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* *Reflection: Rigor
Identifying and Representing Rational Numbers on a Number Line - Section 4: Independent Practice

When I pull together problems for my lesson materials, I am intentional about the level of complexity in the problem sets. I intentionally start off each section (partner practice, independent practice, and my homework) at a level that I feel all of my students will be able to complete. The problem sets increase in complexity as students work through them.

As students are working, whether individually or in pairs, I have the ability to differentiate what students are doing in the moment. If a pair, for example, is quickly finding success with the early partner practice problems, I'll tell them to try a more difficult exercise. I may tell individual students to start the independent work in the middle of the problem set.

I'll identify the more challenging problems on my lesson plan and packet, so that I am immediately ready with an academic challenge.

*Problem Sets*

*Rigor: Problem Sets*

# Identifying and Representing Rational Numbers on a Number Line

Lesson 6 of 8

## Objective: SWBAT identify and represent rational numbers on the number line.

*62 minutes*

#### Think About It

*7 min*

Students work independently on the Think About It problem. After 2-3 minutes of writing time, I have students share their responses with their partners. I want all students to have the opportunity to share what they've taken the time to write about (MP3).

I then have 2-3 students share out with the class what they've written about the plotted point. The **key idea** that comes out during the conversation is that negative rational numbers should count sequentially to the left.

It is likely that a student will share out that the point is at -1/4 or -1 1/4. In fact, I'll circulate while students are sharing and *look* for students that have this very common misconception, and will ask them to share their thinking with the class.

#### Resources

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#### Intro to New Material

*15 min*

To start the Intro to New Material, I have students look at the first example. I ask students what two whole numbers -0.7 falls between and what two whole numbers 0.15 falls between. We then partition the number line into tenths. For the positive numbers, we'll then express the tenths as hundredths. I don't have students change the negative numbers to hundredths; I want students to be comfortable with the wholes being partitioned differently.

**Steps:**

- Determine which two integers the rational number is between.
- Convert fractions and decimals to the same representation.
- Partition the whole.
**Note:**each whole can be partitioned differently. - Plot the numbers -> use a point!

Problem 2 asks students to identify the given point. I ask students to determine which two integers the point falls between. Then, I ask students what the denominator of our number will be, given how the number line is partitioned. Students label the hatch marks, and then identify the number at the point.

Problem 3 gives student the chance to practice partitioning the wholes in different ways.

#### Resources

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#### Partner Practice

*15 min*

Students work in pairs on the Partner Practice problem set. As they work, I circulate around the room and check in with each pair. I am looking for:

- Are students choosing the correct intervals?
- Are students converting all rational numbers to the same representation?
- Are students creating/labeling their number lines correctly?
- Are students plotting both a point and labeling with a letter to represent points on number lines?
- Are students creating/labeling their number lines correctly?
- Are students plotting both a point and labeling with a letter to represent points on number lines?
- Are students rewriting fractions and decimals in the same representation when necessary?
- Are students answering in complete sentences?

I'm asking:

- How did you know how to label the number line with those fractions/decimals?
- How did you know that the point goes there?
- How did you know that the number falls between those two integers?

After 10 minutes of partner work time, students complete the Check for Understanding problem independently. I pull one exemplary piece of student work to display on the document camera, so that students can check their own work and ask any clarifying questions.

#### Resources

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#### Independent Practice

*15 min*

Students work on the Independent Practice problem set.

As students are working, I am checking to be sure that students are partitioning their number lines correctly. When plotting fractions, students should break the number line into equal sized parts according to the denominator. When plotting decimals, students should break the number line into tenths. For numbers out to the hundredths, students will label the tenths in multiples of tens in hundredths (i.e. 0.10, 0.20, etc.)

#### Resources

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#### Closing and Exit Ticket

*10 min*

After independent practice work time, I bring the class back together. I have students show me on their fingers how many answers they selected for Problem 11. This gives me a quick way to see how everyone did with this question. I then tell students that there are three correct answers. I then have students turn and talk with their partners about which answer choices are correct.

Students then work independently on the Exit Ticket to close the lesson.

#### Resources

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- UNIT 1: Number Sense
- UNIT 2: Division with Fractions
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Coordinate Plane
- UNIT 5: Rates and Ratios
- UNIT 6: Unit Rate Applications and Percents
- UNIT 7: Expressions
- UNIT 8: Equations
- UNIT 9: Inequalities
- UNIT 10: Area of Two Dimensional Figures
- UNIT 11: Analyzing Data

- LESSON 1: Integers: Number Lines and Absolute Values
- LESSON 2: Integers in the Real World
- LESSON 3: Interpret Integers in Context
- LESSON 4: Comparing and Ordering Integers
- LESSON 5: Identifying Positive Rational Numbers on Number Lines
- LESSON 6: Identifying and Representing Rational Numbers on a Number Line
- LESSON 7: Comparing Rational Numbers
- LESSON 8: Describing Numbers