The Sieve of Eratosthenes

I saw this pop up on a Facebook group I’m in, and knew it was a perfect activity to do with Funball. While she has a great grasp on multiplication , and has finished the Montessori multiplication sequence, it all happened outside of school.

We worked on the multi-digit sequence early in the summer and I knew she’d picked up single digit multiplication in Kindergarten, but didn’t realise it hadn’t been followed up on and so there hadn’t been any factors work, least common multiple work, or anything like that. The beauty of Montessori and homeschool is that we can go back and fill this in.

She’s been re-doing Tables A, B, and C (very graciously, since I lost the ones she did several months ago…). Tables A and B list the products of numbers 1-10 up to a result of 100. Table C extrapolates that data into a list of factors for each integer, 1-100. Of course some of the numbers don’t have any factors besides 1 and themselves, and so we get to introduce prime numbers.

The sieve of Eratosthenes is a great follow up work once Table C is completed, and it was really fun for Funball and I to do together.

As I’m learning, it’s always more interesting if you can begin with a story:

Eratosthenes was born in Libya, North Africa around 2300 years ago. At the time his town was part of the Greek Civilization. As a young man he moved to Athens to study and made a name for himself in a range of topics: astronomy, history, and geography. I hope we can hear some of those stories another time, but today we’ll hear a story about a mathematical achievement.

Eratosthenes created a sieve. Just like in the kitchen, a mathematical sieve sifts, it sorts. Eratosthenes discovered that numbers could be sifted to create a particular result, and we’re going to follow his process today.

On a hundred chart, we’re going to highlight the number 2, then sieve out (or shade in) all the multiples of two. We’ll highlight the number 3, then sieve out all the multiples of three that are still available, and so on.

So, we followed the process. When we were done, we compared the result to our Table C! Wonderful! I love the connection to history and the visual demonstration. The story also makes the concept that much more memorable.

Sources: (has a great animation!)