Integers: Number Lines and Absolute Values

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.  

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.

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.

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.

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.