Wednesday, November 10, 2010

A Problematic Word Problem

I found this word problem on line at: http://www.analyzemath.com/middle_school_math/grade_8/problems.html

Q: Two different schools (A and B) have the same number of pupils. The ratio of the boys in school A and the boys in school B is 2:1 and the ratio of the girls in school A and the girls in school B is 4:5. Find the ratio of the boys in school A to the girls in school A.

Even though the problem is related to school situation (and therefore might be close to the students) and it is solvable given all the information, I will say this word problem is not practical at all. First of all, it is very unlikely that the two schools have exact same number of students. Secondly, nobody in the administration would ever do this to find out the ratio of the boys and girls in the same school (nowadays, it is just a click away). If I were to put this into a real life situation, it is like I want to go to the UBC bookstore from the Scarfe building on campus, but instead of going straight to the book store, I first go to the bus loop, taking Bus 99 to Broadway Station and then take the Skytrain all the away to Surrey, and then transfer to a bus and come back to UBC, and then get off the bus and rent a bike in SUB, and then finally bike enthusiastically towards the long desired bookstore---who would ever do this?! I think students will solely look at the numbers and do the math as in many similar cases since the problem itself is dry and not very interesting. To rewrite it, I think it would be better to incorporate something that is attracting to children, e.g., something related to animals or games or some interesting facts.

The average length of male bottlenose dolphin is around 2.5 meters, which is the same as the average length of male tiger shark. If the ratio of the length of male and female bottlenose dolphin is 11:10, and the ratio of the length of male and female tiger shark is 12:10. Which one is slightly longer on average, an average female tiger shark or an average female bottlenose dolphin? Can you estimate before calculating it?

Now I am thinking, this is not good enough, since there is a big rang when you think of the word "average"... feeling sympathy towards all math textbook writers. 

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