{"id":245678,"date":"2023-11-24T10:35:55","date_gmt":"2023-11-24T15:35:55","guid":{"rendered":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/creating-3d-models-of-mathematical-problems-in-geogebra-by-valeria-calderon-and-juan-diego-acua%c2%b1a"},"modified":"2023-11-24T10:35:55","modified_gmt":"2023-11-24T15:35:55","slug":"creating-3d-models-of-mathematical-problems-in-geogebra-by-valeria-calderon-and-juan-diego-acua%c2%b1a","status":"publish","type":"post","link":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/creating-3d-models-of-mathematical-problems-in-geogebra-by-valeria-calderon-and-juan-diego-acua%c2%b1a","title":{"rendered":"Creating 3D Models of Mathematical Problems in GeoGebra by Valeria Calderon and Juan Diego Acu\u00c3\u00b1a"},"content":{"rendered":"

In our AP Calculus class, we have learned about derivatives and their applications. During this time, we specifically learned how to find the minimum and maximum of functions, and to apply\u00c2\u00a0 them to real-life problems in optimization and minimization. These insights are used in everyday life to optimize the use of materials, profits, and measurements, as well as, to minimize materials and dimensions.<\/span><\/p>\n

Using our previous knowledge in mathematics, we were able to solve analytical exercises for the use of derivatives in volume optimization in specific geometric figures. By completing the procedures, calculations, and conclusions, we realized that there was a much easier way to fully understand the problems, and to understand the relationship that each measure has with the other. Taking this into account, we created three simulations in GeoGebra, which can be seen in the video shared with the community as evidence of our work.<\/span><\/p>\n

In this process, we went from the written problem to a 3D simulation with sliders that allow us to see how the dimensions of the geometric figure change and how it is rotated through an axis to form the total figure (In exercise 31.b). This process can also be called a solid revolution. In our assigned exercises we had to optimize the volume of a prism based on some initial measurements, which will be seen in the first simulation, with the process of assembling the box, and in the other exercise where we optimized the volume of a cylinder. The latter was created by folding a rectangular piece of material and the volume of another cylinder that used the same rectangle of material, but with measures of height and radius, which will be evidenced in the explanatory video. In the last exercise, measurements of the same sheet of paper had to be optimized, and in the first exercise, the measurements had to be optimized to maximize the volume within the limitations of the given material. This was, overall, a really interesting activity in which we interpreted mathematical problems more tangibly to understand the relationship between the real world and mathematics. We feel proud of the evidence we provided and the applications of real-life problems in our AP Calculus class!<\/span><\/p>\n

Jose Luis Zamora
<\/b>High School Mathematics Teacher<\/span><\/p>\n

Valeria Calder\u00c3\u00b3n and Juan Diego Acu\u00c3\u00b1a<\/strong>
<\/span>Twelfth Grade AP Calculus Students<\/span><\/i><\/p>\n

Resumen:<\/i><\/b><\/p>\n

En el desarrollo del tema de razones relacionadas realizado en la clase de AP C\u00c3\u00a1lculo, se trabajaron algunos ejercicios con enfoque hacia la optimizaci\u00c3\u00b3n de material de construcci\u00c3\u00b3n, capacidad (volumen) y estructura externa de algunos recipientes utilizados en la vida cotidiana. El prop\u00c3\u00b3sito inicial era realizar una explicaci\u00c3\u00b3n matem\u00c3\u00a1tica de la soluci\u00c3\u00b3n \u00c3\u00b3ptima de cada situaci\u00c3\u00b3n problem\u00c3\u00a1tica. La siguiente muestra constituye en un trabajo de calidad dado que los estudiantes utilizaron como complemento a su trabajo, simulaciones del proceso de la soluci\u00c3\u00b3n en la plataforma GeoGebra. En esta, se evidencia el proceso de construcci\u00c3\u00b3n de los modelos 3D de diferentes figuras presentes en las situaciones planteadas y se evidencia la relaci\u00c3\u00b3n visual con el tema. Esta simulaci\u00c3\u00b3n representa c\u00c3\u00b3mo cambian el \u00c3\u00a1rea de los pol\u00c3<\/p>\n","protected":false},"excerpt":{"rendered":"

In our AP Calculus class, we have learned about derivatives and their applications. During this time, we specifically learned how to find the minimum and maximum of functions, and to apply\u00c2\u00a0 them to real-life problems in optimization and minimization. These insights are used in everyday life to optimize the use of materials, profits, and measurements, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":""},"categories":[1],"tags":[61],"_links":{"self":[{"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/posts\/245678"}],"collection":[{"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/comments?post=245678"}],"version-history":[{"count":0,"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/posts\/245678\/revisions"}],"wp:attachment":[{"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/media?parent=245678"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/categories?post=245678"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rochesterapps.com\/rochestereduco\/lions-honor\/wp-json\/wp\/v2\/tags?post=245678"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}