# 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

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

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

$$|a|+|b|$$

$$|a|-|b|$$

$$|b|-|a|$$

### 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.

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.
4. In Fairbanks, it is $$10^\circ$$ colder than it is in Minneapolis.

### 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 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 $$3 + (\text-5)$$: