### Cindy BeckhamSanta Rosa District Schools

#### Description

Primed and Ready is a project designed to use the Sieve of Eratosthenes to determine and display the prime and composite numbers from 1 to 100.

#### Objectives

The student knows if numbers (less than or equal to 100) are prime or composite.

The student uses divisibility rules.

#### Materials

-Transparency of a chart of the numbers from 1 to 100. The first row should include the numbers 1-10, the second row should include the numbers 11-20, and so on until the last row which should include the numbers 91-100.
-Worksheet of 1 to 100 chart of numbers
-Overhead markers – four different colors
-Pencils for students
-Rulers
-White poster board – 1 piece per 2 to 3 students
-Markers, colored pencils, or crayons for students
-Information on Eratosthenes

#### Preparations

1. Set up overhead with pens and transparency
2. Collect materials provided by the teacher.
3. Research Eratosthenes.

#### Procedures

1.Gain attention by showing a picture of Eratosthenes, a Greek scientist and mathematician.

2. Speak to the students about the fact that Eratosthenes had already proven that the world was round hundreds of years before Christopher Columbus lived.

3. Eratosthenes was interested in the properties of numbers. He developed a sieve (a strainer) that allowed the composite numbers from 1 to 100 to fall through, keeping the prime numbers. Repeat his procedure using what we know about factors, multiples, prime numbers, and divisibility.

4. Review the terms: prime, composite, multiples, and divisible.

5. Distribute the worksheets on the Sieve of Eratosthenes. (See attached file.)

6. Using the 1-100 chart of numbers, begin demonstrating to students how to complete the Sieve of Eratosthenes. (Do not finish the sieve. Give the students the following directions to complete it.) First, mark out the number one because it is neither prime nor composite. Next, mark through all the numbers divisible by 2, except 2 because it is prime. Then mark through all the numbers divisible by 3, except 3 because it is prime. Now mark through all the numbers divisible by 5, except 5 because it is prime. Finally, mark through all the numbers divisible by 7, except 7 because it is prime. Have the students do the same on the worksheet provided.

7. Students work together in groups of 2 or 3.

8. Students use the worksheet to help complete a color-keyed poster of the Sieve of Eratosthenes.

9. Students will first need to use rulers and straightedges to create a table on the poster board.

#### Assessments

An instruction sheet is included to help students create a key for their charts.

All prime numbers are left uncolored. --1 point
All composite numbers are colored correctly according to the instruction sheet. --1 point
The number one is marked as neither prime nor composite. --1 point

Students who do not score the first two points will need feedback and additional practice.
Students' ability to use divisibility rules should be evident in the correct coloring of the composite numbers.