# Comparing and Ordering Integers

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## Objective

SWBAT compare and order two or more integers using the number line and by reasoning about absolute value.

#### Big Idea

The order in which numbers are placed on a number line will determine relative value of the numbers.

7 minutes

Students complete the Think About It problem with their partners.

After 3 minutes of work time, I have 2-3 students share out their answers and how they were able to compare the two numbers.

Once students have shared, I frame the lesson by letting students know that they'll learn to compare and order integers using two strategies:  plotting on number lines and finding absolute value of numbers.

## Intro to New Material

15 minutes

To start the Intro to New Material section, I have students explain how to plot -5 and -2 on the given number line.  I then have the class vote on which number they think is greater, and then have 1-2 students share out their rationale.  It's likely that the majority of students will think that -5 is the larger number.

At this point, I'll tell students that we know that a number line goes on forever in both directions. We are learning more about patterns and rules of number lines. As you move to the left, the values of numbers get smaller (i.e. 5, 4, 3, 2, 1…) and as you move to the right, the values of numbers get larger (i.e. 1, 2, 3, 4, 5…). I'll then have students vote again on which number is larger, and again have 1-2 students share out their rationale.  I want students to articulate that -2 is greater than -5, because it is farther to the right on the number line.  Students capture -2 > -5 in their notes, and write down the reasoning.  We then talk about expressing the inequality in another way:  -5 < -2.  I have students turn and talk about the explanation they'd write for this.  I have a student share, and am looking for 'I know that -5 is less than -2 because it is further to the right on the number line.'

Students fill in the key ideas on the page:  Numbers increase in value as you move to the right/up on a number line and numbers decrease in value as you move to the left/down on a number line.

The next problem in this section asks students to order integers.  I have students plot the numbers on the number line.  In order to determine who is further away, students find the absolute value of each number.

The key ideas that go along with this second problem type:  The larger the absolute value of a positive number, the larger the value of the number; the larger the absolute value of a negative number, the smaller the value of the number.

## Partner Practice

15 minutes

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

• Are students paraphrasing and annotating?
• Are students correctly modeling the problem on a number line?
• Are students interpreting the questions correctly?
• Are students using the correct symbols to compare and order values?
• Are students explaining how they used a number line to compare/order values correctly?
• Are students explaining how they applied the concept of absolute value to compare/order values correctly?
• Are students answering in complete sentences?

• How did you know to use the >, < or = sign?
• How did you use the number line to compare the numbers?
• How did you use the absolute value of the numbers to compare the numbers?
• How did you know what the question was asking you to compare?

After 10 minutes of partner work time, students complete the Check for Understanding problem individually.

## Independent Practice

15 minutes

Students work on the Independent Practice problem set.

With the written responses, I am looking to be sure that students are using the key points from this lesson in their answers, whether they're working with number lines or absolute value.

There are open in this problem set that have an infinite number of correct answers (4, 6, 11).  These questions are great to get conversation started with kids.  I can ask why they picked the answer they did, what is another number that would work, what's a number that won't work, etc.

## Closing and Exit Ticket

10 minutes

After independent work time, I have students turn to their partners and share and compare responses to problems 10 - 12.  They'll have the chance to ask questions, and give and receive feedback on their work.

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