tag:blogger.com,1999:blog-1792517942178828492.post4872961593255865721..comments2020-12-06T18:51:19.842-05:00Comments on Mr. Morrissey's Blog : September Essential Questions (Final)Unknownnoreply@blogger.comBlogger4125tag:blogger.com,1999:blog-1792517942178828492.post-36377619589955481842012-10-08T01:02:52.500-04:002012-10-08T01:02:52.500-04:00Ah, that explains it. I guess you can't expect...Ah, that explains it. I guess you can't expect students' questions to be perfectly formed! I was thinking of essential questions as questions written by the teacher to be thought about over the course of the unit.Anonymoushttps://www.blogger.com/profile/13473460516043651891noreply@blogger.comtag:blogger.com,1999:blog-1792517942178828492.post-53734926464419201262012-10-07T19:57:18.536-04:002012-10-07T19:57:18.536-04:00Yongyi,
These were all questions by students. Yongyi,<br /><br />These were all questions by students. 毛博中https://www.blogger.com/profile/02863678591845408596noreply@blogger.comtag:blogger.com,1999:blog-1792517942178828492.post-26433451850719871012012-10-07T02:39:56.356-04:002012-10-07T02:39:56.356-04:00Hmm, some feedback:
1. I assume you mean x-interc...Hmm, some feedback:<br /><br />1. I assume you mean x-intercept for a line, because there's no general method to find exact solutions to f(x) = 0 for any arbitrary function (!) So I'd reword it to "Given the function f(x) = ax + b for some fixed constants a and b, where a is not 0, show that there is a unique x-intercept and explain how to find it."<br /><br />2. Assuming there's no cube root button ;) (then the easiest way would be to raise the number to the 0.33333333... or 1/3 power)<br /><br />3. I'm not sure what the point of this is. If it's to demonstrate that (-a)/b = a/(-b) = -(a/b), then I guess it's okay. The intent is not very clear at the moment.<br /><br />4 & 5. The question "Is 1 a prime number?" makes the question "What is the smallest prime number?" unnecessary.<br /><br />6. The question is imprecise because it doesn't mention that you are talking about integers -- if you were talking about real numbers, then the answer would be different. Between 1 and 5, inclusive, there are 5 integers, infinitely many rational numbers (but countably many), and infinitely many real numbers (but uncountably many). You should attend to precision and say instead, "Explain why if a,b are integers and a < b, then the number of integers between a and b, inclusive, is precisely b - a + 1."<br /><br />7. I guess that is fine.<br /><br />8. I guess that is fine.<br /><br />9. This really isn't a math question... It's a semantic issue. We can say "root of a function" and "zero of a function" and it means exactly the same thing (in my opinion). What they both mean is encapsulated by the following definition: "A root (or zero) of a function f is a number r in the domain of f such that f(r) = 0."<br /><br />10. This is somewhat vague. What kind of answer are you expecting?<br /><br />11. I'm lost on this one! Do you mean whether you can divide P(x) by (x-a) then by (x-b), or by (x-b) then by (x-a), and get the same result? (And do you see how much clearer this revised question is? ;) )<br /><br />12. Common denominator of an equation isn't well-defined. Besides, in the equation x/a + y/b = 6, you just have to think of it as the following equivalent equation: (1/a)x + (1/b)y = 6; note that 1/a and 1/b are just constants and you can treat them as such. You don't have to multiply by any common denominator!<br /><br />13. I would suggest the following question instead: "Why does one sometimes get extraneous solutions to an equation when following a process of solving it? For what types of equations can we be guaranteed not to get extraneous solutions?"Anonymoushttps://www.blogger.com/profile/13473460516043651891noreply@blogger.comtag:blogger.com,1999:blog-1792517942178828492.post-73033959525707430962012-10-07T02:34:35.628-04:002012-10-07T02:34:35.628-04:00This comment has been removed by the author.Anonymoushttps://www.blogger.com/profile/13473460516043651891noreply@blogger.com