Dividing Fractions

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Objective

SWBAT develop an algorithm for dividing fractions.

Big Idea

What does dividing fractions have to do with multiplication?

Do Now

10 minutes

As an introduction to the lesson of dividing fractions, I will assess students' understanding of division and what it means.

Do Now

8 ÷ 4 = 2

Describe what this equation means.  Create a visual model.

I will ask students to share their responses with the class. 

Possible Student Responses:

  • 8 divided by 4 equals 2
  • 2 groups of 4 can fit into 8
  • we can separate 8 into 2 groups of 4
  • 4 goes into 8, 2 times

 

Students should have an understanding that when dividing you are "breaking apart" into equal groups.

Developing an Algorithm

15 minutes

The purpose of this lesson is for students to develop the algorithm for dividing fractions.  Students are more likely to remember the steps if they are a part of creating them.

I will display 3 equations (Division Problems) on the board and ask students to discuss with their groups.  After about 5 minutes, we will discuss the problems as a class.

What do the equations have in common?

  • Students will notice that they are all division problems that involve fractions.

Do you notice any patterns in the equations?

  • Many students will notice that for the first two equations the whole number is being multiplied by the denominator to arrive at the quotient.

If we use the operation of multiplication, what happens to the divisor?  For example, how does the first problem become 10 times 2?

  • Students may realize that the divisor has been flipped.  I will provide them with the vocabulary word "reciprocal".

What about the third equation? Does changing it to multiplication and finding the reciprocal of the divisor give us the quotient?

  • Students should notice that the third equation is different because the first number is a fraction instead of a whole number, but these steps still work.

This leads us to our algorithm for dividing fractions.

I will work through an Division Algorithm Example 1 with the class formalizing the algorithm for them.

Independent Practice

15 minutes

Although this section is labeled Independent Practice, I will encourage students to work on the Independent Practice on their own and then discuss questions with their group.

As students work, I will circulate throughout the room to ensure that they are on task.  Also, it is important to make sure that students are following the algorithm correctly.  A common mistake is for students to forget to use the reciprocal of the divisor.

After 10 minutes, I will begin to call students to the board to show their work.  If the class disagrees with their work, I will ask the student to talk us through their work and we will discuss the problem.

Lesson Summary

5 minutes

As a class students have developed the algorithm for dividing fractions.  The purpose of the lesson summary is two-fold:  1.  To help lower level students better understand how the algorithm was developed and 2.  To promote students' communication of their reasoning.

What ideas that we have learned before were useful in solving this problem?

Possible Student Responses:

  • The algorithm for multiplying fractions.
  • Simplifying fractions.