Try the sieve of Eratosthenes in your classroom! Sure, it’s a powerful prime number activity, but it also helps kids conceptualize patterns of multiples. This lesson is short but mighty.
Ms. Sneed Tries the Sieve of Eratosthenes
Our favorite fourth grade teacher sat at the side table with her teaching partner. “I’d like to dig a little deeper into common multiples before we begin fractions in math.”
Mr. Frank looked up from his laptop. “What did you have in mind?”
“The sieve of Eratosthenes.”
Mr. Frank chuckled. “Okay. What is that?”
As she turned her laptop toward him, Ms. Sneed explained. “It’s a method for finding prime numbers, but it also reinforces common multiples.”
Who Was Eratosthenes?
Ms. Sneed pointed to her screen. “I found this sieve of Eratosthenes lesson over the summer.
“It begins with a quick biography of the mathematician. As you can see, he lived over two thousand years ago in Greece. Actually, he’s best known for being first to calculate the circumference and tilt of the Earth.”
“Impressive,” said Mr. Frank.
“However, he also developed a method of finding prime numbers. Eratosthenes called it a “sieve” because it screens out all multiples to reveal the primes. Using a list of consecutive numbers, he began with two, the first number with two factors. Then he marked out all the multiples of two. The next number, three, was not marked out. Therefore, it must be prime. Then he marked out all the multiples of three. The next number, four, was already marked out, so it was composite. Five, he found, was the next prime. Continuing in this manner, he developed a list of prime numbers.”
Exploring Multiples with a 10 x 10 Number Chart
Ms. Sneed scrolled to the first activity in the sieve of Eratosthenes resource.
“First,” she said, “kids mark multiples of numbers on a 10 x 10 table. This builds conceptual understanding of number patterns, common multiples, composite, and prime numbers.
“As kids mark the multiples, new awareness of the base ten number system emerges. Upper elementary students connect skip counting from earlier grades with multiplication facts. They realize that certain numbers are multiples of more than one number. Tactile and visual patterns also emerge. For this reason, the first activity is limited to marking multiples, looking for patterns, and naming common multiples.”
“Sweet,” said Mr. Frank. “We don’t spend much time on Base 10 number patterns. I think this could really help my students with number sense.”
Finding Prime Numbers with the Sieve of Eratosthenes
Now Ms. Sneed scrolled to the second activity. “Next,” she said, “kids recreate the sieve of Eratosthenes. They circle prime numbers and shade their multiples. As they eliminate composites, they expose the next prime. Specifically, students:
- circle the first prime number (two) and shade its multiples,
- move to the next number that hasn’t been shaded (three), circle it, and shade its multiples,
- move to the next unshaded number (five), circle it, and shade its multiples,
- continue in this fashion until they get to 50, where no more multiples could be found on a table with only 100 numbers, and
- circle all remaining numbers because they are also prime.”
“The same as good old Eratosthenes did.” Mr. Frank smiled. “I think I’m going to like this activity.”
Drawing Conclusions
Scrolling to the next page, Ms. Sneed continued. “An additional worksheet asks them to explain why all prime numbers (except two) are odd, why five is the only prime with that digit in the ones place, why a set of numbers (which kids commonly mistake as prime) are not prime.”
“Wow,” Mr. Frank responded. “That’s powerful. When simplifying fractions, my students often overlook these numbers because they think they’re prime. Especially 57!”
Enjoy Teaching
Ms. Sneed sat back with a satisfied look on her face. “Yep. I was thinking the same thing. Our students will build important number sense – and have some fun too!”
