# Strategies for Dividing Fractions

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## Objective

SWBAT: • Demonstrate the relationship between multiplication and division involving fractions. • Develop strategies for dividing fractions. • Divide a mixed number by a fraction.

#### Big Idea

What strategies do you have for dividing fractions? How do you divide 1 1/8 by ¼? Students apply all that they have learned about dividing with fractions to divide mixed numbers by fractions.

## Do Now

7 minutes

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 student to review dividing whole numbers by fractions, which we worked on in previous lessons.  Some students may draw a picture, while other students may use the algorithm to find the answer.

I have a student explain their answer for each of the problems.  I ask the class if his/her answer makes sense.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

## Quotient Stays the Same

10 minutes

Note:

• For this lesson, each student needs a fraction kit to help model problems.  Example: Fraction Kit

I have volunteers pass out the fraction kits.  We work on the first two problems (that were in the do now) together.  I want students to connect that 2 divided by 1/6 will result in the same answer as 2 x 6.

I have students work on the last three problems in the table independently.  If they get stuck, they can check in with a neighbor.  If students struggle with these problems, I encourage them to draw a picture.

When most students have finished the table we come back together to share out their answers.  Students may have different ways of interpreting the problems.  One student may draw a model of 4 and 2 and say that 2 takes up ½ of 4, therefore 2 divided by 4 is ½.  Another student may connect the division symbol with the fraction bar and know that 2 divided by 4 is the same as 2/4 or ½.  Another student may use long division to answer the problem.  I ask for a student to share a multiplication problem that would confirm that the answer is ½.

## Strategies for Dividing Fractions

15 minutes

I have students look at the problem 1 1/8 divided by ¼.  I quickly ask for a couple students to give estimates and explain how they came up with them.  I tell students that I want them to come up with multiple ways to solve this problem.  I explain that we will come back together and share our strategies.  Students are engaging in MP1: Make sense of problems and persevere in solving them and MP4: Model with mathematics.

As students work, I walk around and monitor student progress.  If students struggle, I encourage them to use the fraction kit to model what is going on.  If students think they are finished I push them to come up with more ways to solve the same problem.

After about five minutes we come back together as a class.  I have a piece of chart paper on the board that I have labeled “Strategies for Dividing Fractions”.  I ask students with different strategies to come to the document camera to show and explain their work.  I ask the class if that strategy works.  Students are engaging in MP7: Look for and make use of structure and MP8: Look for and express regularity in repeated reasoning.

I name the strategy and write it up on the chart paper.  See “Possible Strategies” to get an idea of different strategies students may use.  If students do not mention some of the strategies I present them and ask whether or not they work.  I do not use technical terms (like reciprocal or multiplicative inverse) because I don’t think it is necessary at this time.  If a student mentions that the “break apart” strategy is like the distributive property then we will discuss it as a class.  My goal is that students are comfortable with a strategy and are able to stretch and work to develop another strategy.

## Practice

15 minutes

Note:

• Students will start working on these problems, but they will not have time to finish them.  Students will have time to complete their work in the next lesson.

I have a volunteer read the directions for the practice problems.  I let students know that they will only have time to start these problems and that we will continue to work on it in the next lesson.

Students work on the problems independently.  I walk around and monitor student progress.  I ensure that students are showing two different ways to solve the problem.

If students are struggling, I may ask them some of these questions:

• What is going on in this problem?
• Do you think the answer is more or less than 1?  Why?
• What is your estimate for the problem?  Why?
• Look at the strategies on the poster.  Which strategy do you want to use?
• What is a different way we could solve this problem?