tag:blogger.com,1999:blog-7245208048685880741.post2690533152716546502..comments2023-05-19T10:32:11.137-04:00Comments on Rational Expressions: What makes a good problem?Michael Pershanhttp://www.blogger.com/profile/17046644130957574890noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-7245208048685880741.post-19122446323084813992011-10-23T09:30:38.319-04:002011-10-23T09:30:38.319-04:00Sue: For any 1/n there's always at least a few...Sue: For any 1/n there's always at least a few unit fractions that will work. For example, 1/10 = 1/20 + 1/20. More generally, 1/n = 1/2n + 1/2n. (If I understand the problem correctly, there's precisely one other pair of (a,b) that will ALWAYS work, no matter what n is.)<br /><br />Also, my next posts will be an attempt to catalog some more hooky problems and to explicit redesign problems to be hookier. Short answer is that this is something that I'm still struggling with.<br /><br />Suugaku: What sort of problems have you loved?Michael Pershanhttps://www.blogger.com/profile/17046644130957574890noreply@blogger.comtag:blogger.com,1999:blog-7245208048685880741.post-2035316269503542632011-10-23T09:20:25.065-04:002011-10-23T09:20:25.065-04:00I'll have to think about your question, but th...I'll have to think about your question, but thanks very much for the idea. This is what I have been missing when I think about how I teach my students. I know that it is these kinds of problems that grabbed me and made me love math, but I didn't make the connection that I needed to offer students the same opportunity. I want them to be as fascinated as I am by the subject as I am, but what I see in their faces is boredom. I haven't been offering them hooky problems!Anonymoushttps://www.blogger.com/profile/10422459724445316286noreply@blogger.comtag:blogger.com,1999:blog-7245208048685880741.post-81612151624239516332011-10-19T19:58:36.088-04:002011-10-19T19:58:36.088-04:00Maybe people won't know how to answer that, bu...Maybe people won't know how to answer that, but can offer you examples of problems that hooked them.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-7245208048685880741.post-55012163982495877272011-10-19T18:58:05.309-04:002011-10-19T18:58:05.309-04:00Can 1/n always be written as the sum of two unit f...Can 1/n always be written as the sum of two unit fractions, or just sometimes? I'm guessing always, but I'm trying to figure out how I want to reword your problem statement.<br /><br />I see so many students in my beginning algebra classes struggling with fractions, and this problem may be a big help. I'll pose it to them. (I've seen it before but hadn't thought of it as a pedagogical tool.)Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.com