Course contents document · Math Olympiad (free) · generated 2026-07-15

Math Olympiad: MOEMS Division E (Grades 4–6)

7 core topics + 8 prerequisite topics taught as needed · approximately 4 hours of instruction including spaced review

How the course runs

An adaptive diagnostic (up to 40 questions) places the student on the course's knowledge graph — topics already known are credited, and instruction begins exactly at the learning frontier. Every topic is taught with a worked-example lesson and auto-graded practice; a topic is mastered at 75%+ and then maintained through spaced reviews on an expanding schedule. A cumulative quiz follows every 6 lessons. Prerequisite gaps below the course are detected and taught rather than skipped, so completion certifies the whole tower, not just the top.

Core curriculum

Math Olympiad: MOEMS & AMC 8 · 7 topics

Counting Divisors [M] Divisor count from the prime factorization.
GCD & LCM Relationships [M] The identity gcd(a,b) · lcm(a,b) = a · b.
Digit Problems [M] Reasoning about the digits of a number.
Permutations [M] Ordered arrangements.
The Pigeonhole Principle [M] Guaranteeing a repeat.
Telescoping Sums [H] A sum that collapses to its endpoints.
Sums, Parity & Invariants [M] Elegant closed forms and even/odd reasoning.

Prerequisite material — taught automatically when the diagnostic finds gaps

Arithmetic Foundations · 4 topics
Adding & Subtracting Whole Numbers Multi-digit addition and subtraction.
Multiplication Multiplying whole numbers.
Division Dividing whole numbers.
Exponents Repeated multiplication in shorthand.
Fractions · 4 topics
Equivalent Fractions Different fractions can name the same amount.
Simplifying Fractions Reducing a fraction to lowest terms.
Adding Fractions (Like Denominators) Same-denominator addition.
Adding Fractions (Unlike Denominators) Rewrite over a common denominator first.

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