Math competitions are the best-kept secret in middle school education. Students who participate in MATHCOUNTS, AMC 8, or local math leagues develop problem-solving skills, mathematical confidence, and a peer community that standard classroom instruction can't provide. Competition problems require creative thinking, multiple solution strategies, and mathematical reasoning that goes far beyond "apply the formula and get the answer."
But getting started in math competitions can feel intimidating. Where do you find problems? How do you practice? What if you're not a "math genius"? This guide covers everything a middle school student or parent needs to know about math competition prep — from choosing the right competition to building a practice routine.
Major Middle School Math Competitions
MATHCOUNTS
Grades: 6-8 · Format: School → Chapter → State → National · Cost: Free to participate (school registers)
MATHCOUNTS is the premier middle school math competition in the US. The competition has four rounds: Sprint (individual, no calculator, 30 problems in 40 minutes), Target (individual, calculator allowed, 8 problems in pairs), Team (4 students, 10 problems in 20 minutes), and Countdown (head-to-head speed round for top scorers). Schools form teams and compete at chapter, state, and national levels.
Best for: Students who enjoy the competitive format and want a team experience.
AMC 8
Grades: 8 and below · Format: 25 multiple-choice questions, 40 minutes · Cost: ~$2-3 per student
The AMC 8 is administered by the Mathematical Association of America. It's a single 40-minute test with 25 problems that range from straightforward to very challenging. Scoring is simple: 1 point per correct answer, 0 for blank or wrong. The top scores earn certificates and recognition.
Best for: Students who want a single-day competition without the multi-round commitment of MATHCOUNTS.
Math Olympiad for Elementary and Middle Schools (MOEMS)
Grades: 4-8 · Format: Five monthly contests, 5 problems each · Cost: ~$100 per team
MOEMS runs five 30-minute contests throughout the school year, each with 5 problems. The pacing (one contest per month rather than one big event) makes it less stressful and easier to fit into school schedules.
Best for: Students new to competitions who want a gradual introduction.
How to Start Preparing
Build Foundational Fluency First
Competition problems assume fluency with grade-level content. A student who's still struggling with basic fraction operations isn't ready for competition prep — they need to build foundations first. Use Infinilearn for adaptive practice that ensures all middle school topics are solid before layering on competition-level challenge.
Practice with Real Competition Problems
The best competition prep is doing competition problems. Every major competition publishes past problems for free:
- MATHCOUNTS: Free "Problem of the Week" on their website, plus past competition handbooks for purchase
- AMC 8: Past exams available on the Art of Problem Solving wiki (free)
- MOEMS: Sample problems on their website
Start with older, easier years and work toward recent competitions. Do problems under timed conditions to build test-taking stamina.
Learn Problem-Solving Strategies
Competition problems require strategies that standard curriculum doesn't teach:
- Work backwards. Start from the answer and reverse-engineer the process.
- Try small cases. If the problem asks about 100 objects, try it with 2, 3, and 4 first to find a pattern.
- Draw a picture. Visualization solves problems that algebra makes unnecessarily complex.
- Use process of elimination. On multiple-choice competitions (AMC 8), eliminating wrong answers is a legitimate strategy.
- Look for patterns. Many competition problems have elegant patterns that make complex calculations unnecessary.
Best Prep Resources
Art of Problem Solving (AoPS)
AoPS is the standard resource for competition math. Alcumus (free) provides adaptive practice with competition-style problems. The online courses ($400-800) teach problem-solving strategies through discovery. The community forums connect students with other competition math enthusiasts.
Infinilearn (For Foundational Fluency)
Competition success requires rock-solid foundations. Infinilearn's adaptive system ensures students have no gaps in core middle school math — the content that competition problems assume you know cold. Use Infinilearn for daily practice and AoPS for weekly competition-specific training.
The parent dashboard shows which foundations are solid and which need work before competition prep begins.
MATHCOUNTS School Handbook
The annual MATHCOUNTS handbook contains 300+ problems organized by difficulty. Many math teachers use it even outside of competition prep because the problems are well-crafted and develop genuine mathematical thinking.
Building a Practice Routine
- Daily (15 min): Foundational fluency practice on Infinilearn. This maintains core skills while you build competition skills on top.
- 3x per week (20-30 min): Competition problem sets. Start with 5 problems per session. Time yourself. Review solutions for every problem — even ones you got right — because competition solutions often reveal more elegant approaches.
- Weekly (1 hour): Full practice test under timed conditions. Score it. Analyze errors: was it a careless mistake, a knowledge gap, or a strategy gap?
Tips for Parents
- Don't pressure. Competition math should be an enrichment choice, not a resume-builder. Students who compete because they enjoy the challenge improve faster than students who compete because their parents signed them up.
- Find a math team or club. Competition prep is more effective and more fun in a group. Many schools have MATHCOUNTS teams. If your school doesn't, ask a math teacher to start one, or look for local math circles.
- Celebrate effort, not placement. "You solved 3 more problems than last time" is better motivation than "you need to place in the top 10."
The Bottom Line
Math competitions develop problem-solving skills that standard curriculum doesn't — and they're accessible to any student with solid foundations and a willingness to practice. Build foundations with Infinilearn's adaptive practice, layer on competition problems from AoPS and MATHCOUNTS resources, and practice under timed conditions regularly. Whether your student aims for nationals or just wants the challenge, competition math is one of the best investments in mathematical development available.