6 Best Mathcounts For 10Th Graders That Build Advanced Problem-Solving

Your child flew through MATHCOUNTS in middle school, and you saw the spark ignite. Now they’re in 10th grade, and the landscape of math enrichment looks completely different. It’s a common moment for parents: how do you keep that flame alive without overwhelming them or getting lost in a sea of acronyms? The goal isn’t just "more math," but finding the right challenges that build on their foundation and prepare them for what’s next.

Building on MATHCOUNTS: Top Picks for High School

Remember the energy of those middle school competitions? The speed rounds, the creative problem-solving—MATHCOUNTS built a fantastic foundation. It taught your child to think on their feet and find clever shortcuts.

As they move into high school, the nature of the challenge evolves. Problems become less about rapid calculation and more about deep, abstract thinking. The new frontier is about constructing logical arguments and proving why an answer is correct. This shift requires a new set of tools and a different kind of patience.

The programs we’ll explore are designed to bridge that gap. They represent the best next steps for a 10th grader ready to move beyond the MATHCOUNTS framework. Each one develops a distinct skill, from the formal competition pipeline to collaborative team events and the crucial art of proof-writing.

MAA’s AMC 10/12: The Gateway to USA(J)MO

If your child is looking for the main highway of competitive math, this is it. The American Mathematics Competitions (AMC), run by the Mathematical Association of America, are the most recognized and structured pathway in the United States. For a 10th grader, the journey starts with the AMC 10.

Think of the AMC 10 as the national qualifier. It’s a 25-question, multiple-choice test that covers a wide range of non-calculus topics, demanding much deeper thinking than typical schoolwork. A strong performance here is the first step toward national recognition. Many ambitious 10th graders also take the AMC 12, which includes more advanced trigonometry and logarithmic concepts.

This is more than a one-day event; it’s the start of a sequence. High scorers on the AMC 10 or 12 are invited to the American Invitational Mathematics Examination (AIME), a grueling three-hour, 15-question test with integer answers. Success on the AIME can lead to an invitation to the USA Mathematical Olympiad (USA(J)MO), the pinnacle of high school math. This is the path for the student who thrives on competition and has their sights set on national-level achievement.

Art of Problem Solving: A Curriculum for Competitors

You wouldn’t send a musician to a recital without lessons, and the same is true for math competitions. Art of Problem Solving (AoPS) is the premier training ground for students serious about the AMC pathway. It’s the curriculum that bridges the gap between knowing school math and understanding how to solve truly complex problems.

AoPS offers a complete ecosystem. Their textbooks, particularly the Intermediate series on Algebra, Counting & Probability, and Number Theory, are considered essential reading. They teach concepts from the ground up with a focus on why the math works, not just memorizing formulas. This approach is perfectly suited for the demands of AIME and Olympiad-level thinking.

Beyond the books, their online classes provide structure, accountability, and access to expert instructors. The real magic, however, might be the online community. The AoPS forums are a bustling hub where students from around the world dissect problems, share solutions, and learn from each other. For a 10th grader, this is an investment in a structured, comprehensive curriculum that will serve them through all four years of high school.

ARML: The Power of Team-Based Problem Solving

Does your child draw energy from working with others? If the solitary nature of most math contests feels isolating, the American Regions Mathematics League (ARML) is the perfect antidote. It transforms mathematics into a thrilling, high-energy team sport.

ARML is an annual competition where teams of 15 students gather at university campuses to compete. The event is a whirlwind of activity, including a team round where students work together on a set of problems, a "Power Question" that requires a full, proof-based group write-up, and an exciting, fast-paced relay round. It’s loud, social, and intensely collaborative.

This competition builds skills that others don’t. Students learn to communicate complex ideas under pressure, divide tasks efficiently, and trust their teammates. It’s a powerful lesson that math in the real world is rarely a solo endeavor. If you want to show your child that advanced math can be a social and collaborative pursuit, ARML is an unparalleled experience.

HMMT: A Taste of University-Level Problems

For the student who is already excelling on the AMC and AIME and is hungry for a bigger challenge, there is the Harvard-MIT Mathematics Tournament (HMMT). Run entirely by students from two of the world’s top universities, HMMT is one of the most prestigious and difficult high school competitions available.

The problems at HMMT are known for their elegance, creativity, and extreme difficulty. They often draw on concepts closer to undergraduate mathematics, giving students a genuine preview of what university-level STEM thinking looks like. The competition includes individual subject tests in algebra, geometry, and combinatorics, as well as team-based rounds.

Simply participating in HMMT is an achievement. It places your child in a community of exceptionally bright and motivated peers from around the globe. This isn’t a starting point; it’s an aspirational goal for a 10th grader who is already well-established on the competition circuit and wants to see how they stack up against the very best.

USAMTS: Developing Rigorous Proof-Writing Skills

Many competitions focus on getting the right answer. The USA Mathematical Talent Search (USAMTS) is different: it’s all about the journey. This unique, free competition is designed to develop the crucial skill of mathematical proof-writing, the language of higher mathematics.

The format is incredibly parent- and student-friendly. Students are given a set of five challenging problems and have an entire month to solve them and write up their solutions. They aren’t just circling an answer; they are crafting a complete, logical argument from scratch, explaining every step. This process teaches patience, precision, and a truly deep understanding of the concepts.

For a 10th grader, USAMTS is an ideal way to build the skills needed for the USA(J)MO and beyond. It’s a low-pressure environment to practice the transition from "solver" to "mathematician." If your child needs to work on communicating their ideas clearly and logically on paper, this is one of the most valuable activities they can do.

Brilliant.org: Gamified Learning for STEM Minds

What if the high-stakes, timed-test environment isn’t the right fit? For the student who loves puzzles and "aha!" moments but shies away from formal competition, Brilliant.org offers a fantastic alternative. It’s a self-directed, interactive platform that makes learning feel like a game.

Brilliant replaces lectures and textbooks with hands-on, visual problems. Users learn by doing, dragging-and-dropping, and experimenting their way through concepts. The courses cover a vast range of topics, from competition math mainstays like number theory to fascinating modern subjects like neural networks and quantum computing.

This is the perfect tool for fostering curiosity. A 10th grader can use it to supplement their AMC training by exploring a weak area, or they can ignore the competition track entirely and just follow their interests. It builds intuition and a love for problem-solving for its own sake, which is the most important goal of all.

Choosing the Right Mix of Math Enrichment

Seeing all these options can feel like staring at a restaurant menu where everything looks good. The key is not to order one of everything. It’s about creating a balanced meal that suits your child’s appetite and goals.

Start by having a conversation with your teen. What part of MATHCOUNTS did they love most? The thrill of competition? The cleverness of the problems? Working with friends? Their answer will point you in the right direction. The goal is to match the activity to their intrinsic motivation.

Consider a simple mix-and-match approach. For most, the AMC/AIME pathway (supported by AoPS) forms the core. From there, add an element that fits their personality. If they are a social learner, add ARML. If they need to work on their writing, add USAMTS. If they need a fun, low-pressure outlet, add Brilliant.org.

You don’t have to commit to everything forever. Try one or two things this year and see what sticks. The best plan is one that keeps your child engaged, challenged, and genuinely excited about the beauty of mathematics.

The path beyond MATHCOUNTS is less about finding a single "best" program and more about discovering the right combination of challenges for your child. By focusing on their individual learning style and passions, you can help them build not just a stronger mathematical mind, but also a lifelong love for tackling complex problems. This is an investment in how they think, a skill that will serve them far beyond any competition.