Simplifying Fractions -- When Prime is Slime!

Simplifying fractions is challenging for students, requiring a process where errors are easy to make.  The process is also difficult conceptually causing students lots of questions.  Here are the questions I hear:

What is "simplifying a fraction"?

Simplifying a fraction is finding its smallest equivalent fraction.

Why do I have to do it?

It's easier to work with smallest equivalent fractions.  

How do I do it?

Divide the numerator and denominator by the Greatest Common Factor or "GCF".  

An Organized Approach

I created a Simplifying Fractions Mat.  The Mat gives students a place to complete T-charts on the numerator and denominator then identify the Greatest Common Factor "GCF".  Once identified, students divide by the GCF to find a simplified fraction.  

How do I know when I'm done?

Simplification is complete when the simplified fraction follows at least one of these 4 rules:

1.  Prime is Slime:  When the numerator and denominator are both prime numbers.

2.  Back to Back Jack:  When the numerator and denominator are back to back on a number line.

3.  One and Done:  The numerator of the simplified fraction is 1.

4.  The "No-Rule" Rule:  Sometimes the simplified fraction doesn't follow a rule (i.e. 2/15).  If this is the rule that the simplified fraction follows, make sure all factor pairs have been recorded in the T-charts and the numerator and denominator have been divided by the GCF.

Simplifying fractions, though very necessary, can be challenging.  I hope the FREE Simplifying Fractions Mat simplifies the process for you and your students.

What method(s) do your students use to simplify fraction?

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Resources and Ideas for Teaching Prime and Composite Numbers

Sieve of Eratosthenes

Why Learn About Prime and Composite Numbers?

Dr. Math says: 

"Every time you send a credit card number over the Internet, it gets encrypted by your browser, and the encryption algorithm is based on the theory of prime numbers.  At some point, electronic money will become as common as paper money, and -that- will also be based on the theory of prime numbers.  And, what's used more in the real world than money?"

See the article in full here: Math Forum: Dr. Math

Conceptual Way to Introduce Prime and Composite Numbers

Donna Boucher, Math Coach at Math Coach's Corner, asks her students to identify all arrays of a specific number (i.e. 24).  They are then tasked with creating a poster showing the array, t-chart and organized factor list for each factor pair the class identified.  She hangs the posters around the room and students reflect.  What do you notice?  They may notice some numbers have more factors than others.  Cue vocabulary!  

My summary doesn't do the article justice.  You can access the original article at:

Prime and Composite by Math Coach, Donna Boucher

Video Lessons on Factoring Primes to Simplify Fractions

Math Antics videos are super -engaging and rich with conceptual ideas.  In the Math Antics video: 

Simplifying Fractions Part 1 and Part 2, 

learners see how to simplify fractions by factoring the numerator and denominator to primes then cancelling common factors.

One of my Favorite Resources

is a no-prep activity written by Shelley Rees, called, 

Prime and Composite Numbers Activities

It contains:
What is a Prime Number?  (Definitions and Explanations)
Cross It Out!  100 Number Grid Activity
Factor It and Label It!  List the factors and label numbers as prime or composite
Prime Puzzle:  Prime/Composite Number Coloring Puzzle
What Number Am I?  Use the process of elimination and number sense to solve number riddles
Prime Number Path  Identify prime and composite numbers and color a path.

All of this can be yours at a bargain price of $3.50


I've seen several ways to teach prime and composite numbers.  What are your favorites?

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Free Holiday E-Book with 20 Teacher Tips, freebie links and resource links

Sometimes, as I surf the web, I come across something really awesome.  Like when I came across this free E-book by Shelly Rees.

A lot of the authors of these tips and resources, are authors whose blogs I follow so I was really excited to get all of these freebies!  If you are interested in this free ebook, click on the picture or link  below:

FREE-Holiday-E-Book-with-Teacher-Tips-and-Freebie-Links

What did you enjoy about his free collection?  

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