M2 (M-Squared or "Mentoring Young Mathematicans"), by K. Gavin, T. Casa, S. Chapin, and L. Sheffield. Kendall Hunt, publisher
This is a collection of research-based supplemental units for K - 2 classrooms. It is written by the same people who authored the widely respected M3 materials. The activities are challenging, but they may be used with a whole class or in a smaller group setting within a flexible grouping model. They are not "handouts" for students. Significant teacher engagement is required, and students must have plenty of opportunities to talk and write about the mathematics.
M3 (M-Cubed or "Mentoring Mathematical Minds"), by K. Gavin, J. Dailey, S. Chapin, and L. Sheffield. Kendall Hunt, publisher
These activities are the current "gold standard" for meeting the needs of talented math students in grades 3 - 6. The units are challenging, but they may be used with a whole class or in a smaller group setting within a flexible grouping model. They are not "handouts" for students. Significant teacher engagement is required, and students must have plenty of opportunities to talk and write about the mathematics.
Advanced Common Core Math Explorations series, by J. Burkhart. Prufrock Press, publisher
These are my books. They consist of challenging, engaging, inquiry-based mathematical explorations for upper-elementary and middle school students. I originally developed and refined most of the activities for use in my own classrooms with gifted math students. The explorations support both the content and process (Mathematical Practices) standards of the Common core. Though the materials are designed so that students may work independently for much of the time, student/student and student/teacher conversation is crucial for making effective use of them.
Extending the Challenge in Mathematics: Developing Mathematical Promise in K-8 Students, by Linda Jensen Sheffield. Corwin Press, publisher
Sheffield's book offers a set of open-ended tasks that may be approached by students across a range of age and ability levels. They are tied to big mathematical ideas that talented (and all) students need to understand. This book is a great option for elementary school teachers who are looking for alternatives to "teaching the next topic in the book" when working with students who already know the concepts. I remember using a single activity (Same Sums) with a group of second graders for three months straight. We met once per week for about 45 minutes per session, and it seemed that we never ran out of new questions to ask and things to try! If I had come back to continue the same activity with the same group of kids in third grade, we could easily have done another three months and been learning new things every week.
Statistics for Kids, by Scott Chamberlin. Prufrock Press, publisher
This book for students in grades 4–6 contains open-ended problems in an often neglected topic area. The focus is on using "model-eliciting activities (MEAs)"—problems that require students to investigate real-world situations by creating and analyzing mathematical models that represent them. The scenarios are carefully chosen chosen to reflect the interests of upper-elementary students. The data are realistic but are also designed so that, in order to solve the problems, students must grapple with targeted concepts. This book does not contain formulas and procedures to memorize. Instead, the focus is on developing deep conceptual understanding.
problem solving books by Ed Zaccaro. Prufrock Press, publisher
Ed Zaccaro's popular books offer supplementary problem solving experiences for elementary and middle school students. They incorporate realistic and whimsical situations with entertaining drawings to motivate students to think meaningfully about important mathematical concepts. My favorite book is "10 Things All Future Mathematicians and Scientists Must Know: (But Are Rarely Taught)." In this book, he does not offer tricks or shortcuts but focuses on ten large concepts or habits of thinking such as "Your mind can be fooled," "Occam's Razor," "It's important to keep an open mind," and "It's important to maintain a healthy skepticism." He offers entertaining and instructional real-world stories as examples of these concepts and follows them up with discussion questions and problems.
A Mathematical Mystery Tour, by Mark Wahl. Prufrock Press, publisher
This is a perennially popular book full of activities based on the Fibonacci Numbers and the Golden Ratio. The materials challenge, excite, and inform students about mathematics while introducing them to a well-known set of topics in "recreational" mathematics.
10 Ways To Make Your Class Cozier for Gifted Students, by Ian Byrd
http://byrdseed.com/handouts/byrdseed-10-ways.pdf Ian Byrd has many excellent resources for those who work with gifted students, including this excellent list. The title speaks for itself.
Please contact me if you know of other excellent classroom books for talented and curious math students that should be included on this page!