Interpret Integers in Context

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SWBAT use integers, number lines and absolute value notation to represent quantities in real-world contexts.

Big Idea

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

Think About It

7 minutes

Students complete the Think About It problem in pairs.  After 3 minutes of partner time, the class comes back together to share their responses.  

In this lesson, students will continue to make meaning of integers in real-world contexts.  Also, students will be asked to explain the meaning of 0 in real world contexts.

As students are sharing out, I keep in mind the key points that I want to come out in this discussion.  If, after 3 minutes, students do not get to the explanations as they share, I will summarize: both Jamie’s position and Camille’s positions are described in relation to the same point—sea level.  If we want to represent sea level on a number line, we would use zero, because we talk about negative and positive quantities in relation to the same point—zero.  Therefore, 0 ft represents sea level on a number line.  Jamie is further from Lisa because she is 32 feet further from 0 than Camilla; the magnitude, or size, of her distance from sea level/Lisa is larger than that of Camilla.


Intro to New Material

10 minutes

In this lesson, students will continue to develop their understanding of integers in the real-world.  They will write statements relating to the meaning of zero given a context involving positive and negative numbers.

The problem in the Intro to New Material has many connections to the work students did in the previous lesson, and I expect students to draw from what they've already learned for the first two parts.  Students may want to draw a vertical number line, which fits this context.  

The new learning in this lesson comes when students are asked to think about how far the CIA agent is from the ground floor.  Students will need to apply the concept of absolute value here, as we wouldn't express the agent's distance as -30 floors.  

The equation needed for this situation is |-30| = 30, where -30 represents his location in relation to 0 and 30 represents the number of floors he is away from 0.


Guided Practice

15 minutes

In this lesson, I deviate from my typical lesson flow.  Rather than a Partner Practice section, I'll keep students working in a whole group, as we go through the Guided Practice problems.  I make this choice because I want to address misconceptions immediately.  I also want all students to engage in conversation about the contexts. 

I have students use mini-white boards to show their responses to me in real time.  Students have the hard copied of the problems, and they are expected to annotate the problems as we always do.  Students should annotate with '+' and '-' over the values in the problems.  

As we work through the problems and students flash their answers, I'll ask questions of individual students that check for understanding.  I'm asking:

  • How did you know to represent the context with that integer?
  • How did you know to describe a given integer using those terms?
  • What does the absolute value of the given quantity mean?
  • What does 0 mean in this context?


For students who are struggling to understand each context, you can provide them with a bank of words that denote positive values and negative values.  If students struggle with interpreting relationships between integers and 0, have them plot numbers on a number line to visually show the relationships.


Independent Practice

20 minutes

Students work on the Independent Practice problem set.  As students work, I circulate around the room and check students' work.  I am looking for:

  • Are students paraphrasing?
  • Are students annotating by representing each integer with a '+' or '-'?
  • Are students interpreting the given contexts correctly?
  • Are students writing the correct equations using absolute value to represent the magnitude of the values?
  • Are students correctly describing the meaning of the values in the equations they wrote?
  • Are students answering in complete sentences?


I'll also talk with students, using the same CFU questions that I used during the Guided Practice section.  

Closing and Exit Ticket

10 minutes

After independent practice time, I have students turn and talk with their partners about Problem 9.  The notion of debt comes up often with integer work in this unit, and this problem is a good preview of the work that will happen in the next lesson.

Once students have a chance to talk, I have 2 students share out their thinking around Problem 9 with the entire class. 

Students then independently complete the Exit Ticket to close the lesson.