# Lesson 1

Positive and Negative Numbers

Let’s explore how we represent temperatures and elevations.

### Problem 1

1. Is a temperature of -11 degrees warmer or colder than a temperature of -15 degrees?
2. Is an elevation of -10 feet closer or farther from the surface of the ocean than an elevation of -8 feet?
3. It was 8 degrees at nightfall. The temperature dropped 10 degrees by midnight. What was the temperature at midnight?
4. A diver is 25 feet below sea level. After he swims up 15 feet toward the surface, what is his elevation?

### Problem 2

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 3

Explain how to calculate a number that is equal to $$\frac{2.1}{1.5}$$.

(From Unit 6, Lesson 5.)

### Problem 4

Write an equation to represent each situation and then solve the equation.

1. Andre drinks 15 ounces of water, which is $$\frac35$$ of a bottle. How much does the bottle hold? Use $$x$$ for the number of ounces of water the bottle holds.

2. A bottle holds 15 ounces of water. Jada drank 8.5 ounces of water. How many ounces of water are left in the bottle? Use $$y$$ for the number of ounces of water left in the bottle.

3. A bottle holds $$z$$ ounces of water. A second bottle holds 16 ounces, which is $$\frac{8}{5}$$ times as much water. How much does the first bottle hold?

(From Unit 6, Lesson 4.)

### Problem 5

A rectangle has an area of 24 square units and a side length of $$2\frac34$$ units. Find the other side length of the rectangle. Show your reasoning.

(From Unit 4, Lesson 13.)