##
* *Reflection: Developing a Conceptual Understanding
Integers: Number Lines and Absolute Values - Section 2: Intro to New Material

In this lesson, I guide students to create a number line that has zero as its center, and that counts by an interval of 1 (see Intro to New Material). It's very important that this is not the only representation of a number line that students encounter throughout the unit.

I make sure that in student materials, on homework, on review, and on assessments, students are exposed to a variety of number lines. This means students are seeing:

- a mix of horizontal and vertical number lines
- number lines that either don't have 0 represented, or have 0 represented to the left/right of the center
- number lines that have intervals of whole numbers other than 1 (2, 50, etc.)
- number lines that have integer intervals

I also give students practice with creating their own number lines, and show examples of student work when kids don't use a 0 in the middle.

I don't want students to encounter an unfamiliar number line on a district assessment or on the SBAC assessment and be thrown for a loop.

*Developing a Conceptual Understanding: Variety with Number Lines*

# Integers: Number Lines and Absolute Values

Lesson 1 of 8

## Objective: SWBAT identify and explain the meaning of the absolute value of a number; SWBAT represent integers using a number line.

## Big Idea: Opposite rational numbers have the same distance from 0 on a number line. The absolute value of a number represents the distance from the number to 0.

*60 minutes*

#### Think About It

*7 min*

Students work in pairs on the Think About It problems. After 2-3 minutes of work time, I have the class share out places in the real world where they've seen negative numbers. Common student answers will be the weather (we're in the Northeast), football, and 'money.' When students say 'money,' I push them to get more specific with what they mean.

I have students vote with their thumbs about the second question, and take a few students thoughts on whether or not 3 and -3 can have the same value.

I then frame the lesson by letting students know we're starting a new unit, and that they're going to learn about negative numbers. Students are generally excited to start learning about integers.

#### Resources

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#### Intro to New Material

*15 min*

To start the Intro to New Material section of this lesson, I have students construct their own number lines on a blank piece of paper (-5 to 5). Students will be able to use this number line as a resource over the next several lessons.

As we create our number lines, I share the following **key points** with students:

- 0 represents the middle of a number line and is known as the origin.
- a number line goes on for infinity in both directions, and we show this using arrows on each end of the line.
- integers are all positive and negative counting numbers, including 0
- integers do not include decimals and fractions

Once our number lines are complete, we fill in the notes. I have students brainstorm the non-examples of integers, using fractions and decimals.

I have students **turn-and-talk** with their partners about opposite numbers. I ask students to identify numbers that are opposites on the number line. During the conversation, we'll fill in the notes: ** A number and its opposite have the same absolute value because they are the same distance from 0.**

For Problem 1 in this set, students may need support around how to plot and label points on a number line. I circulate around the room to be sure that the points are on the number line and that the letters are not on the number line.

#### 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 every group. I am looking for:

- Are students labeling their number lines correctly?
- Are students plotting both a point and labeling with a letter to represent points on number lines?
- Are students correctly identifying the absolute value of a number and explaining why two numbers have the same absolute value?
- Are students answering in complete sentences?

I am asking:

- How did you know how to label the number line with those integers?
- How did you know that those two numbers are opposites?
- How did you know that is the absolute value of the number?

After partner work time, students complete the Check for Understanding problem independently. I share one student's work on the document camera, and have that student present his/her work. Students then offer positive and constructive feedback.

#### Resources

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#### Independent Practice

*15 min*

Students work on the Independent Practice problem set.

As students are plotting numbers, I am making sure that they've placed their points on the number line. Students sometimes come to me with the habit of plotting numbers as floating X's *above *the number line, and this lesson provides me the opportunity to break that habit!

The steps that students should be taking as they work:

1. Read the problem and paraphrase- what is the question asking us to find? (e.g. if the problem says “absolute value,” we annotate and write “distance from 0.”)

2. Model the problem using a number line. On the number line I ask my students to:

- Include arrows on both ends
- Have equally spaced intervals
- Points are plotted and labeled
- A statement to the right that says “value increasing’ and a statement to the right that says “value decreasing.”
- If proving that opposite numbers have the same absolute value, the number line should also include two arrows to show the distance of each point from

3. Using arrows, indicate the distance of a number from 0

4. Explain or prove your answer with evidence include the distance of a number from 0.

#### Resources

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#### Closing and Exit Ticket

*8 min*

After independent work time, I have students turn and talk with their partners about Problems 7 - 11. They have the chance to compare answers, ask one another clarifying questions, and adjust their responses if they'd like.

Students 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