My reason for assessing the sample problems as "advanced" is that their level of difficulty and prerequisite knowledge for solving them are far beyond the standards for any middle school math curriculum I have ever worked with in the state of Virginia since my retirement in 2005.
In the state of Virginia, students who,are enrolled in middle school are usually enrolled in Grades 6,7, and 8. Students usually begin high school in Grade 9.
In Virginia, the "average" student takes Algebra 1 in the 9th grade, Geometry in the 10th grade, and Algebra 2 in the 11th grade. Above average students usually take Algebra 1 in the 8th grade (the last year of middle school), Geometry in the 9th grade, and Algebra 2 in the 10th grade.
A small minority of highly advanced students can take Algebra 1 in the 7th grade, Geometry in the 8th grade, and Algebra 2 in the 9th grade. At the middle school where I taught before I retired in 2005, however, Algebra 1 was not yet available for 7th grade students.
In the set of problems presented, problem #42 involves the hyperbola, which is not taught in the state of Virginia until Algebra 2, which most students take in either the 10th or the 11th grade in high school. Having tutored students privately for the past several years, I have not seen the hyperbola presented in any math course curriculum until Algebra 2 is taken.
Problem #41 involves the construction of a circle within given parameters, which is a topic covered in Geometry. Most students take Geometry in either the 9th or 10th grade in high school. Only a small minority of students take Geometry in 8th grade, which is the last year of middle school in the state of Virginia. Problem #39 involves the Triangle Inequality Theorem, which is also not covered until Geometry.
The following is a link to a pdf copy of the 2010 Virginia Standards of Learning (SOL) Test for 8th Grade Mathematics:
If this link opens, you will see a fair representation of the level of problems which are taught in the 8th grade, which is the last year of middle school in the state of Virginia.
Speaking from the trenches, and based upon my nearly 30 years of teaching and tutoring combined, for whatever it may be worth, the sampling of problems presented in the "Five Triangles" blog website more closely resemble advanced problems on the high school level than on the middle school level.
In a message dated 1/18/2013 12:21:42 P.M. Eastern Standard Time, email@example.com writes:
While I haven't taught middle school since 1995, some of these problems seem to call on knowledge which isn't in the repertoire of the average 8th grader and, in some cases, the average 9th grader. I'd be interested in what others, currently involved in middle school mathematics teaching, think. Putting all that aside, these problems do seem accessible to a student who is versed in Algebra I and Geometry, so I'm wondering why you think them for advanced students (I don't say they aren't, by the way). Some of these problems do require some careful thinking and, perhaps, even more importantly an investment of solution time. Is this what you are pointing at? I looked through the archives, by the way. The quality of problems vary as to difficulty and - this is a personal judgement - appeal. I wish I had known about it before as I teach course for teachers-to-be and some of the problems are nice. I rather liked the geometric construction in the original email as I just spent a semester grumbling about student performance on such.
On Jan 17, 2013, at 10:36 PM, firstname.lastname@example.org_ (mailto:email@example.com) wrote:
> Yikes! I taught middle school mathematics for 22 years (1983-2005) and I
> have never seen any middle school math problems quite this difficult > before. Are these for advanced middle school aged students? > > I now do private tutoring for high school students taking Algebra 1, > Geometry, and Algebra 2, and these problems appear to be on the advanced level > for even these subjects. > > Dennis > > > > In a message dated 1/17/2013 10:23:33 P.M. Eastern Standard Time, > firstname.lastname@example.org_ (mailto:email@example.com) writes: > > > > > We blog at __http://fivetriangles.blogspot.com__ (http://fivetriangles.blogspot.com_/) > (_http://fivetriangles.blogspot.com/_ (http://fivetriangles.blogspot.com/) ) with some not-so-commonplace math problems. > > > > > > > [Non-text portions of this message have been removed] > > > > ------------------------------------ > > Yahoo! Groups Links > > >
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