Lesson 2Changing Temperatures

Learning Goal

Let’s add signed numbers.

Learning Targets

  • I can use a number line to add positive and negative numbers.

Warm Up: Which One Doesn’t Belong: Arrows

Problem 1

Which pair of arrows doesn’t belong?

  1. A number line from -10 to 10 with two arrows. One arrow starts at 0 and ends at 3. The other arrow is above the first arrow and starts at 3 and ends at 7.
  2. A number line from -10 to 10 with two arrows. One arrow starts at 0 and ends at 3. The other arrow is above the first arrow and starts at 3 and ends at-6.
  3. A number line from -10 to 10 with two arrows. One arrow starts at 0 and ends at 3. The other arrow is above the first arrow and starts at 3 and ends at 0.
  4. A number line from -10 to 10 with two arrows. One arrow starts at 0 and ends at -4. The other arrow is above the first arrow and starts at -4 and ends at -9.

Activity 1: Warmer and Colder

Problem 1

Complete the table and draw a number line diagram for each situation.

start ()

change ()

final ()

addition equation

a

10 degrees warmer

b

5 degrees colder

c

30 degrees colder

d

40 degrees colder

e

50 degrees colder

  1. A number line from -40 to 50 in increments of 5.
  2. A number line from -40 to 50 in increments of 5.
  3. A number line from -40 to 50 in increments of 5.
  4. A number line from -40 to 50 in increments of 5.
  5. A number line from -40 to 50 in increments of 5.

Problem 2

Complete the table and draw a number line diagram for each situation.

start ()

change ()

final ()

addition equation

a

30 degrees warmer

b

35 degrees warmer

c

15 degrees warmer

d

15 degrees colder

  1. A number line from -40 to 50 in increments of 5.
  2. A number line from -40 to 50 in increments of 5.
  3. A number line from -40 to 50 in increments of 5.
  4. A number line from -40 to 50 in increments of 5.

Are you ready for more?

Problem 1

Number line with point a+b on the left and in the center, 0. Arrow A starts at 0 and goes to the right. Arrow b above a starts at the end of arrow a and goes to the a + b point

For the numbers and represented in the figure, which expression is equal to ?

Activity 2: Winter Temperatures

Problem 1

One winter day, the temperature in Houston is Celsius. Find the temperatures in these other cities. Explain or show your reasoning.

  1. In Orlando, it is warmer than it is in Houston.

  2. In Salt Lake City, it is colder than it is in Houston.

  3. In Minneapolis, it is colder than it is in Houston.

  4. In Fairbanks, it is colder than it is in Minneapolis.

  5. Use the thermometer applet to verify your answers and explore your own scenarios.

Print Version

One winter day, the temperature in Houston is Celsius. Find the temperatures in these other cities. Explain or show your reasoning.

  1. In Orlando, it is warmer than it is in Houston.

  2. In Salt Lake City, it is colder than it is in Houston.

  3. In Minneapolis, it is colder than it is in Houston.

  4. In Fairbanks, it is colder than it is in Minneapolis.

  5. Write an addition equation that represents the relationship between the temperature in Houston and the temperature in Fairbanks.

Lesson Summary

If it is outside and the temperature increases by , then we can add the initial temperature and the change in temperature to find the final temperature.

If the temperature decreases by , we can either subtract to find the final temperature, or we can think of the change as . Again, we can add to find the final temperature.

In general, we can represent a change in temperature with a positive number if it increases and a negative number if it decreases. Then we can find the final temperature by adding the initial temperature and the change. If it is and the temperature decreases by , then we can add to find the final temperature.

We can represent signed numbers with arrows on a number line. We can represent positive numbers with arrows that start at 0 and points to the right. For example, this arrow represents +10 because it is 10 units long and it points to the right.

A number line with the numbers negative 10 through 10 indicated. An arrow starts at 0, points to the left, and ends at negative 4.There is a solid dot indicated at 4.

We can represent negative numbers with arrows that start at 0 and point to the left. For example, this arrow represents -4 because it is 4 units long and it points to the left.

A number line with the numbers negative 10 through 10 indicated. An arrow starts at 0, points to the left, and ends at negative 4.There is a solid dot indicated at 4.

To represent addition, we put the arrows “tip to tail.” So this diagram represents :

A number line with the numbers negative 10 through 10 indicated. An arrow starts at 0, points to the right, and ends at 3. A second arrow starts at 3, points to the right, and ends at 8. there is a solid dot indicated at 8.

And this represents :

A number line with the numbers negative 10 through 10 indicated. An arrow starts at 0, points to the right, and ends at three. A second arrow starts at 3, points to the left, and ends at negative 2. There is a solid dot indicated at negative