Hard Math for Elementary School is new category of math book. The author 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 3^rd 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 4^th grade to try it.

A workbook (sold separately) contains over 100 challenging worksheets to reinforce the lessons of each section. PLEASE don't buy a copy of the book without also getting a copy of the workbook. It's really hard for anyone (let alone a 3^rd grader) to learn hard concepts and figure out whether they really understand them without working through applying them. For many kids the back-and-forth between the text and the workbook is the central experience of Hard Math.

An answer key for the workbook is also available. You can buy it cheaply on Amazon or view it for free on Prof. Ellison's MIT website.