## Prime Real Estate

### Christine AustinLee County School District

#### Description

This is a hands-on procedure that utilizes the “Sieve of Eratosthenes” to identify prime numbers from 1-100. Eliminating all the multiples of the first four prime numbers identifies primes. The 25 numbers that remain are all primes!

#### Objectives

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

#### Materials

-One overhead transparency of the 100 Number Chart (See Associated File)
-A highlighter marker for each student
-Pencils
-A sieve, strainer, or colander of any kind
-Chalkboard/chalk OR white board/marker(s)

#### Preparations

1. Make one copy per student plus one overhead copy of the 100 Number Chart. (See Associated File)
2. Gather highlighters for students and overhead markers or chalk for teacher.
3. Obtain a working overhead projector.
4. Ascertain that chalkboard/chalk or white board/marker is available.
5. Obtain a sieve, colander, or strainer.

#### Procedures

1. Present the class with your colander/sieve. Lead the class in a discussion of its uses as a cooking strainer, or a sand sifter. Emphasize that what is LEFT in the sieve is our object of interest today.

2. Tell the class that they are going to “throw” the numbers from 1-100 in their own sieves and sift out all but some special numbers! Introduce Eratosthenes as a famous Greek mathematician from thousands of years ago. Explain how Eratosthenes developed this procedure to find these special numbers.

3. Review the terms “multiple” and “factor.” Write examples from students on the board.

4. Lead a short class discussion of the relationship between multiples and factors.

5. Introduce the term “prime number,” present examples on the board, and discuss what “makes them prime” in terms of the number of factors.

6. Lead the students to name the first four prime numbers and write them on the board (2,3,5,7).

7. Hand out the 100 Number Chart (See Associated File) and a highlighter to each student.

8. Direct the students to highlight the first four primes that are written on the board AND THEN PUT THE HIGHLIGHTER AWAY FOR NOW!

9. The number “1” does not fit the definition of prime OR composite, and it needs to be crossed off first.

10. Remind the students that numbers that have 2 as a factor cannot be prime, and then model on the overhead:
-Two (2) is highlighted because it is prime, but all multiples of 2 are NOT prime.
-Call on students to list aloud the factors of 4, 6, 8, and 10. Emphasize that since these numbers have more than two factors, they are NOT prime and must be crossed off.
-Direct students to cross off all multiples of 2, [lightly, in pencil]. Model this on the overhead sheet by crossing off all multiples of 2. Count aloud to model this.
-Remind the students that all even numbers are multiples of 2; the students can use that knowledge to help them cross off.

11. Model crossing off of all multiples of 3. Demonstrate that multiples are “count-by” numbers that can be found by crossing off every third number. Model this for the multiples of 3 at least halfway through the chart, counting aloud by threes. Let students complete crossing off multiples of threes.

12. Direct students to cross off all multiples of 5 and 7 on their own or with a partner. The teacher should complete this also, but with the overhead turned off. The teacher should then circle the 25 primes for clarity.

13. When the students are finished, tell them that there should be 25 numbers left on their paper, “in the sieve.” Direct them to count how many numbers they have left (including the original five highlighted primes).

14. When the students have completed this step, ask if anyone has more/less than 25 numbers. If so, they should repeat the steps until they have 25.

15. Most students will have 25 by this point. Turn on the overhead and allow students to compare their papers to the overhead, correcting any errors. The teacher should circulate to facilitate this, providing feedback to all students.

16. If the papers are correct, direct the students to highlight the remaining primes.

17. This paper should be kept by students for reference, future lessons, and extensions. Have them save it wherever they save other important class papers.

18. Wrap-up the lesson with a discussion of what prime numbers are, and introduce the term “composite” as numbers that are NOT prime, have more than 2 factors, etc.

#### Assessments

EVIDENCE: Each student produces a 100 Number Chart (See Associated File) with the 25 primes highlighted.

CRITERIA: All 25 primes between 1-100 are highlighted and correct.

#### Extensions

Accommodations for Special Education:
-All work can be done with a partner.
-Students may have notes about multiples, factors, etc.
-Seat ESE students closer to teacher for more direct feedback at each step.
-Use graphic examples to show factors, etc., such as geoboards or multiplication charts.

Accommodations for ESOL:
-Correlate terms such as “multiples,” “factors,” “primes,” etc. to the corresponding words in the students’ home language(s).
-Use graphic examples to show factors using diagrams, geoboards, etc.

Extensions:
-Use the Weblinks below or other reference material to write a powergraph about Eratosthenes.

#### Attached Files

This file contains the 100 Number Chart and the answer key.     File Extension: pdf