tag:blogger.com,1999:blog-2433841880619171855.post8210118001166785244..comments2024-03-27T21:09:44.320+00:00Comments on Pat'sBlog: Two ways to Solve a Geometry ProblemUnknownnoreply@blogger.comBlogger5125tag:blogger.com,1999:blog-2433841880619171855.post-26915606113236297382013-06-25T01:01:27.554+01:002013-06-25T01:01:27.554+01:00CCSSI math, I absolutely LOVE the quadrilateral a...CCSSI math, I absolutely LOVE the quadrilateral area problem, and I can see why so many would have a problem with it... Even when they don't have to see what isn't there (it is all there in front of them), they have trouble if it is not where they expect it. Somehow I think if you dotted the given legs of the two right triangles that alone would increase success (and reduce the potential for learning) by 50%... <br /><br />I admit I had to think hard about the two circles and a triangle.. and imagined a special case to make it all work out. <br /><br />Thanks for the comment and the links, I will probably return to these when I process a little. Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-69242702912595291072013-06-24T21:51:54.138+01:002013-06-24T21:51:54.138+01:00Pat wrote:
>I will protest that there are NO g...Pat wrote:<br /><br />>I will protest that there are NO geometry problems for which visualization is a detriment.<br /><br />We never suggested such, and agree with you that visualization is a key skill--that can be developed through cleverly designed problems, and then usefully applied in myriad situations.<br /><br />Unfortunately, it is difficult to explain the subtle value of such skills to a student, but it is one of the many possible answers to the perennial "when will we use this?" question.<br /><br /><br />Pat also wrote:<br /><br />>And geometry, it seems, often asks us to see a line that isn't there<br /><br />Unfortunately, not often in American K-12 mathematics education. The New York State Regents geometry course, which is considered comparatively difficult, includes proofs, but the complete diagram is already drawn (can someone point us to a counterexample in a Regents exam 6 point question?)<br /><br />http://www.nysedregents.org/Geometry/<br /><br />Common Core's SMP 7 mentions drawing "auxiliary lines", but it remains to be seen how this manifests itself throughout K-12. It's only specifically mentioned once more, in the optional HS (+) standard, G-SRT 9.<br /><br />You found our soft spot, because we particularly favor problems where you have to draw "auxiliary" lines to aid in solving.<br /><br />This elementary school problem perplexed many, as a discussion on reddit revealed:<br /><br />http://www.reddit.com/r/math/comments/1c46c7/does_this_quadrilateral_area_problem_really/<br /><br />The above-mentioned middle school "fraternal triangles" problem, as well, and continuing to fairly challenging HS geometry proofs:<br /><br />https://docs.google.com/file/d/0B6lw97EHbvfHRVo5MnpPVjlJZjA/editCCSSI Mathematicshttps://www.blogger.com/profile/12318317536740240935noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-69188857858553518422013-06-23T16:20:00.747+01:002013-06-23T16:20:00.747+01:00Nice problem. Worth sharing in mathematics for ii...Nice problem. Worth sharing in <a href="http://testabhyas.hubpages.com/hub/mathematics-for-iitjee" rel="nofollow"> mathematics for iitjee </a> section.Arihant Kotharihttps://www.blogger.com/profile/12589701673480609250noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-1135815953456444212013-06-20T21:36:01.380+01:002013-06-20T21:36:01.380+01:00Nice problems, don't know how I've missed ...Nice problems, don't know how I've missed your sight, but you've won a fan here. <br />I will protest that there are NO geometry problems for which visualization is a detriment. My first thought about the second was that Tri AFC was 1/2 of AEC because AF is the median of AEC. It gives a foot in the door where I know "something". If it leads to a dead end, I still have some information. <br />Looking at the first problem (square and triangles in inscribed similar shapes, it made me want to pursue the progression for regular n-gon ratios. <br />Later though, a busy day, Thanks for writing and the nice blog.<br /> Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-28030605909454817172013-06-20T20:26:55.840+01:002013-06-20T20:26:55.840+01:00Yep, looks familiar indeed:
http://fivetriangles....Yep, looks familiar indeed:<br /><br />http://fivetriangles.blogspot.com/2012/08/34-area-ratios.html<br /><br />But then, some problems require a bit more than just visualization skills:<br /><br />http://fivetriangles.blogspot.com/2013/06/77-fraternal-triangles.htmlCCSSI Mathematicshttps://www.blogger.com/profile/12318317536740240935noreply@blogger.com