Uri Treisman showed years ago that an excellent strategy for getting students up to speed was to have them work in groups on extra challenging problems.
MBP, at Rational Expressions, just offered up a good problem that is challenging enough to make me work hard, and approachable enough for the students in a fractions class to work on as their 'Research Into Fractions'. MBP and I have different requests stemming from this problem. MBP wants to know what makes a problem 'hooky'. (If you can't answer that, maybe you can offer MBP an example of a problem that really hooked you.) I want to know what other problems would be good for my imagined students in this imagined class. Problems that involve fractions, and make the students work hard with fractions, that start out approachable, and have enough hook to get the students working persistently.
Here's my version of the problem MBP offered:
Any fraction of the form 1/n is called a unit fraction. 1/2 can be written as the sum of two other unit fractions (1/3+1/6).
- Can this be done for all unit fractions?
- Find a rule for the number of ways to do this.
Got any challenging fraction problems that a newbie might enjoy chewing on?