# Lesson 2: Changing Temperatures

## 2.1: Which One Doesn’t Belong: Arrows

Which pair of arrows doesn't belong?

1.
2.
3.
4.

## 2.2: Warmer and Colder

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

start ($^\circ\text{C}$) change ($^\circ\text{C}$)  final ($^\circ \text{C}$) 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
1.

2.

3.

4.

5.

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

start ($^\circ\text{C}$) change ($^\circ\text{C}$) final ($^\circ\text{C}$) addition equation
a -20 30 degrees warmer
b -20 35 degrees warmer
c -20 15 degrees warmer
d -20 15 degrees colder
1.

2.

3.

4.

## 2.3: Winter Temperatures

1. One winter day, the temperature in Houston is $8^\circ$ Celsius. Find the temperatures in these other cities. Explain or show your reasoning.
1. In Orlando, it is $10^\circ$ warmer than it is in Houston.
2. In Salt Lake City, it is $8^\circ$ colder than it is in Houston.
3. In Minneapolis, it is $20^\circ$ colder than it is in Houston.
2. In Fairbanks, it is $10^\circ$ colder than it is in Minneapolis. What is the temperature in Fairbanks?

GeoGebra Applet WtaGDhSN

## 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 $\text-7^\circ$. Again, we can add to find the final temperature.

$42 + (\text-7) = 35$

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.

$3+ (\text-7) = \text-4$

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.

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 $3+5$:

And this represents $3 + (\text-5)$: