Thursday 8 September class

Topics:
• We discussed some of the homework problems: the socks problems from the second day (30 August) and the algebraic problems from last time.

If you need more review of using the quadratic formula, here are some good sources:
Webpages: Regents Prep (good explanation), Algebra Lab (this has practice problems where you can enter your answer and it checks it - excellent for practice!)
Videos: Khan Academy, Patrick's Just Math Tutorials (this link is to Example 1; there are links below the video to two more examples)

New topic: Prime numbers and Prime Factorization
Most of this is from the reading: prime numbers and prime factorization of natural numbers (from Math is Fun), except when other links are provided.
 • What is a prime number?
   Note: divisibility rules are linked at the end of the reading from Math is Fun
 • Finding prime numbers using the sieve of Eratosthenes: here is the grid that I printed out
 • Finding the prime factorization of a natural number (this is done in the reading)


Homework:
• Journal assignment: write a definition of prime number. Explain in your own words what the prime factorization of a natural number is: give at least 3 examples to illustrate it.

Problems:
Find (by hand, using any of the methods we discussed in class) the prime factorization of each of these numbers:
30, 48, 143, 41

Next topic: We will state the Fundamental Theorem of Arithmetic, and then prove that there are infinitely many prime numbers (here's another description of the proof). Along the way we encounter the Division Algorithm, which explains one of the steps in that proof.