Unit 7, Lesson 1
Positive and Negative Numbers
Accelerated 6
1.1
Warm-up
Notice and Wonder: Memphis and Bangor
What do you notice? What do you wonder?
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What do you notice? What do you wonder?
Here are three number lines and three situations involving changes in temperature. Represent the change in temperature for each situation on a number line, and then answer the question.
Discuss with a partner:
How did each of you name the resulting temperature in each situation?
How do temperatures above 0 compare to temperatures below 0?
Come up with an example other than temperature where numbers below 0 make sense.
Come up with an example where numbers below 0 do not make sense.
Here are five thermometers. The first four thermometers show temperatures in degrees Celsius
Five vertical thermometers, a through e. Thermometer a is shaded up to 1. Thermometer b is shaded up to 2. Thermometer c is shaded up to the halfway point between 3 and 4. Thermometer d is shaded to the halway point between negative 1 and 0. Thermometer has tick marks labeled negative 20, blank, blank, negative 5, blank, blank, ten, blank, blank, 25.
Elena says that the thermometer shown here reads
Here is a picture of some sea animals. The number line on the left shows the vertical position, in meters, of each animal above or below sea level.
A graph. Vertical axis is labeled vertical position, in meters. 5 tick marks. Scale from negative 15 to 15, by 5s. Horizontal axis has no label or scale. Seagull is at 10. Dolphin is at 3. Penguin is at 0. Shark is at negative 3. Fish is at negative 7. Octopus is at negative 10.
The jumping dolphin?
The flying seagull?
The octopus?
The jumping dolphin?
The flying seagull?
The octopus?
The jumping dolphin?
The flying seagull?
The octopus?
The table shows the elevations of various cities.
| city | elevation (feet) |
|---|---|
| Harrisburg, PA | 320 |
| Bethell, IN | 1,211 |
| Denver, CO | 5,280 |
| New Orleans, LA | -8 |
| Death Valley, CA | -282 |
| New York City, NY | 33 |
| Miami, FL | 0 |
Which city on the list has the second highest elevation?
A different city not on this list has a higher elevation than New Orleans, LA. Select all numbers that could represent the new city’s elevation. Be prepared to explain your reasoning.
Pause here for a whole-class discussion.
Here are two tables that show the elevations of the highest mountain peaks on land and the lowest trenches in the ocean. Distances are measured from sea level.
| mountain | continent | elevation (meters) |
|---|---|---|
| Everest | Asia | 8,848 |
| Kilimanjaro | Africa | 5,895 |
| Denali | North America | 6,168 |
| Aconcagua | South America | 6,961 |
| trench | ocean | elevation (meters) |
|---|---|---|
| Mariana Trench | Pacific | -11,033 |
| Puerto Rico Trench | Atlantic | -8,600 |
| Tonga Trench | Pacific | -10,882 |
| Sunda Trench | Indian | -7,725 |
Positive numbers are numbers that are greater than zero. 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, 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 that 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.
Another example is elevation, which is a distance above or below sea level. An elevation of 0 refers to sea level. Positive elevations are higher than sea level, and negative elevations are lower than sea level.
In this context, a bird flying in the sky would have a positive elevation because it is higher than sea level. An octopus or a shark would have a negative elevation because it is swimming below sea level.
A negative number is a number that is less than 0.
A positive number is a number that is greater than 0.
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