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Whelk-Come to Mathematics: Using Rational Functions to Investigate the Behavior of Northwestern Crows
Part One - Make a Conjecture

 
Make a Conjecture
Conduct an Experiment
Analyze the Data
Work to a Conclusion

Sea gulls and crows feed on various types of mollusks by lifting them into the air and dropping them onto a rock to break open their shells. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. The crows appear to be selective; they pick up only large-sized whelk. They are also persistent. For instance, one crow was observed to drop a single whelk 20 times. Scientists have suggested that this behavior is an example of decision-making in optimal foraging.

Why do you think crows consistently fly to a height of about 5 meters before dropping a whelk onto the rocks below?

Possible Flight Paths

Large Whelk

Running Time - 1:07 sec. *
File Size - 2.2 meg.


Think About This Situation

Consider the dropping of large whelks by northwestern crows.
  1. Which flight path, A or B, do you think the crows use most? Why?
      
  2. What factors do you think influence the height at which the crows choose to drop the whelk?
     
  3. Do you think there is a minimum or maximum number of drops required to break a whelk?
     
  4. Do you think there is a minimum or maximum height at which a whelk can be dropped to break?
     
  5. What classroom experiment could model the dropping of whelks to collect and analyze data?
    • What questions would you attempt to answer in your experiment?
    • How would the relationship between the number of drops and the height of the drops help you answer your questions?
       
  6. Sketch a possible graph of the number of drops required to break a whelk as a function of the height of the drop. How are your answers above evident in your graph?

 

 

Make a Conjecture
Conduct an Experiment
Analyze the Data
Work to a Conclusion

Credits and Reference
© 2000 - National Council of Teachers of Mathematics


CD Version last updated: August 8, 2000