Hooks

What is a "Hook?"

A "hook" is a question that (hopefully) motivates students to work through the drudgery of acquiring some basic calculation skills so that they can later be applied to solving more interesting math problems. They often also illustrate the connection between mathematics and the "real" world.

Hooks only work if they are eventually followed up by the teacher showing the students how mathematics can be used to answer the question posed.

Exponents and Logarithms ....

"Y'know how scientists say one dinosaur lived 1.5 billion years ago but this other one lived 2 billion years ago? Well, how do they know? Were they there?"

Sample Problem
Many people mistakenly believe that carbon dating can be used to determine the age of dinosaur bones. In fact, carbon-14 has a half life of about 5730 years which only makes it useful for dating events within the last 35 000 to 50 000 years. However, this half-life does make it useful to archeologists.

If the mammoth bones discovered in this article are found to have only 10% of the amount of uranium-233 (half-life 162 000 years) a live mammoth should have, how long ago did this mammoth die?

Contributed by Darren Kuropatwa.

Probability ....

"Y'know how when you go to the doctor for a really important test and you call him up for the results and he says: Well, we have to do some more tests. Why are doctors so cagey?"

Sample Problem
Suppose a test for cancer is known to be 98% accurate. This means that the outcome of the test is correct 98% of the time. Suppose that 0.5% of the population have cancer. What is the probability that a person who tests positive for cancer has cancer?

Contributed by Darren Kuropatwa.