# Identifying and Representing Rational Numbers on a Number Line

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## Objective

SWBAT identify and represent rational numbers on the number line.

#### Big Idea

Rational numbers and number lines can be used to represent real world situations.

7 minutes

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.

## Intro to New Material

15 minutes

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:

1. Determine which two integers the rational number is between.
2. Convert fractions and decimals to the same representation.
3. Partition the whole. Note: each whole can be partitioned differently.
4. 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.

## Partner Practice

15 minutes

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?

• 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.

## Independent Practice

15 minutes

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.)

## Closing and Exit Ticket

10 minutes

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.