tag:blogger.com,1999:blog-8231784566931768362.post9040336142003461423..comments2023-09-09T08:21:55.454-04:00Comments on MathNotations: Challenge Their Minds Day 1 - A 'Means to an End'Dave Marainhttp://www.blogger.com/profile/13321770881353644307noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-8231784566931768362.post-2009471655307281712009-09-24T12:07:48.485-04:002009-09-24T12:07:48.485-04:00this is a good thing to do at the beginning of the...this is a good thing to do at the beginning of the year to see what kind of students you are dealing with.Anonymoushttps://www.blogger.com/profile/14020851763664969558noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-30378198098962048082009-08-21T21:25:01.060-04:002009-08-21T21:25:01.060-04:00Watchmath,
The problem indicated 100 different num...Watchmath,<br />The problem indicated 100 different numbers!<br />This slowed many down but the more conceptual<br />students intuited that it could be done.Dave Marainhttps://www.blogger.com/profile/13321770881353644307noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-55995923363685565662009-08-21T20:26:07.546-04:002009-08-21T20:26:07.546-04:00Doesn't allowing the data to be reals in (0,1)...Doesn't allowing the data to be reals in (0,1) make the problem trivial? Because now any x in (0,1) can always be an average (just take one hundred of x's).watchmathhttp://www.watchmath.com/vlognoreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-26745583375467091512009-08-21T14:11:26.257-04:002009-08-21T14:11:26.257-04:00tc--
I intended it to mean all real values between...tc--<br />I intended it to mean all real values between 0 and 1. <br /><br />watchmath--<br />I really like the guesstimate/differences method. It's valuable both in statistics and for deepening understanding of averages for younger children. As you noted it can be used to compute the actual mean, to construct a data set with a desired mean, or to verify that a given number is the mean (differences sum to zero). The differences must be defined carefully of course as value - mean. <br /><br />I do think the high school problem leads to higher conceptualization about the density of rational or real numbers. I observed students solving this and the variety of approaches was so gratifying to me. The ensuing brief discussion was rich. I'll let you conjecture about what they came up with.Dave Marainhttps://www.blogger.com/profile/13321770881353644307noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-57560837972194202442009-08-21T13:14:18.371-04:002009-08-21T13:14:18.371-04:00Hi Dave,
For the high school problem, did you int...Hi Dave,<br /><br />For the high school problem, did you intend that the numbers be between 0 & 1 (i.e. fractions), or either 0 or 1 (two-valued). The answer doesn't change either way, but how students may approach the problem would change.<br /><br />Or maybe, it begs a two-parter with the distinction above. <br /><br />TCUnknownhttps://www.blogger.com/profile/06449079338919787252noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-89356422211036183312009-08-21T13:13:02.109-04:002009-08-21T13:13:02.109-04:00This is a good problem. I taught about this when I...This is a good problem. I taught about this when I was in middle school (I think). So basically start with a guess average and inspect for each data whether it is off or exceed the average, total this and the average will be the guess average + (total off/number of data).<br /><br />So for<br />1,1,1,...,1,2<br />Guess average is 1 only 2 off from this number by +1. So the average is 1+(1/100). <br />All the other problems can be solved in this manner.watchmathhttp://www.watchmath.com/vlognoreply@blogger.com