In this activity, students make sense of adding signed numbers using the context of temperature (MP2). They connect increases in temperature with positive numbers and decreases in temperature with negative numbers and then represent these increases and decreases on a number line. Students repeatedly add numbers to 40 and then to -20 to see that adding a positive number is the same as moving to the right on the number line and adding a negative number is the same as moving to the left on the number line (MP8). 

The purpose of this discussion is to review how adding positive and negative numbers can be represented on a horizontal number line. Here are some questions for discussion: 

• “How can we represent an increase in temperature on a number line?” (an arrow pointing to the right)
• “How can we represent a decrease in temperature on a number line?” (an arrow pointing to the left)
• “How are positive numbers represented on a number line?” (arrows pointing to the right)
• “How are negative numbers represented on a number line?” (arrows pointing to the left)
• “How can we represent a sum of two numbers?” (Draw the arrows so the tail of the second is located at the tip of the first.)
• “How can we determine the sum from the diagram?” (The sum is the number at the tip of the second arrow.)
• “What happens when we add a positive number to another number?” (The sum is located to the right of the first number on the number line.)
• “What happens when we add a negative number to another number?” (The sum is located to the left of the first number on the number line.)

In this activity, students reason about the temperature differences in different cities and connect them using an addition equation (MP2). Students may think of temperatures that are colder in terms of subtraction, which is one correct way to represent the situation. The focus in this activity is how to think about a situation with colder temperatures in terms of addition. Students will have an opportunity to connect addition and subtraction in a future lesson.

In the digital version of the activity, students use an applet to represent the change in temperature on a thermometer. The applet allows students to set the starting temperature and the temperature change and to see an equation that represents the situation. The digital version may be useful for students who would benefit from a visual representation of increasing and decreasing temperatures. The digital version may also be useful as a tool for students to check their work.

The goal of this discussion is for students to think about how to represent a colder temperature in terms of addition. Begin by inviting students to share their response and reasoning for finding the temperature in Minneapolis. If students correctly describe the situation in terms of subtraction with an equation such as , acknowledge that perspective, then ask them if they can also think of it in terms of addition.

If no students used a number line, display this diagram for Minneapolis for all to see, and consider discussing the following questions:

• “How is the temperature of 8 degrees in Houston shown in the diagram?” (With an arrow pointing to the right with a magnitude of 8 and starting at 0.)
• “How is the change in temperature of 20 degrees colder in Minneapolis shown in the diagram?” (With an arrow pointing to the left with a magnitude of 20 and starting at the tip of the first arrow.)
• “How does this diagram show addition?” (When the tail of the second arrow is located at the tip of the first arrow, the diagram represents the sum of the two numbers.)
• “How can we represent this situation with an addition equation?” ( .)