1. Foundation Building (Elementary / Early Middle School – Gauss, Kangaroo, Caribou)

• Number Sense & Operations
  • Speed and accuracy with whole numbers, fractions, decimals, percents
  • Prime numbers, factors, multiples, divisibility rules
• Problem-Solving Basics
  • Translating word problems into equations
  • Working systematically and eliminating wrong answers (MCQ strategy)
• Patterns & Sequences
  • Arithmetic & geometric patterns
  • Visual/spatial patterns and logical reasoning
• Geometry & Measurement
  • Perimeter, area, volume basics
  • Symmetry, transformations, angles
• Logical Reasoning & Puzzles
  • Games, riddles, and brain teasers
  • Deductive reasoning strategies

2. Intermediate Level (Middle School – Pascal, AMC 8, Gauss Gr. 7–8, Math League)

• Algebraic Thinking
  • Equations, inequalities, ratios, proportions
  • Word problems with algebraic expressions
• Number Theory
  • Modular arithmetic (remainders, divisibility)
  • Properties of primes, GCF/LCM, Diophantine equations (intro)
• Geometry
  • Angle chasing, triangles, quadrilaterals, circles
  • Coordinate geometry basics
• Combinatorics & Probability
  • Counting principles, permutations, combinations (intro)
  • Probability with multiple events
• Competition Skills
  • Time management during contests
  • Estimation, mental math, and elimination techniques

3. Advanced Level (High School – Cayley, Fermat, Euclid, AMC 10/12, AIME)

• Algebra & Functions
  • Polynomials, factoring, quadratic equations, systems of equations
  • Functional equations and sequences
• Advanced Number Theory
  • Modular arithmetic, congruences
  • Fermat’s Little Theorem, divisibility theorems
• Geometry
  • Similarity, congruence, cyclic quadrilaterals
  • Coordinate geometry and analytic methods
  • Trigonometry: sine rule, cosine rule, identities
• Combinatorics & Probability
  • Advanced counting (stars & bars, binomial theorem applications)
  • Conditional probability and expected value
• Inequalities & Optimization
  • AM-GM, Cauchy-Schwarz, problem-solving with inequalities
• Proof Writing (Euclid, AIME)
  • Constructing rigorous, step-by-step proofs
  • Explaining reasoning clearly under time limits

4. General Skills for All Levels

• Speed & Accuracy: Drills for fast computation and careful checking
• Problem-Solving Strategies: Guess-and-check, working backwards, symmetry, casework
• Past Papers & Mock Exams: Regular practice under timed conditions
• Mindset Training: Growth mindset, resilience, and handling “hard” problems without discouragement

5. Learning Formats

• 1-on-1 personalized coaching for high-level competitors
• Flexible delivery: in-person, online, or hybrid
• Customized prep plans for specific contests (Gauss, AMC, Kangaroo, Pascal, Cayley, Fermat, Euclid, Waterloo CEMC series, etc.)