Here are two problems I used in my calculus 1 class, just after teaching them the definition of the derivative and discussing average and instantaneous rates of change.

1. My car has a digital read out with the average fuel economy.  I used to have a car which also had the instantaneous fuel economy.
   
   What is the difference between these two fuel economies?  Under what circumstances is each more useful?  How can I use the average fuel economy feature to approximate my instantaneous fuel economy?  (Your answer should be  2-5 complete sentences).
2. Read the article at
   http://www.slate.com/blogs/bad_astronomy/2015/09/03/ice_loss_greenland_and_antarctica_lost_5_trillion_tons_since_1992.html .
   You can use this QR code to access it
   
3. Then answer the following questions. Give all answers in complete sentences with units.

• What is the average rate of change of the mass of Antarctica’s ice?
• What is the average rate of change of the mass of Greenland’s ice?
• Looking at the graphs, do you think it is reasonable to talk about the instantaneous rate of change for these quantities?  Why or why not?