Download conics - aucksecmaths

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
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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:
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Draw and discuss conic sections
Apply an understanding of conic sections to real life situations.
Planned learning experiences
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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.
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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
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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
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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:
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3.1 Apply the geometry of conic sections in solving problems
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3 credits
Internal
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Spotlight on
Pedagogy
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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
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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.
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Students design investigations, explore and use patterns and relationships in data and they
predict and envision outcomes.
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Students deal with uncertainty and variation, they seek patterns and generalisations.
Using language, symbols and texts
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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
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Students listen to others, they accept and value different viewpoints.
Students work in groups, they debate solutions, negotiate meaning and communicate
thinking.
Managing self
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Students develop skills of independent learning.
Students are prepared to take risks, make decisions, and persevere.
Participating and contributing
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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:
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Innovation, inquiry and curiosity by thinking critically, creatively, and reflectively
Community and participation for the common good
Māori/Pasifika
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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
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ESOL Online
Links
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http://www.youtube.com/watch?v=SvYje3L57zY
http://www.facebook.com/pages/Finding-the-acoustic-sweet-spot-in-a-cinema/105190622852094
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http://britton.disted.camosun.bc.ca/jbconics.htm
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Connections
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http://www.homeconceptdecoration.com/unique-the-mahina-housedecoration%E2%80%93-futuristic-mansion-of-a-bond-movie-in-kawau-island-north-ofauckland/
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