Lesson 6Changing 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

Which pair of arrows doesn’t belong?

Activity 1: Warmer and Colder

Problem 1

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

	start ( $^{\circ} C$ )	change ( $^{\circ} C$ )	final ( $^{\circ} C$ )	addition equation
a	$+ 40$	10 degrees warmer	$+ 50$	$40 + 10 = 50$
b	$+ 40$	5 degrees colder
c	$+ 40$	30 degrees colder
d	$+ 40$	40 degrees colder
e	$+ 40$	50 degrees colder

Problem 2

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

	start ( $^{\circ} C$ )	change ( $^{\circ} C$ )
a	$- 20$	30 degrees warmer
b	$- 20$	35 degrees warmer
c	$- 20$	15 degrees warmer
d	$- 20$	15 degrees colder

Are you ready for more?

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 $a$ and $b$ represented in the figure, which expression is equal to $| a + b |$ ?

$| a | + | b |$
$| a | - | b |$
$| b | - | a |$

Activity 2: Winter Temperatures

One winter day, the temperature in Houston is $8^{\circ}$ Celsius. Find the temperatures in these other cities. Explain or show your reasoning.

open applet in presentation mode

In Orlando, it is $10^{\circ}$ warmer than it is in Houston.
In Salt Lake City, it is $8^{\circ}$ colder than it is in Houston.
In Minneapolis, it is $20^{\circ}$ colder than it is in Houston.
In Fairbanks, it is $10^{\circ}$ colder than it is in Minneapolis.
Use the thermometer applet to verify your answers and explore your own scenarios.

Print Version

One winter day, the temperature in Houston is $8^{\circ}$ Celsius. Find the temperatures in these other cities. Explain or show your reasoning.

In Orlando, it is $10^{\circ}$ warmer than it is in Houston.
In Salt Lake City, it is $8^{\circ}$ colder than it is in Houston.
In Minneapolis, it is $20^{\circ}$ colder than it is in Houston.
In Fairbanks, it is $10^{\circ}$ colder than it is in Minneapolis.
Write an addition equation that represents the relationship between the temperature in Houston and the temperature in Fairbanks.

Lesson Summary

If it is $42^{\circ}$ outside and the temperature increases by $7^{\circ}$ , then we can add the initial temperature and the change in temperature to find the final temperature.

$42 + 7 = 49$

If the temperature decreases by $7^{\circ}$ , we can either subtract $42 - 7$ to find the final temperature, or we can think of the change as $- 7^{\circ}$ . Again, we can add to find the final temperature.

$42 + (- 7) = 35$

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 $3^{\circ}$ and the temperature decreases by $7^{\circ}$ , then we can add to find the final temperature.

$3 + (- 7) = - 4$

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.

To represent addition, we put the arrows “tip to tail.” So this diagram represents $3 + 5$ :

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 $3 + (- 5)$ :