# Lesson 1

Positive and Negative Numbers

Let’s explore how we represent temperatures and elevations.

### Problem 1

1. A whale is at the surface of the ocean to breathe. What is the whale’s elevation?

2. The whale swims down 300 feet to feed. What is the whale’s elevation now?

3. The whale swims down 150 more feet more. What is the whale’s elevation now?

4. Plot each of the three elevations as a point on a vertical number line. Label each point with its numeric value.

### Problem 2

1. A fish is 12 meters below the surface of the ocean. What is its elevation?
2. A sea bird is 28 meters above the surface of the ocean. What is its elevation?
3. If the bird is directly above the fish, how far apart are they?

### Problem 3

1. Represent each of these temperatures in degrees Fahrenheit with a positive or negative number.

• 5 degrees above zero
• 3 degrees below zero
• 6 degrees above zero
• $$2\frac34$$ degrees below zero
2. Order the temperatures above from the coldest to the warmest.

### Problem 4

It was $$\text- 5 ^\circ \text{C}$$ in Copenhagen and $$\text- 12 ^\circ \text{C}$$ in Oslo. Which city was colder?

### Problem 5

Han wants to buy a \$30 ticket to a game, but the pre-order tickets are sold out. He knows there will be more tickets sold the day of the game, with a markup of 200%. How much should Han expect to pay for the ticket if he buys it the day of the game?

(From Unit 6, Lesson 4.)

### Problem 6

Two students are both working on the same problem: A box of laundry soap has 25% more soap in its new box. The new box holds 2 kg. How much soap did the old box hold?

• Here is how Jada set up her double number line.
• Here is how Lin set up her double number line.

Do you agree with either of them? Explain or show your reasoning.

(From Unit 6, Lesson 4.)