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"When students learn ‘facts’ in context, it makes the math more interesting. It’s also a powerful way to help them remember what they’ve learned — even after the next summer break.

So What is a Sieve of Eratosthenes, Anyway?

"Outside of math class, a sieve is like a strainer – it’s used to separate liquids from solids. I use one regularly to remove water from spaghetti once it’s done cooking. In math, a sieve is a strategy or formula that “filters” numbers that don’t belong in a certain category.

"This particular sieve rules out composite numbers, leaving only primes. Eratosthenes’ innovation was to find prime numbers by process of elimination. Counting by 2’s up to 100, he could easily prove that 50 of those numbers were not prime. Next he would count up by 3’s, 5’s, 7’s, and so on. He skipped 4’s, 6’s and other composite numbers – any multiple of 4 or 6 had already been eliminated from consideration as they were multiples of 2.

Are Primes Really That Important?

"As interesting as primes are, I’m a lot more interested in what the Sieve teaches students about multiplication and the relationships between numbers. This activity will have your students looking at multiplication in a whole new way. It’s an “open task,” meaning that each student will learn something unique.

"For some, the sieve is a way to master times tables. For others, it will help with common denominators or factoring expressions. The sieve also highlights patterns that can improve mental math with all four operations.

Ready to Share the Sieve Magic with Your Students?

"The Sieve of Eratosthenes is a fun and engaging lesson that will provide lasting benefits to students of any age. The basic idea is this: pick a color for each single digit number. (Eliminate 1 because it’s neither prime nor composite. Not to mention the ‘ones’ times tables aren’t very interesting or challenging). Draw a colored circle in the box for ‘2,’ and put a small ‘x’ of the same color in each multiple of two.

"Once students finish drawing, you can build a rich discussion around the patterns they will find in the numbers. As you go through each multiple, different patterns arise and overlap with each other. Seeing the patterns visually will help to connect multiplication to division, and older students can use this as a tool to support factoring, LCM, GCF, and more.

"If you’re ready to try this out with your class, you can download the worksheet and key for free from our Teachers Pay Teachers site.

"If you want the entire package, including background on Eratosthenes, lesson plans, notice/wonder graphic organizer, and a group work rubric, you can download that from our TpT site as well."

Jim Lerman's insight:

A first-rate math activity from about 3rd grade all the way up through remedial math in college. The math literacy that facility with the Sieve enables is fundamental to reaching the next stage where students are prone to stumble -- fractions.