Hard Math for Elementary School

Hard Math for Elementary School is new category of math book. The author, MIT professor Glenn Ellison, calls it a math enrichment textbook. The idea is to make it easy for teachers or parents to supplement what kids are getting in school with with complementary lessons that are harder, deeper, and more fun.
Hard Math has chapters to accompany most textbook topics: addition with carrying, multiplication, fractions, etc. It covers other important topics - prime numbers, counting, probability - that are being squeezed out of many curricula. And it has chapters on topics which may not be as important -- tiling floors, solving number puzzles, making polyhedra out of marshmallows and toothpicks -- but that make the book more fun and develop higher-level reasoning skills.
Hard Math can be used in many different ways. Some parents will enjoy reading it together with their child. A teacher can give the book to an exceptional student who could read through it on her own whenever she's done early with the regular math lesson. Or a teacher could treat the book as a set of lesson plans for his or her top math group: each section of the book can serve as a set of lecture notes and the students could then work separately or together on the corresponding workbook page. Hard Math can similarly be a blueprint for an after school math club.
Hard Math is designed to be accessible to very advanced 3rd graders. But Hard Math is very hard. Most parents will find that there's a lot in it that they don't know and most advanced kids will be better off waiting until at least 4th grade to try it.
A workbook (sold separately) contains over 100 challenging worksheets to reinforce the lessons of each section. An answer key for the workbook is also available (and cheap).