurricular research classes for students has helped high school students pursue research projects and also publish their results.
More about James can be found on his website www.jamestanton.com.
This book is different! Most "problem books" contain many difficult and thought-provoking problems that are usually tackled with pencil and paper. The problems contained in such books tend to be at the level of the Mathematics Olympiad. As an example of such a text I refer you to Mathematical Olympiad Challenges by Andreescu and Gelca (Birkhäuser, 2000). As the subtitle of the book under review indicates, the problems in this book are more activity-oriented. Some use pencil and paper, but most require that the students actually move around. Continued...