In this partner activity, students take turns ordering rational numbers from least to greatest. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

If some students place negative numbers in order of increasing absolute value on the left side of 0, consider asking:

• “How did you determine the order of the numbers less than 0?”
• “How would the numbers be ordered on a number line to the left of (or below) 0?”

The purpose of this discussion is for students to share their strategies for comparing and ordering rational numbers. Here are some questions to consider:

• “Which numbers did you place first? Why?”
• “Which numbers were hardest to place, and which were the least difficult?”
• “How does placing negative numbers compare to placing positive numbers?”
• “How did you use numbers you had already placed to reason about where to place new numbers?”
• “Describe any difficulties you experienced and how you resolved them.”

In this activity, students refine their language to be more precise when they use terms, such as “greater than,” “less than, “opposite,” and “negative” (MP3). 

The goal of this discussion is to give students the opportunity to use precise language as they compare the relative positions of rational numbers. Give students 2–3 minutes to discuss their responses with a partner before a whole-class discussion. Ask students to share their partner’s reasoning, especially if it was different than their own. Here are some questions to consider:

• “Did you ever have a different answer than your partner? If so, were you both correct? If not, how did you work to reach an agreement?”
• “How can we tell if two numbers are opposites?” (They are the same distance from 0 but on opposite sides of 0.)
• “How can we tell if one number is greater or less than another number?” (Numbers toward the right are considered greater, and numbers toward the left are considered less.)