tag:blogger.com,1999:blog-756329316658223587.post2719554326113069283..comments2024-03-10T10:02:58.044+01:00Comments on Matemáticas na Rúa: Un triángulo dobradoJJhttp://www.blogger.com/profile/16829561981417320165noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-756329316658223587.post-65757647181959362072015-06-30T13:14:46.594+02:002015-06-30T13:14:46.594+02:00Following the famous TIMSS Video study Japanese cl...Following the famous TIMSS Video study Japanese classroom we could enjoy (<a href="http://matematicasnarua.blogspot.com.es/2015/02/un-problema-do-timss-1999-study-video.html" rel="nofollow">here</a>), I believe this kind of problems is best-suited for collaborative work. Anyway, Spain has a tiny Geometry curriculum, because we are still in the aftermath of Bourbaki New Math. Thus, we spend most of the year doing Arithmetic and Algebra; in High School working in mostly-algebraic functions exercises . Take a look at Year 8 curriculum (<a href="http://www.boe.es/diario_boe/txt.php?id=BOE-A-2007-238" rel="nofollow">full document</a>):<br />Bloque 4. Geometría.<br />Figuras con la misma forma y distinto tamaño. La semejanza. Proporcionalidad de segmentos. Identificación de relaciones de semejanza.<br />Ampliación y reducción de figuras. Obtención, cuando sea posible, del factor de escala utilizado. Razón entre las superficies de figuras semejantes.<br />Utilización de los teoremas de Tales y Pitágoras para obtener medidas y comprobar relaciones entre figuras.<br />Computing, computing, computing!JJhttps://www.blogger.com/profile/16829561981417320165noreply@blogger.comtag:blogger.com,1999:blog-756329316658223587.post-49421616266090170012015-06-30T04:49:14.664+02:002015-06-30T04:49:14.664+02:00Here is one possible solution we envisioned when p...Here is one possible solution we envisioned when posting this problem (and rating it 3 stars), optimistic that it falls within the capabilities of Yr8 students (some of whom admittedly may need encouragement):<br /><br />https://docs.google.com/document/d/1ZidEHSoCFWdSRnv2kDXTNRDF0GK-WKDu-YtZcQKmswI/edit<br /><br />Doubting the typical Yr8 student's ability is understandable, but raising the ante is the point of our blog, to which we add this note: problems that require multiple skills, such as drawing auxiliary lines, the recognition of similar triangles oriented obliquely, and extended arithmetic manipulation with proportions, square roots, etc., are commonly posed in certain "top-tier" mathematics nations' classrooms (which may explain why they are top-tier.)Five Triangleshttps://www.blogger.com/profile/12846752710456413605noreply@blogger.comtag:blogger.com,1999:blog-756329316658223587.post-63347039187149599772015-06-29T23:42:06.466+02:002015-06-29T23:42:06.466+02:00Nice aproach too, PBrohan! Regarding to Stewart...Nice aproach too, PBrohan! Regarding to Stewart's Theorem, you can add my <a rel="nofollow">next blog post</a> to your references (esentially it's a bunch of Pythagoras' uses)<br />On the other topic, I thought LATEX worked fine here... $e^{\pi \cdot i}+1=0$JJhttps://www.blogger.com/profile/16829561981417320165noreply@blogger.comtag:blogger.com,1999:blog-756329316658223587.post-14204923852007228432015-06-29T18:48:41.192+02:002015-06-29T18:48:41.192+02:00I've never seen Stewart's Theorem before, ...I've never seen Stewart's Theorem before, that's something I'm going to have to look up.<br />Our solution doesn't use any maths past Year 8, although they would probably need to use a calculator to compute the final step.<br />I'm sorry for the handwriting, but I can't get the TeX markup to work in comments: http://imgur.com/0fSu4OnPBrohanhttp://twitter.com/pbrohannoreply@blogger.comtag:blogger.com,1999:blog-756329316658223587.post-86325740691781464312015-06-15T21:08:11.272+02:002015-06-15T21:08:11.272+02:00Nice problem and nice way of finding MQ as well, t...Nice problem and nice way of finding MQ as well, though I think that 8 graders may lack the algebraic machinery (and, as you pointed, the persistence) necessary to solve the equations.<br />Anyway, keep the flow of interesting problems going, you have fans around here ;)JJhttps://www.blogger.com/profile/16829561981417320165noreply@blogger.comtag:blogger.com,1999:blog-756329316658223587.post-10369635865882142062015-06-15T18:42:36.278+02:002015-06-15T18:42:36.278+02:00Unha desvantaxe de alumnos que dependen de fórmula...Unha desvantaxe de alumnos que dependen de fórmulas ou xeometría coordinada para resolver problemas desta natureza é que os profesores poden representar problemas máis difíciles para que tales enfoques fanse demasiado pesado, e quizais imposible. É sintomático da educación matemática occidental a concentrarse en solucións directas, pero en países do Extremo Oriente, os alumnos aprenden a mirar para algo que pode cambiar un problema en algo máis simple.<br /><br />Aquí está un diagrama que fai MQ máis fácil de atopar, e limita o problema coas competencias da 8º grao, tales como Pitágoras Teorema e triángulos semellantes.<br /><br />https://docs.google.com/document/d/1MHcPizlSD_PEJyrJVrit0tQLqIK9tWn2rsGtBJHb6AU/editFive Triangleshttps://www.blogger.com/profile/12846752710456413605noreply@blogger.comtag:blogger.com,1999:blog-756329316658223587.post-15691523561734262072015-06-11T12:36:44.148+02:002015-06-11T12:36:44.148+02:00Obrigado, Cibrán. A esencia analítica da túa soluc...Obrigado, Cibrán. A esencia analítica da túa solución permite propoñer o problema en Matemáticas I. Estou pensando que podía facer unha entrada sobre o Teorema de Stewart que sexa axeitada para a situación actual da Xeometría no curriculum. A ver.JJhttps://www.blogger.com/profile/16829561981417320165noreply@blogger.comtag:blogger.com,1999:blog-756329316658223587.post-13303356600190362522015-06-11T00:52:00.908+02:002015-06-11T00:52:00.908+02:00Creo que nunca vira unha referencia ao teorema de ...Creo que nunca vira unha referencia ao teorema de Stewart. Así que me entretiven buscando outra solución. Como non vía a forma de metercha aquí, deixeina por acolá:<br />http://retallosdematematicas.blogspot.com.es/2015/06/triangulo-redobrado.htmlCibránhttps://www.blogger.com/profile/05434153873163086551noreply@blogger.com