# Many Names for Fractions

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## Objective

SWBAT: • Identify the numerator and denominator of a fraction and how each relates to the part and the whole • Develop strategies for finding equivalent fractions • Simplify a fraction

#### Big Idea

What does it mean for two fractions to be called equivalent? Students develop strategies for generating equivalent fractions and simplifying fractions.

## Do Now

10 minutes

Note:

• I use the pre test data to determine whether or not students need practice finding equivalent fractions.  If not, I move on to the next lesson.

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to connect multiplying and dividing whole numbers by one to multiplying and dividing fractions by 1.

Students participate in a Think Pair Share.  I call on students to share out their thinking.  For problem 3, I am looking to see if students connect their answers to problem 1 and 2.  Some students may use an algorithm to solve these problems.  What is important to me is that students can explain their answer and why their answer is correct (MP3).

## Fraction Review

5 minutes

We work on these problems together.  I want students to recognize that with each new rectangle the shaded amount does not change, but the number and size of the parts increase or decrease.  This allows for us to use multiple names to represent the same fraction.  These fractions are equivalent because they have the same value, but they look different.  Students will work on developing a strategy for generating equivalent fractions and simplifying fractions in the next section.

## Many Names for Fractions

40 minutes

I tell students that their job is to work on the problems in the next section and come up with a strategy to generate multiple fraction names for the same quantity. I have students work in partners.  Students are engaging with MP8: Look for and express regularity in repeated reasoning.  As students work, I walk around and monitor student progress and behavior.

If students struggle, I may ask them some of the following questions:

• What does the numerator of a fraction represent?
• What does the denominator of a fraction represent?
• If you divide only the shaded area of the rectangle, would you be able to create a new name for the fraction?  Why or why not?
• As you divide the whole into more parts, what happens to the size of the parts?  What happens to the denominator as this happens?
• Why are ______ and ________ equivalent?
• Will the strategy you’re using always work?  Why or why not?

If students successfully complete their work, they move on to work on the challenge problems.

## Closure and Ticket to Go

10 minutes

For Closure I ask students, “What does it mean if two fractions are equivalent?”  Then I ask them to share out their strategies for generating equivalent fractions and simplifying fractions.  I want students to connect that they are multiplying by forms of one and then to connect this with the rectangular models.  Write 7/10 on the board.  I say that I am going to create an equivalent fraction whose denominator is three times the size of the original denominator.  What is the new denominator?  What must be the new value of the numerator?  How do you know?  When students understand equivalence they can apply it to figuring out how to add and subtract fractions.

I pass out the Ticket to Go and students complete it independently.  Then I pass out the HW Many Names for Fractions.