Timing: Friday night 7:00 - 9:00 PM, Weekly

Date: Starting from June 27th 2025

Class Location: Google Meet

AMC 10 Problem-Solving Bootcamp: Number Theory & Counting/Probability.

Number Theory Essentials

Objective: Build a strong foundation in number theory with key definitions and tools.

Topics Covered:

• Divisibility rules, GCD & LCM
• Prime factorization
• Euclidean Algorithm
• Fundamental Theorem of Arithmetic

Activities:

• Solve 5–6 AMC-style warmup problems
• Group mini-challenges using Euclidean Algorithm
• Wrap-up quiz (5-minute timed)

Modular Arithmetic Mastery

Objective: Develop fluency in modular arithmetic and its applications.

Topics Covered:

• Congruence notation and properties
• Modular addition, multiplication
• Solving linear congruences
• Remainder problems (Chinese Remainder Theorem intro)

Activities:

• “Find the remainder” problem drills
• Real AMC 10 modular arithmetic questions
• Partner problem-solving

Number Theory in Action

Objective: Apply multiple number theory concepts in complex problems.

Topics Covered:

• Diophantine equations (intro)
• Problem types mixing modular arithmetic and divisibility
• Tricks with digits, base systems

Activities:

• Practice “harder than they look” problems
• Teach-back method: students explain 1 problem to the class
• Exit ticket: solve 1 problem + write strategy used

Counting Fundamentals

Objective: Introduce the basics of combinatorics with a strategic lens.

Topics Covered:

• Permutations, combinations
• Complementary counting
• Factorial notation and logic puzzles

Activities:

• Visual combinatorics (draw arrangements, trees)
• Group challenge: how many ways?
• Strategy circle: when to use direct vs. indirect counting

Casework & Overcounting

Objective: Handle complex scenarios with clear, structured counting.

Topics Covered:

• Casework strategy
• Avoiding overcounting
• PIE (Principle of Inclusion-Exclusion)

Activities:

• Solve AMC 10 casework examples together
• Student-led discussion: when is PIE useful?
• Practice worksheet with guided solutions

Probability Basics & Pitfalls

Objective: Understand probability fundamentals and common traps.

Topics Covered:

• Basic probability (equally likely outcomes)
• Complementary probability
• Conditional probability (intro)
• Expected value (basic idea)

Activities:

• Dice and coin toss games
• Probability “trap” problems – why intuition fails
• Kahoot quiz or gamified review

Advanced Counting & Probability

Objective: Tackle high-level problems combining probability and counting.

Topics Covered:

• Expected value (strategic problems)
• Pascal’s Triangle, binomial coefficients
• Mixed problems: counting + probability + logic

Activities:

• Solve 3 multi-step AMC 10 questions in groups
• Create-your-own-question activity
• Timed mini-mock (10 minutes, 4 questions)

Mock Test + Strategy Session

Objective: Simulate real test conditions and reflect on strategies.

Activities:

• 45-minute AMC-style mini-test (12–15 problems)
• Group review: different approaches to key problems
• Strategy toolbox: how to guess smart, time manage, skip or stay
• Final Q&A + confidence-building wrap-up