Task
The table below shows the lowest elevation above sea level in three American cities.
City 
State 
Elevation above sea level 
Elevation below sea level 
Denver 
Colorado 
5130 

New Orleans 
Louisiana 
8 

Seattle 
Washington 
0 

Finish filling in the table as you think about the following statements. Decide whether each of the following statements is true or false. Explain your answer for each one.
 New Orleans is $\lvert 8 \rvert$ feet below sea level.
 New Orleans is $8$ feet below sea level.
 New Orleans is $8$ feet below sea level.
 Seattle is $0$ feet above sea level.
 Seattle is $\vert 0 \rvert$ feet below sea level.
 Denver is $5130$ feet below sea level.
 Denver is $\lvert 5130\rvert $ feet below sea level.
 Denver is $\lvert 5130 \rvert$ feet below sea level.
IM Commentary
The purpose of this task is to help students interpret signed numbers in a context as a magnitude and a direction and to make sense of the absolute value of a signed number as its magnitude. The questions about the elevation of New Orleans are fairly natural: it is a standard convention to use positive numbers to represent elevations above sea level and negative numbers below sea level. However, it is possible to represent them the other way around. The questions about Denver, while they may seem unnatural, are there to see if students understand that in this kind of context, positive numbers are chosen to represent distances in an arbitrary direction relative to an arbitrary elevation, and that once the reference elevation and positive direction are chosen, the negative values can also be interpreted in the context.