Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Activity The Big Bang Theory - 3 Purpose To investigate conic sections in real life situations. Achievement objectives M 8-1 Apply the geometry of conic sections Indicators Demonstrates understanding of conic sections, including circles, ellipses, parabolas, hyperbolas, including links to transformations and definitions of loci. Connects equations in parametric and Cartesian form and the graphs of conic sections, including understanding the standard equation of each type of conic section. Identifies and uses key features of conic sections, such as vertices, foci, asymptotes, and intercepts. Specific learning outcomes Students will be able to: Draw and discuss conic sections Apply an understanding of conic sections to real life situations. Planned learning experiences Play: http://www.youtube.com/watch?v=SvYje3L57zY Show: http://www.facebook.com/pages/Finding-the-acoustic-sweet-spot-in-acinema/105190622852094 The sweet spot is a term used by recording engineers to describe the intersection of focal points from conic shaped speakers, in this position an individual is fully capable of hearing the stereo audio mix the way it was intended to be heard by the mixer. Assuming there are two speakers at the front of the cinema which are pieces of conic sections, experiment with different speaker shapes and sizes to place the sweet spot as close to Sheldon’s seat as possible. Sheldon’s seat is 8m from the screen and level with the height of the centre of the speakers. d:\478168350.doc Page 1 1. Which is the best conic section to place the sweet spot at Sheldon? Write the equations of these graphs to model the situation and draw an appropriate diagram. 2. Consider the variables in this scenario. What factors would a sound engineer take into account when setting up a cinema? Possible adaptations to the activity: A whispering gallery is usually constructed in the form of an ellipsoid, with an accessible point at each focus. When a visitor stands at one focus and whispers, the line of sound emanating from this focus reflects directly to the dish/focus at the other end of the room, and to the other person. Circular whispering galleries may provide "communication" from any part on the circumference to the diametrically-opposite point on the circumference. Read more: http://wiki.answers.com/Q/How_do_whispering_galleries_work#ixzz1b09z8klO Plasmonic Whispering Gallery Microcavity Paves the Way to Future Nanolasers http://newscenter.lbl.gov/news-releases/2009/01/22/plasmonic-whispering-gallery/ Find the shape and proportions of some whispering galleries around the world. Model a whispering gallery using diagrams of conic sections. Cross curricular links Architecture Art and Design Extension/enrichment ideas The world is my egg http://www.nbmcw.com/articles/architects-a-project-watch/612-the-cybertecture-egg-newjewel-in-mumbai.html d:\478168350.doc Page 2 http://webecoist.com/2010/04/01/egg-shaped-architecture-art-from-amazing-to-bizarre/ http://twistedsifter.com/2010/03/the-egg-buildingbeijing-china/ http://www.travelandleisure.com/articles/the-worlds-ugliest-buildings/8 http://www.travelandleisure.com/articles/the-worlds-ugliest-buildings/9 http://en.wikipedia.org/wiki/List_of_Hyperboloid_structures http://www.google.com/search?q=conic+sections+in+buildings&hl=en&sa=G&rlz=1G1GGLQ_ENU K366&prmd=imvns&tbm=isch&tbo=u&source=univ&ei=EYabTtzGHqSaiAeL2virAg&ved=0CGUQsA Q&biw=862&bih=440 http://www.popularmechanics.com/technology/engineering/architecture/worlds-strangeststadiums-gallery-ericsson-globe#fbIndex14 http://www.popularmechanics.com/technology/engineering/architecture/worlds-strangeststadiums-gallery#fbIndex1 http://www.popularmechanics.com/technology/engineering/architecture/worlds-strangeststadiums-gallery-ericsson-globe#fbIndex8 http://britton.disted.camosun.bc.ca/jbconics.htm http://www.youtube.com/watch?v=Sl61eTk-LOM http://wn.com/Conic_Sections_in_our_daily_life Check out some of the links above to conic sections in real life. Design the blue prints for your conic building. Find dimensions, surface areas and volumes for the purposes of costing. Investigate materials used for constructing such buildings and find some interesting Mathematical problems that Architects and Builders may have encountered in their design and/or construction. Planned assessment This teaching and learning activity could lead towards assessment in the following achievement standard: 3.1 Apply the geometry of conic sections in solving problems d:\478168350.doc 3 credits Internal Page 3 Spotlight on Pedagogy create a supportive learning environment where discussion and analysis is encouraged encourage reflective thought and action enhance the relevance of new learning facilitate shared learning Key competencies Thinking Students select appropriate methods and strategies when solving problems. Students make deductions, they justify and verify, interpret and synthesis and they create models. Students hypothesise, investigate, analyse and evaluate. Students design investigations, explore and use patterns and relationships in data and they predict and envision outcomes. Students deal with uncertainty and variation, they seek patterns and generalisations. Using language, symbols and texts Students use symbols and diagrams to solve problems. Students use ICT appropriately. They capture their thought processes, recording and communicating mathematical ideas. Students interpret word problems and visual representations. Relating to others Students listen to others, they accept and value different viewpoints. Students work in groups, they debate solutions, negotiate meaning and communicate thinking. Managing self Students develop skills of independent learning. Students are prepared to take risks, make decisions, and persevere. Participating and contributing Students contribute to a culture of inquiry and learning. They share strategies and thinking and they empower and enable others. Values Students will be encouraged to value: d:\478168350.doc Page 4 Innovation, inquiry and curiosity by thinking critically, creatively, and reflectively Community and participation for the common good Māori/Pasifika Ka Hikitia Compass for Pasifika success Culturally specific buildings can be explored. Home Designs unique beach slope, here The Design House Mahina – Futuristic Mansion with a film of James Bond in Kawau Island, north of Auckland. The Mahina – Maori to the moon – have been designed in a crescent-shaped curve with the glass ceiling to floor and a modern white decor. Planning for content and language learning ESOL Online Links http://www.youtube.com/watch?v=SvYje3L57zY http://www.facebook.com/pages/Finding-the-acoustic-sweet-spot-in-a-cinema/105190622852094 http://britton.disted.camosun.bc.ca/jbconics.htm Connections http://www.homeconceptdecoration.com/unique-the-mahina-housedecoration%E2%80%93-futuristic-mansion-of-a-bond-movie-in-kawau-island-north-ofauckland/ d:\478168350.doc Page 5