concepts and methodology in mathematics education - Nelson ...

QUESTION: How many Prime numbers are there less than 100? Write them down and memorise the first tenPrime numbers. Take turns with your partner and say them to each other without looking at your books.Now explain to each other your understanding of what a prime number is.You have just completed an activity in which you discovered prime numbers according to the “Sieve ofEratosthenes”. So more information about this method and Sieve, follows below:Eratosthenes was a mathematician who lived from 276BC to 194BC. He was known as the wise man ofAlexandria. Although he was born in Cyrene, a Greek colony just west of Egypt, he spent most of his workingdays in Alexandria. At some point during his early life he studied at Plato’s school in Athens. At about 30years of age he was invited to Alexandria by King Ptolemy II to serve as tutor for his son and heir. As amathematician, one of Eratosthenes’s great inventions was his method for finding all prime numbers lessthan a given integer n. He called this invention the “Sieve of Eratosthenes”.The search for prime numbers has fascinated mathematicians over the ages. We know that there are aninfinite number of primes, but we have no way to predict which numbers of prime. We need to test eachnumber to see if it has exactly two factors, i.e. 1 and the number itself. For very large numbers this testingtakes a long time! In 1994, David Slowisnski, a computer scientist at Cray Research, found a prime numberwith 258,716 digits!8. Prime NumbersThink and Discuss:What is a Prime Number?A prime number has only 2 factors, 1 and itself. The fundamental theorem of arithmetic states that everynumber is either a prime number or it can be expressed as a product of prime numbers in only one way. Thismakes prime numbers mathematically important.Mathematicians do not consider 1 as a prime number as there are many theorems about prime numbersthat are not true about 1.1 has only one factor – itself. A composite number has more than 2 factors.Practical ActivityDiscuss the following questions with a colleague to clarify your thinking:What is the smallest prime number?Why is the number 1 not considered to be a primenumber?How many primes end in 2? Give a reason for youranswerWhy are there no primes which are multiples of 10?28