Simplifying Fractions

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Objective

SWBAT simplify fractions to the simplest form.

Big Idea

This lesson will help students recognize when fractions are in simplest form.

Warm-up/Launch

15 minutes

Today's lesson continues to focus on equivalent fractions.  The emphasis of this lesson is on simplifying fractions and also determining when a fraction is in simplest form.

To get the students warmed up, I start with a review from yesterday.  To do this, I post 3 fractions on the board and ask students to find 3 equivalent fractions for each.

An example of 3 fractions I might use are:

1/8

6/24

3/9

After students are given time to work on this independently, I encourage students to turn and talk about strategies used, more than solutions arrived at. While students are working on this warm-up task.  I pull a small group of students who were struggling yesterday.  I want to help them get off to a successful start today.

I call on students to come to the board and share their solutions and strategies.  It is important to remind students that there are unlimited equivalent fractions.  These answers are not the only correct examples.  

I am sure to have at least one student share an example of simplifying fractions because this is also a strategy for finding equivalence. 

To help the students see where we are moving with this lesson, I draw extra attention to the simplified fraction.  Then I write the focus questions on the board.

• Can this fraction be simplified?

• Is it in simplest form?

• How do you know?  

I tell the students that these questions will be the focus questions for today.  

Guided Practice

15 minutes

How do you know when a fraction is in the simplest form?  

This question is something that students struggle with explaining.  They use terminology that isn't specific enough to say what they really mean.  It is important to help students become more precise with their language so that they can communicate their understanding more effectively (MP6 - Attend to precision). 

I write 1/5 on the board and ask students to think about the focus questions.

• Can it be simplified?

• Is it is simplest form?

• How do you know? 

(I use the first 2 questions interchangeably, because I like to ask important questions in different ways to try to connect with students who process information differently)

This fraction is an easy starting point, because 1 has only 1 factor - 1.  Students realize that this can not be simplified because "other than 1 you can't divide the numerator by anything". I record this explanation on the board, as a good starting point.  I never erase it as we progress, because  I like the students to see how much their thoughts can grow in a class discussion. 

Next, I write the fraction 3/5 and challenge their explanation.  Three has more factors than just 1.  But this fraction is still in simplest form.  How do you know?  "This fraction is in simplest from, because I know that 3 and 5 are both prime numbers"  Prompting is needed to help students explain that prime numbers are numbers with only 1 factor pair.  They feel comfortable in explaining that since they are both prime, you can't divide them any more.

To build on this, I write 3/15 on the board.  And say that 3 is a prime number.  Does that mean this fraction is in simplest form?  I allow students to turn and talk about this question.

The agree that it is not, because 3, although it is prime, is a factor of 15.  So 3 and 15 can both be divided by 3.  

This discussion allows me to introduce canceling factors as a method for reducing fractions.  (See Using factorization to simplify fractions screencast.

I demonstrate a few more examples of this method of reducing fractions.  Always presenting the canceling factors method and the dividing by a fractional representation of 1.  While doing this, I use the phrase common denominators repeatedly.  I haven't introduced the term officially, but I use it consistently to get the students familiar with it.

Independent Practice

20 minutes

Students practice simplifying fractions and finding the simplest form of given fractions (based on the various directions provided).

While they are working in pairs, I circulate to the different groups and ask them the 3 focus questions.

• Can it be simplified?

• Is it is simplest form?

• How do you know? 

I want to ensure that students are thinking beyond the process.  

I encourage students who take many steps to get to the simplest form as well as those who identify the greatest common factor right away.  As long as students are able to identify a common factor and then evaluate the new fraction for a common factor between the numerator and denominator.

I have attached a few videos of some discussions I have with student pairs while circulating.

Group Share

5 minutes

This is my favorite part of the lesson.  Students are asked to choose on problem from the day that they want to discuss.  We have time for 3 different problems.  I am always impressed with the questions students ask.  

The "choice of problem" share allows student to build off a common experience, make connections, share strategies, and ask questions. 

I have attached a How do you know it is in simplest form? screencast to explain the discussion that arose from one student's question. This shows how through dialogue, students can enrich their language development in math.