Lesson 2
Changing Temperatures
Let's add signed numbers.
2.1: Which One Doesn’t Belong: Arrows
Which pair of arrows doesn't belong?
2.2: Warmer and Colder

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 
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
For the numbers \(a\) and \(b\) represented in the figure, which expression is equal to \(a+b\)?
\(a+b\)
\(ab\)
\(ba\)
2.3: 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.
 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.
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 \(427\) to find the final temperature, or we can think of the change as \(\text7^\circ\). Again, we can add to find the final temperature.
\(42 + (\text7) = 35\)
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.
\(3+ (\text7) = \text4\)
We can represent signed numbers with arrows on a number line. We can represent positive numbers with arrows that start at 0 and point 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 \(3 + (\text5)\):