# The Case of the Cooling Corpse Task

I got a chance to work through the case of the cooling corpse task at a common core workshop that I attended (OGAP) during the summer of 2013. This is a fun way to bring some creativity into the classroom and explore Newton’s Law of Cooling. I am blogging about the activities that we worked through in an effort to both make them easier to find in the future and to hopefully inspire others.

We were given the following instructions that were adapted from *A Watched Cup Never Cools* (Key Curriculum Press, 1999).

*The following is a synopsis of the first part of an unpublished story. Your task is to solve the mystery and write the rest of the story. Your conclusion must include the mathematics of the solution. It should be written in story form and incorporate the mathematics within the dialogue and other prose as smoothly and naturally as possible. Be creative, but don’t arrest the wrong individual! *

It was a dark and stormy night. Holmes and Watson were called to the scene of the murder by Inspector Lestrade of the police. The victim was a wealthy but cruel man. He had many enemies.

The most likely suspects are the wife, the business partner, and the butler. Each has an equally strong motive. Each also has an alibi. The wife claims to have spent the entire evening at the theater across town. She was seen leaving the theater at 10:30 p.m. and returned home at 11:00 p.m., going straight up to her bedroom. Her return was verified by the upstairs maid. The business partner claims to have spent the evening working on papers at the office. His wife and household staff verified that he returned home at 10:30 p.m. The butler was on his night off. He claims to have been at the local pub until 10:00 p.m. The butler returned to his quarters above the carriage house at 10:05 p.m. and did not leave. This was verified by the other servants.

The body was found in the victim’s study. Holmes arrived at the scene at 4:30 a.m. The room was unusually warm and stuffy. One of the police officers went to open a window. Holmes admonished him to delay that action until he had completed his investigation of the crime scene. He instructed Watson to determine the temperature of the body. This was found to be 88.0°F. Holmes questioned the servants as to the room temperature during the evening and learned that the man had liked the room warm and that the temperature in the study was always very near the current 76°F. Holmes asked Watson to take the temperature of the body again at the conclusion of his inspection of the scene, two hours after the first reading. It was 85.8°F.

A Watched Cup Never Cools © 1999 Key Curriculum Press

Solving this requires the use of Newton’s Law of Cooling. The presence of the number e in the equation means that students will need familiarity with logarithms in order to solve the equation needed to crack the case.

During the Common Core Workshop, we labeled this activity as addressing these standards:

F-BF.1.B

F-LE.1

F-LE.5

I really wanted to do this activity this year with my Algebra 2 students, but we ran out of time!

## More Activities for Teaching Logarithms

- Precalculus Graduation Stickers
- Evaluating Logarithms Auction Activity
- Swap Two – A Logarithms Task
- Exponents Chart (Powers of 2 to 9)
- Earthquakes and Explosions – a Logarithms Problem Based Assessment (PBA)
- Amy Gruen’s Exponent Puzzles
- Solving Logarithmic Equations Foldable
- Converting Between Exponential and Logarithmic Form Foldable
- Logarithm Tarsia Puzzle Activity
- The Case of the Cooling Corpse Task
- Change of Base Formula Notes
- Properties of Logarithms Foldable