Lesson 1Positive and Negative Numbers

Learning Goal

Let’s explore how we represent temperatures and elevations.

Learning Targets

I can explain what 0, positive numbers, and negative numbers mean in the context of temperature and elevation.
I can use positive and negative numbers to describe temperature and elevation.
I know what positive and negative numbers are.

Lesson Terms

negative number
positive number
rational number

Warm Up: Notice and Wonder: Memphis and Bangor

A weather report for Memphis, TN and Bangor, ME.

What do you notice? What do you wonder?

Activity 1: What’s the Temperature?

Problem 1

Here are five thermometers. The first four thermometers show temperatures in Celsius. Find the temperatures.

Problem 2

Elena says that the thermometer shown here reads $- {2.5}^{\circ} C$ because the line of the liquid is above $- 2^{\circ} C$ . Jada says that it is $- {1.5}^{\circ} C$ . Do you agree with either one of them? Explain your reasoning.

A thermometer is labeled from negative 4 through 5 with negative at the bottom of the thermometer. There are tick marks halfway between each integer. The thermometer is shaded from the bottom of the thermometer to the tick mark between negative 2 and negative 1.

Problem 3

One morning, the temperature in Phoenix, Arizona, was $8^{\circ} C$ and the temperature in Portland, Maine, was $12^{\circ} C$ cooler. What was the temperature in Portland?

Activity 2: Seagulls Soar, Sharks Swim

Here is a picture of some sea animals. The number line on the left shows the vertical position of each animal above or below sea level, in meters.

A vertical number line with animals above or below sea level. A bird and dolphin are above sea level. A turtle is at sea level and a shark, octopus, and fish are below sea level.

Problem 1

How far above or below sea level is each animal? Measure to their eye level.

Problem 2

A mobula ray is 3 meters above the surface of the ocean. How does its vertical position compare to the height or depth of:

The jumping dolphin?
The flying seagull?
The octopus?

Problem 3

An albatross is 5 meters above the surface of the ocean. How does its vertical position compare to the height or depth of:

The jumping dolphin?
The flying seagull?
The octopus?

Problem 4

A clownfish is 2 meters below the surface of the ocean. How does its vertical position compare to the height or depth of:

The jumping dolphin?
The flying seagull?
The octopus?

Problem 5

The vertical distance of a new dolphin from the dolphin in the picture is 3 meters. What is its distance from the surface of the ocean?

Are you ready for more?

The north pole is in the middle of the ocean. A person at sea level at the north pole would be 3,949 miles from the center of the earth. The sea floor below the north pole is at an elevation of approximately -2.7 miles. The elevation of the south pole is about 1.7 miles. How far is a person standing on the south pole from a submarine at the sea floor below the north pole?

Activity 3: High Places, Low Places

Problem 1

Here is a table that shows elevations of various cities.

city	elevation (feet)
Harrisburg, PA	$320$
Bethell, IN	$1, 211$
Denver, CO	$5, 280$
Coachella, CA	$- 22$
Death Valley, CA	$- 282$
New York City, NY	$33$
Miami, FL	$0$

On the list of cities, which city has the second highest elevation?
How would you describe the elevation of Coachella, CA in relation to sea level?
How would you describe the elevation of Death Valley, CA in relation to sea level?
If you are standing on a beach right next to the ocean, what is your elevation?
How would you describe the elevation of Miami, FL?
A city has a higher elevation than Coachella, CA. Select all numbers that could represent the city’s elevation. Be prepared to explain your reasoning.
1. -11 feet
2. -35 feet
3. 4 feet
4. -8 feet
5. 0 feet

Problem 2

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 and answer the questions.

point	mountain	continent	altitude (meters)
C	Everest	Asia	$8, 848$
H	Kilimanjaro	Africa	$5, 895$
E	Denali	North America	$6, 168$
A	Pikchu Pikchu	South America	$5, 664$

point	trench	continent	altitude (meters)
F	Mariana Trench	Pacific	$- 11, 033$
B	Puerto Rico Trench	Atlantic	$- 8, 600$
D	Tonga Trench	Pacific	$- 10, 882$
G	Sunda Trench	Indian	$- 7, 725$

open applet in presentation mode

Which point in the ocean is the lowest in the world? What is its elevation?
Which mountain is the highest in the world? What is its elevation?
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?
Which is farther from sea level: the deepest point in the ocean, or the top of the highest mountain in the world? Explain.

Print Version

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.

mountain	continent	altitude (meters)
Everest	Asia	$8, 848$
Kilimanjaro	Africa	$5, 895$
Denali	North America	$6, 168$
Pikchu Pikchu	South America	$5, 664$

trench	continent	altitude (meters)
Mariana Trench	Pacific	$- 11, 033$
Puerto Rico Trench	Atlantic	$- 8, 600$
Tonga Trench	Pacific	$- 10, 882$
Sunda Trench	Indian	$- 7, 725$

Which point in the ocean is the lowest in the world? What is its elevation?
Which mountain is the highest in the world? What is its elevation?
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?
Which is farther from sea level: the deepest point in the ocean, or the top of the highest mountain in the world? Explain.

Are you ready for more?

A spider spins a web in the following way:

It starts at sea level.
It moves up one inch in the first minute.
It moves down two inches in the second minute.
It moves up three inches in the third minute.
It moves down four inches in the fourth minute.

Assuming that the pattern continues, what will the spider’s elevation be after an hour has passed?

Lesson Summary

Positive numbers are numbers that are greater than 0. Negative numbers are numbers that are less than zero. The meaning of a negative number in a context depends on the meaning of zero in that context.

For example, if we measure temperatures in degrees Celsius, then 0 degrees Celsius corresponds to the temperature at which water freezes.

In this context, positive temperatures are warmer than the freezing point and negative temperatures are colder than the freezing point. A temperature of -6 degrees Celsius means that it is 6 degrees away from 0 and it is less than 0. This thermometer shows a temperature of -6 degrees Celsius.

If the temperature rises a few degrees and gets very close to 0 degrees without reaching it, the temperature is still a negative number.

A vertical thermometer with the numbers negative 8 through 8 indicated. The thermometer is shaded starting from the bottom of the thermometer to negative 6.

Another example is elevation, which is a distance above or below sea level. An elevation of 0 refers to the sea level. Positive elevations are higher than sea level, and negative elevations are lower than sea level.

A graph of vertical elevation from -10 to 10 and 0 being sea level. There is a bird at 10, a dolphin at sea level, a shark at -5 and an octopus at -10.