Week 3

Prime Factorization
Hi, kids. By the end of this task, you will be able to

1. define what prime factorization is,
2. use the factor tree or the division method to find the prime factorization of any number, &
3. properly use the words: prime and composite.

Average online time: 3 hours
Average offline time: 2 hours
Suggested Schedule: click here



STEP 1. Activating Prior-Knowledge
Let's take a poll!






STEP 2. Remembering Prime Numbers
Turn on your speakers, or put your headphones on.
As you listen to Mr. Romero, answer the following questions.

1. What's the definition of a prime number?
2. What is the smallest prime number?
3. Are even numbers also prime numbers? Why? 
4. How do we know if a number is prime?
5. What do we call the numbers that are not prime?

As you listen, write down on your notebook the answers to these questions. These are some strategies you might use:

• Listen once in order to get the main idea, then listen two or three times to get specific details
• As you listen take notes using symbols, drawings, or complete sentences
• Use visual clues to help you figure out meaning

Video retrieved from http://www.youtube.com/watch?v=woQc32mWC4M

■ How well did I answer the questions above? Here you'll find it out.
■ By now, you should know the difference between prime and composite numbers. Let's play a fun game. Click here.


STEP 3. Prime Numbers less than 100

Eratosthenes, an ancient Greek, designed a method to find out the prime numbers, this method is known as the Sieve of Eratosthenes. A sieve is a device that helps you sort out particles of different sizes; its bottom is full of tiny holes.

Let's follow Eratosthenes' method

■ Print this hundreds chart
■ Cross off number 1.
■ Circle number 2 which is the first prime number and cross off all the multiples of 2.
■ Circle the next number in the table, number 3, and cross off all the multiples of 3.
■ Continue doing this procedure until you have finished with all the numbers of the first row.
■ The numbers you didn't cross off correspond to the prime numbers!
■ Count them and compare your result to this one.
■ Do this activity with any size of the Eratosthenes table. Click here.

  STEP 4. What is Prime Factorization?

We can define it as the string of prime factors whose multiplication is the given number. There are two methods to find out such string.

Factor tree method

Let’s use a factor tree to find the prime factorization of 84.

Let's look at the last row, it only contains prime numbers. We have found the prime factorization of 84.

84 = 2 x 2 x 3 x 7


We can also write it down using exponents. The factor 2 repeats twice, so what do we do?
Let's check this out:

84 = 2 to the second power x 3 x 7



The division method
Let's watch a video. Take notes as you learn how to break up a composite number into just prime numbers.

Video retrieved from http://www.youtube.com/watch?v=JjHUnjyP3jE

 STEP 5. Checking what I know.
Dear student take these two tests to check your knowledge about prime factorization.






 STEP 6. Extended Practice.
Click on the images to have access to additional information about prime numbers and prime factorization.

 STEP 7. Assessing what I understand.

You need to create a Glogster (an interactive poster fully designed by yourself) about a) what a prime number is, b) how to find the prime factorization of a given number, and c) four examples of composite numbers greater than 50.

■ Watch this tutorial about how to use Glogster.
■ Visit this public Glogster to see how people around the world are using this fantastic tool.
■ Read the evaluation criteria.
■ Sign in at Glogster website and start designing your own poster!
■ Once you have your Glogster, send the link to abogoya@rochester.edu.co
■ If you have any question, please leave a comment at the end of this entry. I'll be happy to help you out!