In this activity, positive and negative numbers are used to represent changes in a quantity. Students consider a table showing the changes in inventory of cell phones at one store and make sense of it in the given context (MP2).

The purpose of this discussion is for students to share their thinking about what positive and negative numbers mean in the context of inventory and change. Begin by inviting students to share their responses and reasoning for the first two questions. Consider discussing the following questions:

• "What is the difference between the -2 in the inventory column and the -2 in the change column?" (One represents that 2 phones have been ordered but are not available in inventory, while the other represents the number of phones that were sold on Monday.)
• "What is the difference between a positive number in the inventory column and a positive number in the change column?" (A positive inventory means that the store has the cell phone in stock, while a positive change means that the store gets a shipment of phones that day.)

If time allows, invite students to share their responses and reasoning for the remaining questions.

In this activity, students track the elevation changes of a hiker on Mount Kilimanjaro. Students are free to use any strategy to determine the hiker's beginning or final elevation or their change in elevation for each given day, but they must be able to explain their reasoning (MP3).

Monitor for students who use these different strategies for the last problem about the difference between the hiker's final and beginning elevations.

• Drawing a number line diagram
• Finding the final elevation by adding or subtracting the meters hiked up or down, then finding the difference between the final and beginning elevations
• Finding the difference between the meters hiked up and the meters hiked down

The goal of this discussion is for students to make connections between different representations of a situation. Display 2–3 approaches from previously selected students for all to see. Use Compare and Connect to help students compare, contrast, and connect the different approaches. Here are some questions for discussion:

• “What do the approaches have in common? How are they different?”
• “Did anyone solve the problem the same way but would explain it differently?”
• “How does the hiker's beginning and final elevation show up in each method, if at all?”
• “Are there any benefits or drawbacks to one representation compared to another?”

In this activity, students plot points in a coordinate plane to create a rectangle. They find the lengths of each side by finding the horizontal or vertical distance between points. Students attend to precision in language as they distinguish between distance (which is unsigned) and difference (which is signed) (MP6). 

In the digital version of the activity, students use an applet to plot points in a coordinate plane. The digital version may reduce barriers for students who need support with fine-motor skills.

The goal of this discussion is for students to compare the distance between two numbers with the difference between two numbers. Here are some questions for discussion:

• “How can you find the difference between two numbers?” (Subtract one number from the other.)
• “When finding the difference between two numbers, does the order matter?” (Yes, we need to subtract the final number from the beginning number.)
• “How can we find the distance between two numbers?” (We can use a number line and count the distance between the two numbers. We can subtract the two numbers.)
• “When finding the distance between two numbers, does the order matter?” (No, we are just looking for the magnitude of the change, not the direction of the change.)
• “How can we see this distinction between difference and distance in the points we drew in the coordinate plane?” (When finding the difference between the -coordinates of and , the order we subtracted mattered, but when finding the distance between the two points, the order did not matter.)

If not mentioned in students' explanations, emphasize that differences can be positive or negative (or 0) depending on the order of the numbers subtracted. Distances cannot be negative.