## Beacon Lesson Plan Library## In Your Prime## Melanie Malone## DescriptionThis activity allows students to find prime numbers on their own. They use a method developed a few thousand years ago to discover the primes that are less than 100.## ObjectivesThe student uses concepts about numbers, including primes, factors, and multiples, to build number sequences.## Materials-Pencil-Copies of the 100 Chart (Sieve of Eratosthenes: see attached file) -Paper for writing down results -Transparency of 100 Chart -Optional teacher resource: -Historical Connections in Mathematics- (Volume 3), by Luetta and Wilbert Reimer, 1992, AIMS Education Foundation -Transparencies of Eratosthenes information ## Preparations1. Run copies of the chart.2. Gather information about Erotosthenes. 3. Make transparencies of information and chart for class use. ## Procedures1. Lesson introduction: Begin this activity by putting a series of transparencies about Eratosthenes on the overhead. These transparencies can be made from Volume 3 of the AIMS series, -Historical Connections in Mathematics.- The series gives interesting information about Eratosthenes including how he determined the circumference of the earth using angles and distances. Point out to students that during Columbus’ time, they thought the earth was flat. It makes one wonder what happened between the two time periods! It also discusses his life as the head librarian for the Alexandria library and his contributions to prime numbers. Students really enjoy the portraits of the mathematicians.2. After discussing the gentleman responsible for this procedure, pass out the 100 chart tables for students to use. Use a transparency of this so that students can refer to it during the step-by-step instructions. 3. Have students cross out the number -1-. Remember, one is not classified as a prime. 4. Have students circle the number -2-. The number two is the only even prime and the smallest prime number. After they circle -2-, have them cross out every other even number (or every second number after 2). This is a good time to reinforce the term -multiple- and refer to these as multiples of 2. 5. Have students circle the number -3-. Have them cross out every third number or every other multiple of 3. 6. The next open number is the number -5-. Have students put a circle around it and then have them cross out every fifth number or any number that ends in 5 or 0. Again, use the term -multiples of 5-. **Students should be noticing that they are crossing out some numbers more than once. Optional: start a discussion about Least Common Multiples or simply common multiples. This chart is full of alternate ideas to use. Ask the students why we didn't stop on the number four or six. Why are they, and their multiples, already crossed out? 7. The next number that has not been crossed out should be the number -7-. Have students put a circle around the number -7-. Then have them cross out every seventh number or all remaining multiples of 7. 8. After they have completed the number 7 series, all remaining numbers should be prime. They should begin to circle all remaining numbers that have not been crossed out. There should be 25 remaining. You can also get into a discussion about why we don’t have to continue the process beyond the number 7. 9. Have skeptical students try to find other factors of the remaining numbers using divisibility rules. Note: As students begin to pick up on the process, have them provide the steps and rationale along the way. ## AssessmentsHave students list 10 of the 25 prime numbers on a test. Also, ask them questions like: -What is the only even prime number?- Optional: ask facts about Erotosthenes.Score responses on accuracy, providing reinforcement activities for those scoring below 80% or some other appropriately designated target. ## Return to the Beacon Lesson Plan Library. |