Factors & Multiples (Classical)

Number theory is one of the oldest branches of mathematics. Euclid was writing about prime numbers and divisibility over two thousand years ago, and the Sieve of Eratosthenes — a method your fourth grader will actually use in this program — dates back to ancient Greece. There’s something genuinely cool about handing a kid a tool that mathematicians have relied on for millennia.

This 9-week program walks through the classical foundations of factors and multiples at a Grade 4 level. It’s structured as a progression, each week building on the last, with systematic drill that gives kids real fluency rather than surface-level exposure.

Week 1 starts with the basics — what factors and multiples actually are, how to find factor pairs, and how multiplication and division connect to each other. Week 2 moves into prime and composite numbers, including the Sieve of Eratosthenes for identifying primes up to 100. Kids tend to find the sieve satisfying. Crossing off numbers according to a rule and watching the primes emerge feels more like a puzzle than a lesson.

Week 3 introduces divisibility rules for 2, 3, 4, 5, 6, 9, and 10. These are mental math shortcuts that pay dividends for years. Week 4 tackles Greatest Common Factor (GCF), and Week 5 covers Least Common Multiple (LCM) — both taught through systematic listing so kids understand the process before they ever see a shortcut. Week 6 is prime factorization with factor trees, which connects back to the prime number work from Week 2 in a way that makes the whole system feel coherent.

The last three weeks are where things get interesting. Week 7 applies everything to number patterns and multi-step word problems. Week 8 pushes into logical reasoning — generating patterns, spotting hidden features, thinking about why numbers behave the way they do. Week 9 is a cumulative assessment across all eight previous weeks.

The classical approach here isn’t about being old-fashioned for its own sake. It’s about treating number theory as intellectual heritage worth passing down carefully. Drill builds automaticity. Structured progression builds understanding. And honestly, the material itself is just interesting — prime numbers, divisibility, the fundamental theorem of arithmetic. These ideas have captivated mathematicians for centuries because they reveal how numbers actually work beneath the surface.

Each week includes 5 practice worksheets with full answer keys. The whole thing is designed to print and go.