##
* *Reflection: Discourse and Questioning
Many Names for Fractions - Section 4: Closure and Ticket to Go

After grading the pre-test, I saw that I needed to include this lesson in Unit 4. After discussing the do now, I drew a number line and asked students to think about this question: What fraction is *exactly* between 2/6 and 3/6? This question is similar to a question that was on the pre-test. I told students that we were not going to talk about their ideas until the end of the lesson. Unit 4.1 Question.jpg

As an extra part of the closure, I returned to this question. Students participated in a **Think Pair Share. **I walked around and listened to students talk. I asked one student to share his thinking. He said that you could create equivalent fractions for 2/6 and 3/6 that both had 12 as the denominator. You would get 4/12 and 6/12, so 5/12 would be exactly between them. Then I called on a girl who I had heard talk during the think pair share. She said that she had thought that 2.5/6 was exactly between the two fractions. I asked the class if she was correct. Another student explained that she was correct because if you multiply 2.5/6 by 2/2 you would create 5/12. About 1/3 of the class said, “Ohhhhhh” at the same time. It was clear that many students had initially thought of 2.5/6, but had abandoned it.

Over the next few lessons, I will include questions that build on this concept. For example, I may ask, “Which fraction is exactly between ¼ and 1/3?” I will ask if 21/72 is correct. I want students to extend their knowledge of equivalent fractions to realize that 21/72 is equivalent to 7/24.

# Many Names for Fractions

Lesson 2 of 19

## 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.

*65 minutes*

#### Do Now

*10 min*

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)**.

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#### Fraction Review

*5 min*

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.

#### Resources

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#### Many Names for Fractions

*40 min*

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.

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#### Closure and Ticket to Go

*10 min*

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.**

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Thank you for a clear straight forward lesson. I plan to use it with my fourth graders. The formatting on the homework needs to be adjusted. Thank you!

| 2 years ago | Reply

OMG! You are the bomb with fractions and helping me to organize my teaching! Thank you!

| 2 years ago | Reply

Awesome worksheets! thanks for the upload, definitely going to imitate this lesson.

-Drew

| 3 years ago | Reply*expand comments*

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- UNIT 1: Intro to 6th Grade Math & Number Characteristics
- UNIT 2: The College Project - Working with Decimals
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Fraction Operations
- UNIT 5: Proportional Reasoning: Ratios and Rates
- UNIT 6: Expressions, Equations, & Inequalities
- UNIT 7: Geometry
- UNIT 8: Geometry
- UNIT 9: Statistics
- UNIT 10: Review Unit

- LESSON 1: Pretest
- LESSON 2: Many Names for Fractions
- LESSON 3: What Fraction of the Section Does Each Person Own?
- LESSON 4: Which Fraction is Greater?
- LESSON 5: Adding and Subtracting Fractions Day 1
- LESSON 6: Adding and Subtracting Fractions Day 2
- LESSON 7: Looking for Patterns + Show What You Know
- LESSON 8: Representing Fraction Multiplication
- LESSON 9: Representing Fraction Multiplication Day 2
- LESSON 10: Mixed Number Multiplication
- LESSON 11: The Multiplying Game
- LESSON 12: Connecting Multiplication and Division
- LESSON 13: Dividing Whole Numbers by Fractions
- LESSON 14: Dividing Fractions by Fractions
- LESSON 15: Strategies for Dividing Fractions
- LESSON 16: Strategies for Dividing Fractions Day 2 + Show What You Know
- LESSON 17: Unit Review
- LESSON 18: Unit Closure
- LESSON 19: Unit Test