Lesson 2

Sifting for Primes

Est. Class Sessions: 1–2

Summarizing the Lesson

Question 4 asks students to list all the primes between 1 and 100—all the numbers that are not crossed out. After students have completed their charts to 100, direct them to work with a partner or in a small group to complete Questions 5–7. Students can record their observations on note cards or self-adhesive notes. Ask students to share the patterns they found in Question 5. Collect students' observations on a chart paper titled “Prime Number Patterns.” Responses might include:

  • You need to find only the multiples of prime numbers.
  • 2 is the only even prime number.
  • Except for 2 and 5, prime numbers don't end in 2, 4, 5, 6, 8, or 0.
  • Prime numbers do end in 1, 3, 7, and 9. However, not all numbers that end in 1, 3, 7, or 9 are primes.
  • Some prime numbers are separated by only one other number such as 3 and 5, 11 and 13, or 17 and 19. These are called twin primes.
  • 2 and 3 are the only two primes that are next to each other.

As students work on Questions 6–7, ask:

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  • What does it mean to be a prime number? Give an example. (It only has two factors—1 and itself. For example, 2, 17, and 19 are prime.)
  • How can you decide if 43 is prime or composite? (Look on the sieve.)
  • What if you don't have a sieve? (Skip count by the primes [2s, 3s, 5s, 7s, etc.] and see if you hit it like we did for the sieve.)
  • How can you use your calculators? (Find all the factors by dividing to find which numbers divide evenly. If the only factors are one and the number itself, it is prime.)
  • Is 43 prime or composite? How do you know? (It is prime. The only factors are 1 and itself. It isn't even and it doesn't end in 5 or 0, so it is not a multiple of 2 or 5. If you divide by 3 or 7 using the calculator, it doesn't come out even.)
  • Is 39 prime or composite? How do you know? (It is composite. It is a multitple of 3.)

Ask students to complete Check-In: Questions 8–10 in the Student Guide independently.

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Use Check-In: Questions 8–10 on the Sifting for Primes pages in the Student Guide and the corresponding Sifting for Primes Feedback Box in the Teacher Guide to assess students' abilities to identify and categorize prime and composite numbers [E1]; identify multiples of a number [E2]; and find all the factors of a number between 1 and 100 [E5].

Once students have sifted for primes from 1 to 100, assign the Homework section that asks them to find the primes from 101 to 200. Students should work on the same 200 Chart that was started in class. Remind students to begin by crossing out all of the multiples of 2 from 101 to 200. They will then cross out the multiples of 3, the multiples of 5, etc. After they complete the assignment, discuss that they only needed to check up to multiples of 13.

Student Guide:
Student Activity Book:
Master: