Our textbooks like to give “Real World” problems. Too many times these are at the end of the section or under a section called “Modeling” and they are so canned, they are unrealistic - thus defeating their purpose. This pedagogical paradigm that our textbooks frame assumes that we should teach skills before content but this is like teaching vocabulary without context and in the world of vocabulary learning, context is everything (think spelling bee... Can you use this in a sentence?) We need to be always teaching context for math just like any other language always uses context and the Malaysian Flight 370 disappearance is a perfect example. Many people are wondering – why haven't we found the floating stuff that we see with the satellite?
What a perfect related rates problem.
If I wasn't on spring break right now, I'd ask my calculus class this exact question. Here's the information:
-7 days ago the Australian government spotted a big object floating in a location 1,400 miles south of Perth
-The current in the South Indian Ocean flows at 1m/s.
-We can imagine that the search area becomes a sector area (assuming its still floating) – we can make up some reasonable angle such as it can move 15 degrees in either direction from the center line of the current.
Now ask the question again given this information and see what happens in a calculus class. A follow up question might be: what is the rate at which the search area is changing every day/hour/minute/second. I would love to see students problem solving (making diagrams, asking questions, etc) and seeing why its so hard to find debris in the ocean.
I found this information on CNN.com so why not integrate literacy into the lesson by having students read for information (your English/Social Studies/Science teachers will love you because they always assume that students are learning math the way they did 25 years ago). As of yesterday, CNN also states “ the current search area is 2.97 million (Thanks to Dan Meyer for checking me on the details) square miles” - that's roughly the size of the continental US. Can you imagine 15 planes and 30 ships trying to find something 100 feet long somewhere in the continental US?
A great follow-up discussion would be how to maximize the efficiency of searching, hoping that they find the objects soon would be even more remarkable.
(Want to make this an Trig/Precalc lesson? Ask students about how the sector area and how height changes the distance which a person can see on the ocean – how many ships are necessary and of what height to cover the search area?)
For more problems like this check out Stu Swartz's "Ripped From the Headlines" at mastermathmentor.com