# Positive and Negative Numbers

Warmup

In the following demonstration of integer addition, the addends are modeled by using small blocks marked with 1 or -1. Press the gray buttons to form the first positive or negative addend and the green buttons to form the second addend.

Activity #1

Exploring Positive and Negative Numbers using a Thermometer.

In the applet below are three situations involving changes in temperature. • Represent each change on the applet, and draw it on a number line.

(1.) At noon, the temperature was 5 degrees Celsius. By late afternoon, it has risen 6 degrees Celsius. What was the temperature late in the afternoon?

(2.) The temperature was 8 degrees Celsius at midnight. By dawn, it has dropped 12 degrees Celsius. What was the temperature at dawn?

(3.) Water freezes at 0 degrees Celsius, but the freezing temperature can be lowered by adding salt to the water. A student discovered that adding half a cup of salt to a gallon of water lowers its freezing temperature by 7 degrees Celsius. What is the freezing temperature of the gallon of salt water?

Activity #2

Positive and Negative Numbers in Terms of Elevation.

Here are two tables that show the elevations of highest points on land and lowest points in the ocean. Distances are measured from sea level. • Drag the points marking the mountains and trenches to the vertical number line.
• Then answer the questions that follow. (1.) Which point in the ocean is the lowest in the world? What is its elevation?

(2.) Which mountain is the highest in the world? What is its elevation?

(3.) If you plot the elevations of the mountains and trenches on a vertical number line, what would 0 represent? What would points above 0 represent? What about points below 0?

(4.) What would points above 0 represent?

(5.) What would points below 0 represent?

(6.) Which is farther from sea level: the deepest point in the ocean, or the top of the highest mountain in the world? Explain.

Activity #3

`Interpret Data From a Table.`

Here below is a table that shows elevations of various cities. • Study the data and answer the questions below.

(1.) On the list of cities, which city has the second highest elevation?

(2.) How would you describe the elevation of Coachella, CA, in relation to sea level?

(3.) How would you describe the elevation of Death Valley, CA, in relation to sea level?

(4.) If you are standing on a beach right next to the ocean, what is your elevation?

(5.) How would you describe the elevation of Miami, FL?

(6.) A city has a higher elevation than Coachella, CA. Select all numbers that could represent the city’s elevation.

Challenge #1

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

Andre drinks 15 ounces of water, which is of a bottle. How much does the bottle hold? Use for the number of ounces of water the bottle holds. Challenge #2

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

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 for the number of ounces of water left in the bottle.

Challenge #3

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

A bottle holds ounces of water. A second bottle holds 16 ounces, which is times as much water. How much does the first bottle hold?

Quiz Time