## Division Problems.png - Section 2: Developing an Algorithm

# Dividing Fractions

Lesson 4 of 10

## Objective: SWBAT develop an algorithm for dividing fractions.

*45 minutes*

#### Do Now

*10 min*

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.

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#### Developing an Algorithm

*15 min*

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.

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#### Independent Practice

*15 min*

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.

#### Resources

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#### Lesson Summary

*5 min*

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.

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##### Similar Lessons

Environment: Urban

Environment: Urban

Environment: Urban

- UNIT 1: First Week of School
- UNIT 2: Properties of Math
- UNIT 3: Divisibility Rules
- UNIT 4: Factors and Multiples
- UNIT 5: Introduction to Fractions
- UNIT 6: Adding and Subtracting Fractions
- UNIT 7: Multiplying and Dividing Fractions
- UNIT 8: Algorithms and Decimal Operations
- UNIT 9: Multi-Unit Summative Assessments
- UNIT 10: Rational Numbers
- UNIT 11: Equivalent Ratios
- UNIT 12: Unit Rate
- UNIT 13: Fractions, Decimals, and Percents
- UNIT 14: Algebra
- UNIT 15: Geometry

- LESSON 1: Multiplying Fractions
- LESSON 2: Creating Word Problems for Multiplying Fractions
- LESSON 3: Multiplying Mixed Numbers
- LESSON 4: Dividing Fractions
- LESSON 5: Dividing Mixed Numbers Algorithm
- LESSON 6: Operations with Fractions Review
- LESSON 7: Fractions Word Problems Review
- LESSON 8: Number Sense Unit Exam
- LESSON 9: Test Corrections
- LESSON 10: Fractions Unit Project