1 / 14

Why Prime Numbers?

Why Prime Numbers?. An evaluation of prime numbers: Their use and teaching methods William S.M. Dunn South Carolina State University Mentor: Dr. Caroline Eastman. Research Objectives. To understand and analyze prime numbers and their applications

jacob
Download Presentation

Why Prime Numbers?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Why Prime Numbers? An evaluation of prime numbers: Their use and teaching methods William S.M. Dunn South Carolina State University Mentor: Dr. Caroline Eastman

  2. Research Objectives • To understand and analyze prime numbers and their applications • Find out the teaching standards and expectations for students to learn about prime numbers • Construct a feasible lesson plan in order to teach prime numbers in an appropriate learning environment

  3. Background: Definition • What is a Prime Number? • A positive integer >1 • A number that has exactly two divisors, 1 and itself • A number that cannot be factored

  4. Background: Applications • What are some modern uses and applications of prime numbers? • RSA Encryption/Cryptography • Cicadas • Factoring

  5. Background: Educational Standards • What are the Educational Standards and expectations for learning about Prime Numbers? Grades 3-5: Number and Operations Standard: Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Expectation G: Describe classes of numbers according to characteristics such as the nature of their factors.

  6. Background: Educational Standards cont. Grades 6-8: Number and Operations Standard: Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Expectation F: Use factors, multiples, prime factorization, and relatively prime numbers to solve.

  7. Why is Prime Numbers such a difficult subject to teach? • The table to the right shows a list of prime numbers less than 100 • Looking at the first few primes, shown above, it is noticeable that prime numbers become less and less frequent. However, any fears that the prime numbers may eventually die out are unnecessary. There is in fact an infinity of primes. Despite this limitless supply of primes identifying primes is not as straight forwards as might be expected. .

  8. Lesson PlanSubject: AlgebraHomework: Students will have to create their own sieve in order to find the first 40 prime numbers. They also will be given a list of numbers to not only factor but tell whether the number is prime or notPurpose/Objective of the Lesson: The purpose of the lesson is to give knowledge of prime numbers. The students will be able to recognize and find prime numbers. They will also be able to use prime numbers in problem solving situations such as factoring, and simple encryption.Class Activity Guided Practice: 1. Notes on Prime Numbers and uses 2. Examples of Using the Sieve of Eratosthenes 3. Factoring Examples 4. Learning about Encryption Independent Practice: 1. Worksheet on Factoring 2. Practice Using the Sieve 3. Encryption practice with a classmateSummary/Closure: With a review period to ensure understanding I willend the section with a test or quiz focusing on newly learned techniques for finding and using prime numbers

  9. Using the Sieve of Eratosthenes

  10. Prime Factorization

  11. 1. Choose a partner 2.Pick any prime number < 20 Pick a Simple Word to encrypt ( at least 3 but less than 7 words Using the corresponding Numbers to letters (a=1,b=2….) multiply each letter by the prime number picked and show partner the numbers Your partner will have to factor the numbers to find the letters, prime number picked, and the mystery word. Example: The Student chooses the word MATH Now they choose the prime 7 to encode the word M=13 A=1 T=20 H=8 The numbers their partner receive are: 91 7 140 56 Encryption Practice

  12. Conclusion With an open-ended research objective, I have come to the conclusion that prime numbers will remain and always be a difficult subject to teach for some of the following reasons: • There is an infinite number of primes, and everyday there is a new one discovered.( the largest known to date is 4,053,946 digits long) • No real formula to find all primes • The subject area is somewhat advanced for the young minds that it is exposed to.

  13. Acknowledgements/Thank-You’s • Mentors: Dr. John Bowles and Dr. Caroline Eastman • RCS Mentor: Roxanne Spray • REU Program and fellow participants • LS-SCAMP

  14. Questions???

More Related