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.

1. At noon, the temperature was 5 degrees Celsius. By late afternoon, it had risen 6 degrees Celsius. What was the temperature late in the afternoon?
2. The temperature was 8 degrees Celsius at midnight. By dawn, it had 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?

   

   

   

Discuss with a partner:

1. How did each of you name the resulting temperature in each situation?

2. How do temperatures above 0 compare to temperatures below 0?    

3. Come up with an example other than temperature where numbers below 0 make sense.

4. Come up with an example where numbers below 0 do not make sense.

The table shows the elevations of various cities.

1. Which city on the list has the second highest elevation?

2. How would you describe the elevation of Harrisburg, PA, in relation to sea level?
3. How would you describe the elevation of Death Valley, CA, in relation to sea level?
4. How would you describe the elevation of Miami, FL?

5. 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.

   • -11 feet
   • 3 feet
   • -4 feet
   • -9 feet
   • 0 feet

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

1. Which trench in the ocean is the lowest in the world? What is its elevation?
2. Which mountain's peak is the highest in the world? What is its elevation?
3. Which is farther from sea level: the deepest point in the ocean, or the top of the highest mountain in the world? Explain your reasoning.
4. Plot the elevations of the mountain peaks and ocean trenches on the vertical number line.