Best Math Competition Books for Kids, by Grade and Contest
The math olympiad and competition books worth buying, sorted by grade and contest: the official past-problem books from MOEMS, Math Kangaroo, CML and MATHCOUNTS, plus the Art of Problem Solving textbooks, and who each one suits.
· 8 min read
Prep guides by contest: Math Kangaroo Noetic MOEMS CML AMC 8
Free practice problems: Math Kangaroo Noetic MOEMS CML AMC 8
On this page · 6 sections
Math competition books for kids come in two kinds. Official contest books are collections of past problems, published by the contest itself: MOEMS, Math Kangaroo, CML and MATHCOUNTS all sell them. Teaching books, mainly from Art of Problem Solving (AoPS), explain the math step by step and work for any contest. A child with a contest a few months away gets the most from the official book for that contest. A child who loves math and has years ahead gets more from a teaching book.
Every detail below comes from the publisher’s or the contest’s own page, checked in October 2026. We don’t use affiliate links.
The short list by grade
| Grades | Contest | Book | Publisher |
|---|---|---|---|
| 1–2 | Math Kangaroo | Grades 1–2 books (two volumes) | Math Kangaroo USA |
| 2–3 | CML | CML book for Grade 2–3 | Continental Mathematics League |
| Ages 6–13 | Any | Beast Academy, levels 1–5 | AoPS |
| 3–4 | Math Kangaroo | Grades 3–4 books (two volumes) | Math Kangaroo USA |
| 4–6 | MOEMS Division E | Math Olympiad Contest Problems for Elementary and Middle Schools (Volume 1) | MOEMS |
| 4–6 | CML | CML book for Grade 4–6 | Continental Mathematics League |
| 5–6 | Math Kangaroo | Grades 5–6 books (two volumes) | Math Kangaroo USA |
| 6–8 | MOEMS Division M | Math Olympiad Contest Problems Volume 3 | MOEMS |
| 6–8 | AMC 8, MATHCOUNTS, MOEMS | Prealgebra | AoPS |
| 6–8 | MATHCOUNTS | School Handbook; MATHCOUNTS Competitions | MATHCOUNTS |
| 6–8 | Any | Competition Math for Middle School | AoPS |
| 7–8 | Math Kangaroo | Grades 7–8 books (two volumes) | Math Kangaroo USA |
| 7 and up | AMC 8, MATHCOUNTS | The Art of Problem Solving, Volume 1: the Basics | AoPS |
Official contest books
These are the closest thing to the real test: the problems were written for that contest, at that level, in that format.
MOEMS: the “math olympiad” books
In elementary and middle school, “math olympiad” usually refers to MOEMS (Math Olympiads for Elementary and Middle Schools), so these are the classic math olympiad books. MOEMS sells them in its official store and lists them on its resources page. Division E is grades 4–6; Division M is grades 6–8.
| Book | Author or editors | What’s in it |
|---|---|---|
| Math Olympiad Contest Problems for Elementary and Middle Schools (Volume 1) | Dr. George Lenchner | 400 Division E problems from the 1979/80–1994/95 contests |
| Math Olympiad Contest Problems, Volume 2 | Richard Kalman | Division E problems from 1995/96–2004/05 and 175 Division M problems from 1998/99–2004/05 |
| MOEMS Contest Problems, Volume 3 | Richard Kalman and Nicholas J. Restivo | 200 Division E and 200 Division M problems, 2005/06–2012/13 |
| MOEMS Contest Problems, Volume 4 (The International Edition) | Nicholas J. Restivo, Jonathan J. Phegan and Pauline Kokloff | 100 Division E and 100 Division M problems, plus problems from APSMO, MOEMS’s Australian affiliate |
| Math Olympiad Contest Problems, Volume 5 | MOEMS | APSMO Junior (Division E level) and Senior (Division M level) problems, 2018–2022 |
| Creative Problem Solving in School Mathematics, Second Edition | Dr. George Lenchner | A book on problem solving by the author of Volume 1, listed with the MOEMS practice books |
Which one first: for a Division E child, Volume 1 is the classic and holds the most Division E problems. For a Division M child, Volume 3 has the most Division M problems. MOEMS also sells sets of several volumes. Stock runs out at times (one volume was on back order when we checked), so if a book is a holiday gift, order early.
MOEMS also posts a free sample contest for each division and a weekly problem with solutions on the same resources page. Try those before you buy.
Math Kangaroo: past tests by grade band
Math Kangaroo USA sells two volumes of past problems for each grade band, one with the even-year tests and one with the odd-year tests, or both as a bundle. Every problem comes with a solution, and each book is sold as a physical or a virtual copy.
| Grade band | Problems per volume |
|---|---|
| Grades 1–2 | 240 |
| Grades 3–4 | 312 |
| Grades 5–6 | 360 |
| Grades 7–8 | 300 |
Questions are color-coded by difficulty: easy, medium and hard. Math Kangaroo also sells the original printed test booklets from single years, if you want a child to sit one complete paper the way it looked on contest day.
CML: the CML books by grade band
The Continental Mathematics League sells books of past problems with solutions by grade band and year range: Grade 2–3 (2016–2020 and 2021–2026), Grade 4–6 (2011–2015, 2016–2020 and 2021–2026) and Grade 7–9 (2011–2015 and 2016–2020). Parents can order them directly. CML also posts a free sample test for every grade (see the CML FAQ).
Pick the band your child competes in this year. Grades 2–3 have 3 meets a season and grades 4–9 have 5, with problems written for each level.
MATHCOUNTS: the handbook and past competitions
For grades 6–8, MATHCOUNTS publishes its own practice material:
- The School Handbook comes out every school year. The public edition has 200 problems with an answer key and step-by-step explanations (MATHCOUNTS). Registered coaches get a 250-problem edition free.
- MATHCOUNTS Competitions volumes and The Most Challenging MATHCOUNTS Problems Solved collect past contest problems (past competitions page). Both are sold in the MATHCOUNTS store.
- Free: last year’s chapter and state competitions, with answer keys and solutions, are free to download on the same page.
Noetic and AMC 8: no official book
Noetic Learning doesn’t sell a book. It sells past tests with solutions for grades 2–8, one season at a time or bundled by grade. For the AMC 8, the MAA posts the 2023 AMC 8 with solutions for free and sells collections of past contests; for a book, most families use the AoPS titles below.
Teaching books from Art of Problem Solving
AoPS books teach the topics contests test, and every title below comes with full solutions. They suit a child who wants to get better at math over years, whatever the contest.
| Book | Author(s) | Level (publisher’s) | Good for |
|---|---|---|---|
| Beast Academy | AoPS | Ages 6–13, levels 1–5 | Elementary kids who like puzzles; comic-style Guide books plus Practice books with step-by-step solutions |
| Prealgebra | Richard Rusczyk, David Patrick, Ravi Boppana | Middle school | The first AoPS book for most contest kids; the publisher names MATHCOUNTS, MOEMS and the AMC 8. Over 1,000 problems, separate solutions manual |
| Competition Math for Middle School | Jason Batterson | Middle school | Algebra, counting, probability, number theory and geometry in one book; over 700 examples and problems with full solutions |
| The Art of Problem Solving, Volume 1: the Basics | Sandor Lehoczky, Richard Rusczyk | Grades 7–10 | Contest strategy for MATHCOUNTS and the AMC 8, 10 and 12; separate solutions book |
| Introduction to Counting & Probability | David Patrick | Grades 7–10 | A child who has finished Prealgebra and can solve linear equations |
| Introduction to Number Theory | Mathew Crawford | Grades 7–10 | Same prerequisite; primes, divisibility, bases, remainders |
Beast Academy has four books per level (A to D), so buy the first book of a level, not the whole level, as a gift. At level 1, Guide and Practice are combined into one book; from level 2 they’re separate books, and most families buy both.
How to choose (and use) a book
- Contest within six months: the official book for that contest and grade band. Nothing else matches the style so closely.
- No contest yet, or a child who reads math for fun: Beast Academy (elementary) or AoPS Prealgebra (middle school).
- Buy one book. A 400-problem book lasts a whole season at 3 to 5 problems a sitting.
- Use past problems twice. Early on, work through them untimed and talk about each mistake. In the last month, set the contest’s real time limit and score a full set.
- Expect hard answers to need explaining. Official books give solutions, but they’re written for teachers and coaches. Plan to sit with your child on the problems they miss.
Where our guides fit: the official books give a child lots of real problems; our prep guides teach the strategy for each topic in that contest’s format, with a free sample of each. Many families use both, the guide first and the official book for timed practice.
Free practice before you buy
Check whether your child likes this kind of problem before you spend money on a book. Each of these is free and printable:
- Math Kangaroo practice tests and problems by grade band
- MOEMS practice problems for Division E and Division M
- CML practice problems by grade, with links to CML’s own sample tests
- Noetic practice problems for grades 2–6
- AMC 8 practice problems and a full AMC 8 practice test
Not sure your child is ready for a contest at all? Start with the readiness checklist by grade.
This guide is not affiliated with or endorsed by Math Olympiads for Elementary and Middle Schools (MOEMS®). “MOEMS” is a trademark of its respective owners. This guide is not affiliated with or endorsed by Math Kangaroo USA or Kangourou sans Frontières. “Math Kangaroo” is a trademark of its respective owners. This guide is not affiliated with or endorsed by Continental Mathematics League. “Continental Mathematics League” is a trademark of its respective owners. This guide is not affiliated with or endorsed by Noetic Learning. “Noetic Learning Math Contest” is a trademark of its respective owners. This guide is not affiliated with or endorsed by the Mathematical Association of America (MAA) or the American Mathematics Competitions. “AMC 8” is a trademark of its respective owners. This guide is not affiliated with or endorsed by the MATHCOUNTS Foundation. “MATHCOUNTS” is a trademark of its respective owners. It is also not affiliated with or endorsed by Art of Problem Solving or Beast Academy. All book details come from each publisher’s official pages and can change.
Where to go from here
For a contest-by-contest plan, read how to prepare for MOEMS, how to prepare for Math Kangaroo or how to prepare for the AMC 8. For middle schoolers, the best math competitions for 7th and 8th graders covers MATHCOUNTS and the AMC 8.