The Cooling Corpse

Introduction

Sets the stage for the WebQuest. Helps to create interest in the activity, provide background information and foreshadow what is to come. Could you be a homicide detective? How can differential equations help to solve a murder case? What does calculus have to do with a murder mystery? Can we apply some of our recently acquired skills to help a detective solve a murder mystery?

Task

Describes what students are expected to do in terms of both process and product. The task should involve higher-order thinking skills and the transformation of information. It should be both doable and interesting. Put on your detective hats! On a dark and stormy night, Sherlock Holmes and his faithful sidekick, Watson, have been called to investigate a murder. The victim had several enemies that would benefit from his demise. The first, his wife, claims to have been at the theatre and was seen leaving at 10:30, returning home by 11:00 pm. this was verified by the household staff. The second, the butler, was at a local pub until 10:00 pm and returned to his quarters at 10:05 pm.Other ervants confirmed this time. The third, his business partner, spent the evening at his office, returning home at 10:30 pm. This was also confirmed by his wife and househld staff. The body was found in the victim's home office where the temperature was a stuffy 76 degrees. At 4:30 am, the temperature of the body was 88 degrees. Two hours later the body had cooled to 85.8 degrees. Can you determine the time of death? Who was the murderer?

Steps that students should go through in acoomplishing the task. Because the steps of the process are clearly defined and provided in the WebQuest, teachers are able to access and implement ready-made WebQuests easily and effectively.

You will need to use Newton's Law of Cooling as well as what we have been studying about differential equations in order to solve this problem. Once you write a differential equation, you can solve it using separation of variables and determine the time that the murder occurred. You will also need to know that an average body temperature is 98.6 degrees. You may find all of this information on the website below.

Resources

Set of information resources that are needed to complete the task. Resources may be internet-based, experts available via email or realtime conferencing and searchable databases on the internet. Other resources may include books, magazines, newspapers and CD-ROMs that are available in the classroom or school library. You already have your class notes, now find out just what Newton's Law of Cooling is about. You can look in your text, other calculus books or search online. Here is one site that may be useful.There are several more below. stripe.colorado.edu/gssrp/research/wenkang.paper3

Evaluation

Criteria for evaluation are clearly identified, often through the use of a rubric. This helps both students and teachers understand elements of the process and product through which students are expected to demonstrate their learning.

You will write a story incorporating all of the given facts and the method in which you solved the murder. Be creative, use dialogue and remember to include all of the mathematics you used in order to reach your conclusion. You don't want to arrest the wrong person!

Conclusion

Brings closure to the WebQuest. It reminds students of what they have learned and can point them in new directions for further exploration and learning. Can you think of other applications for Newton's Law of Cooling? How could you speed up the cooling down of a just out of the oven cake?

Web Resource www.sosmath.com

Search under differential equations

Web Resource

www.ugrad.math.ubc.ca/coursedoc/math100/notes/diffeqs/cool.html

Web Resource www.math.tamu.edu/~fnarc/m308h/m308h_prj1.html