This 15-day course is designed to help middle school students master essential math foundations and develop problem-solving strategies for MATHCOUNTS and AMC8 competitions. Each day includes three sessions (two hours each), totaling six hours of instruction per day. Students will build a solid knowledge base, learn competition techniques, and practice with real and simulated exams to boost their confidence and performance.

1. Foundational Knowledge: Develop proficiency in Number Theory, Algebra, Geometry, and Counting/Probability from the ground up.
   
   

2. Competition Skills: Learn common problem-solving methods, time management, and test-taking strategies tailored to MATHCOUNTS and AMC8.
   
   

3. Targeted Practice & Feedback: Reinforce learning through daily homework, regular quizzes, and simulated tests, with in-depth analysis of mistakes.
   
   

4. Mindset & Strategy: Provide coaching on managing pressure, improving speed and accuracy, and maintaining a positive mindset during competitions.

Daily Schedule Highlights

Each day consists of three sessions (Morning, Afternoon, Evening), two hours each. Below is a sample outline of the 15-day plan, which can be adjusted based on individual needs and progress.

Day 1

• Morning (2 hrs)
  
  

  • Course Introduction: Goals, MATHCOUNTS & AMC8 format and question types
    
    

  • Basic Math Refresher: Arithmetic, fraction-decimal conversions, negatives, absolute values
    
    

• Afternoon (2 hrs)
  
  

  • Algebra Basics I: Simple equations, expression manipulation
    
    

  • Classroom practice & discussion
    
    

• Evening (2 hrs)
  
  

  • Geometry Basics I: Common polygons, perimeter and area formulas
    
    

  • Group activity for geometry recognition
    
    

  • Homework: Reinforcing algebra and geometry fundamentals
    
    

Day 2

• Morning (2 hrs)
  
  

  • Number Theory Basics I: Prime vs. composite, factors and multiples, divisibility tricks
    
    

  • Practice & Q&A
    
    

• Afternoon (2 hrs)
  
  

  • Algebra Basics II: Systems of linear equations, basic inequalities, application problems
    
    

  • Class exercises to strengthen equation-solving habits
    
    

• Evening (2 hrs)
  
  

  • Geometry Basics II: Triangles, polygons, angle calculations
    
    

  • Integrated practice with Day 1 material
    
    

  • Homework: Number theory and algebra problems
    
    

Day 3

• Morning (2 hrs)
  
  

  • Counting & Probability Basics I: Permutations, combinations, simple probability
    
    

• Afternoon (2 hrs)
  
  

  • Progress Test #1 (covering Days 1-2)
    
    

    • 1-hour quiz + 1-hour feedback and discussion
      
      

  • Error analysis and correction methods
    
    

• Evening (2 hrs)
  
  

  • Competition Strategies: How to read questions effectively, problem selection, quick solving tips
    
    

  • Homework: Strategy-based practice
    
    

Day 4

• Morning (2 hrs)
  
  

  • Geometry Intermediate I: Circles, arcs, surface area, and volume basics
    
    

  • Practice & Q&A
    
    

• Afternoon (2 hrs)
  
  

  • Number Theory Intermediate I: Modular arithmetic, digit problems, parity
    
    

  • Classic competition problem analysis
    
    

• Evening (2 hrs)
  
  

  • MATHCOUNTS Past Papers I: Selected sample questions by topic
    
    

  • Group discussion & training
    
    

Day 5

• Morning (2 hrs)
  
  

  • AMC8 Past Papers I: Typical question types, common pitfalls
    
    

• Afternoon (2 hrs)
  
  

  • Algebra Intermediate I: Quadratic equations, applications in geometry/number theory
    
    

• Evening (2 hrs)
  
  

  • Mixed Practice: Combining algebra, geometry, and number theory
    
    

  • Homework: Comprehensive problem set
    
    

Day 6

• Morning (2 hrs)
  
  

  • Counting & Probability Intermediate I: More complex permutations, probability models, tricky scenarios
    
    

• Afternoon (2 hrs)
  
  

  • Progress Test #2 (covering Days 3-5)
    
    

    • 1-hour test + 1-hour analysis and feedback
      
      

• Evening (2 hrs)
  
  

  • Mindset & Time Management: Coping with competition stress, optimizing exam time usage
    
    

  • Homework: Correcting mistakes from test, targeted review
    
    

Day 7

• Morning (2 hrs)
  
  

  • Geometry Intermediate II: Similarity, congruence, coordinate geometry basics
    
    

• Afternoon (2 hrs)
  
  

  • Speed Math & Quick Techniques: Mental math, estimation methods, process-of-elimination strategies
    
    

• Evening (2 hrs)
  
  

  • Group Q&A: Addressing common or individual questions
    
    

  • Homework: Reinforcing quick-solving techniques
    
    

Day 8

• Morning (2 hrs)
  
  

  • MATHCOUNTS Past Papers II: Medium-level questions, timed practice
    
    

• Afternoon (2 hrs)
  
  

  • AMC8 Past Papers II: Medium-level questions, reading comprehension strategies
    
    

• Evening (2 hrs)
  
  

  • Mini-Quiz & Practice: Quick in-class test with immediate feedback
    
    

  • Homework: Similar past-paper drills
    
    

Day 9

• Morning (2 hrs)
  
  

  • Advanced Problem-Solving Tactics: Breaking down difficult problems, reverse thinking, casework
    
    

• Afternoon (2 hrs)
  
  

  • Geometry Intermediate III: Coordinate and 3D geometry, multi-topic integration
    
    

• Evening (2 hrs)
  
  

  • Progress Test #3 (covering Days 6-8)
    
    

    • 1-hour quiz + 1-hour discussion
      
      

Day 10

• Morning (2 hrs)
  
  

  • Counting & Probability Intermediate II: Step-by-step counting, basic dynamic approaches
    
    

• Afternoon (2 hrs)
  
  

  • Number Theory Intermediate II: Advanced divisibility, special sequences, remainders
    
    

• Evening (2 hrs)
  
  

  • Consolidated Practice: Targeting tricky questions in counting and number theory
    
    

  • Homework: Focus on challenging topics
    
    

Day 11

• Morning (2 hrs)
  
  

  • Mock Test #1 (MATHCOUNTS style): Full-timed simulation
    
    

• Afternoon (2 hrs)
  
  

  • Test Review & Feedback: Detailed error analysis, common pitfalls
    
    

• Evening (2 hrs)
  
  

  • Targeted Drills: Individual weak points from the mock test
    
    

  • Homework: Reinforcement exercises
    
    

Day 12

• Morning (2 hrs)
  
  

  • Mock Test #2 (AMC8 style): Full-timed simulation
    
    

• Afternoon (2 hrs)
  
  

  • Test Review & Feedback: Compare MATHCOUNTS vs. AMC8 approaches, common pitfalls
    
    

• Evening (2 hrs)
  
  

  • Confidence & Exam Strategy: Final tips on revision, handling nerves
    
    

  • Homework: Patch up gaps, finalize test strategies
    
    

Day 13

• Morning (2 hrs)
  
  

  • Final Geometry Sprint: High-frequency concepts, tricky geometry formulas, past “killer” problems
    
    

• Afternoon (2 hrs)
  
  

  • Final Algebra Sprint: Comprehensive coverage of linear and quadratic problem setups
    
    

• Evening (2 hrs)
  
  

  • Advanced Practice & Q&A: Last push before final tests
    
    

  • Homework: Comprehensive set of problems
    
    

Day 14

• Morning (2 hrs)
  
  

  • Final Number Theory Sprint: Focus on critical test concepts, common divisibility and remainder issues
    
    

• Afternoon (2 hrs)
  
  

  • Final Counting & Probability Sprint: Complex permutations/probability questions, final clarifications
    
    

• Evening (2 hrs)
  
  

  • Overall Review & Strategy: Recap key points, finalize competition plan
    
    

Day 15

• Morning (2 hrs)
  
  

  • Full-Length Combined Exam (MATHCOUNTS & AMC8 Style): Timed simulation of both formats
    
    

• Afternoon (2 hrs)
  
  

  • Final Exam Review & Comprehensive Feedback: Summarize knowledge gaps, provide individualized advice
    
    

• Evening (2 hrs)
  
  

  • Course Conclusion & Motivation: Sharing experiences, long-term plans, Q&A

1. • Books: AoPS (Art of Problem Solving) materials / official MATHCOUNTS & AMC8 past papers / MATHCOUNTS Handbook

• Expert Guidance: Experienced instructors and teaching assistants to ensure individualized attention.
  
  

• Comprehensive Coverage: All key topics for MATHCOUNTS & AMC8 are thoroughly addressed.
  
  

• Frequent Testing & Feedback: Timely insights into student performance, enabling targeted improvements.
  
  

• Mindset & Strategy Focus: Beyond math skills, learn crucial soft skills for success under pressure.