In this activity, students return to the context of a thermometer to examine rational numbers that are not integers. Students compare and interpret the signed numbers, including a temperature that is not pictured, to make sense of them in context (MP2).

If some students struggle to estimate temperatures that are between two markings, consider asking:

• "What would the temperatures be at the markings directly above and directly below the thermometer's level?"
• "What temperature would be halfway in between those two numbers?"

The purpose of this activity is to remind students of how to compare two values using inequality notation. Begin by inviting students to share their responses for the temperature shown on each thermometer. 

Then discuss the last question, asking students to explain their reasoning until they come to an agreement that is colder than . If not brought up in students’ explanations, introduce the notation , and remind students that this is read, "Negative 4 is less than negative 3." Explain that -4 is farther away from 0 than -3 is, and point to the location of -4 on a thermometer to show that it is below -3. On the negative side of the number line, that means -4 is less than -3. Familiarity with “less than” notation will be useful for describing their reasoning in the next activity.

In this activity, students continue to interpret signed numbers in context and begin to compare their relative locations on a vertical number line in order to make sense of signed number (MP1). The number line is labeled in 5-meter increments, so students have to interpolate the height or depth for some of the animals. Students are also given the height or depth of other animals that are not pictured and asked to compare these to the height or depth of the animals shown.

Monitor for students who recognize that there are two possible answers to the last question depending on whether the new dolphin is 3 meters above or below the original dolphin. 

If students measure to the top or bottom of the animal, remind them that we are using the eyes of the animal to measure their height or depth.

Some students may struggle to visualize where the albatross, seagull, and clownfish are on the graph. Consider having them draw or place a marker where the new animal is located while comparing it to the other animals in the picture.

The purpose of this discussion is for students to share their reasoning for the height or depth of each new animal. A key idea of this discussion is that distances above and below sea level can be represented using signed numbers. The depths of the shark, fish, and octopus can be expressed as negative numbers because they are below sea level, while the heights of the remaining animals can be expressed as positive numbers because they are above sea level.

Begin by inviting students to share their responses and reasoning to the fourth question about the relative position of the clownfish. Record and display their verbal descriptions using signed numbers. For example, if a student says the clownfish is 5 meters below the dolphin, write “-5”.

Finally, ask students to share their responses and reasoning to the last question about the height of the new dolphin. Invite a previously selected student to explain why there are two possible answers to the last question. (The new dolphin could be 3 meters above or below the original dolphin.)

In this partner activity, students take turns ordering rational numbers from least to greatest. Students start with a set of integers first, then add rational numbers second. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

The purpose of this discussion is for students to share their strategies for comparing and ordering rational numbers. Highlight strategies that use the magnitude of a number and its additive inverse. Here are some questions to consider:

• “Which numbers did you place first? Why?”
• “Which numbers were hardest to place, and which were the easiest?”
• “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?”
• "How did you decide where to put the fractions?"
• "How is related to ?"
• “Describe any difficulties you experienced and how you resolved them.”

Introduce the convention that number lines are usually drawn horizontally, with the negative numbers to the left of 0. If any groups put their slips in order vertically, consider asking them to reposition their slips to match the orientation of a horizontal number line.