Elementary (Grades 5th & 6th) Mathematics Lesson

Sieve of Eratosthenes

Adapted from Scott Foresman-Addison Wesley

Submitted by: Angel Greenley

Objective: Identify prime & composite using a hundreds chart.

Materials: OH of 100’s chart; Hundreds chart for each student (can be obtained from

colored pencils;

Lesson:

  1. Explain to students that they are going to use a hundred chart to find all of the prime numbers. Ask students if they know what a prime number is? (a number with only 2 factors, 1 and itself). If no one volunteers information; leave the question unanswered and revisit it later.
  2. Give students background information about Eratosthenes.
  • Eratosthenes was born in Cyrene (in what is now Libya) about 230 B.C. He developed a method for determining if a number is prime. It is called the Sieve of Eratosthenes because it “strains out” prime numbers from other numbers.
  1. First we are going to cross out 1. 1 is a special number and is neither prime nor composite.
  2. Next we will start by counting by 2’s and color in all of the multiples of 2 except 2. Watch students as they begin to color in their hundreds chart. Some students will discover that they can color down the columns rather than counting by 2’s – this is acceptable.

1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
11 / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20
21 / 22 / 23 / 24 / 25 / 26 / 27 / 28 / 29 / 30
  1. Once all students have colored in the 2’s, explain that they are now going to continue with 3. (I have students change colors). Remind them that they are not to color in 3. Ask students if we can use the same shortcut that we used when coloring by 2’s (color down the columns). Ask them to explain why or why not.

1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
11 / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20
21 / 22 / 23 / 24 / 25 / 26 / 27 / 28 / 29 / 30
  1. Next have them begin counting by 4’s. See if anyone discovers that the 4s are all colored in. Have someone explain why.. (It was colored in when you did the 2s).
  2. Continue with the rest of the numbers 5-9. As you try a new number, such as 6, discuss why the multiples of 6 are already colored in. (Multiples of 6 are even numbers and all of the even numbers were colored when they colored the 2s. This works because 2 is a factor of 6).

1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
11 / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20
21 / 22 / 23 / 24 / 25 / 26 / 27 / 28 / 29 / 30
31 / 32 / 33 / 34 / 35 / 36 / 37 / 38 / 39 / 40
41 / 42 / 43 / 44 / 45 / 46 / 47 / 48 / 49 / 50
51 / 52 / 53 / 54 / 55 / 56 / 57 / 58 / 59 / 60
61 / 62 / 63 / 64 / 65 / 66 / 67 / 68 / 69 / 70
71 / 72 / 73 / 74 / 75 / 76 / 77 / 78 / 79 / 80
81 / 82 / 83 / 84 / 85 / 86 / 87 / 88 / 89 / 90
91 / 92 / 93 / 94 / 95 / 96 / 97 / 98 / 99 / 100

If students haven’t already stated what a prime number is, have them look at their chart. Tell them that the numbers not colored are all prime numbers. Have students make conjectures as to what a prime number is. (If necessary, lead them to listing the factors of the prime numbers). Students should discover that prime numbers have only 2 factors: 1 and the number itself.

(Use a concept map to help students understand the definition of prime).