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