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Connect with Maths ~ Discovering Sustainability & Maths in a World Heritage Icon

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Sydney Opera House is a state, national and World Heritage-listed item described by UNESCO as ‘a masterpiece of human creative genius’. What is lesser known is that in designing the Opera House, Jorn Utzon was inspired by nature. Building on this legacy, the Opera House has an Environmental Sustainability Plan that aims improve resource efficiency, protect the environment and engage and inspire others about sustainability.

The purpose of the session is to give real life case studies of mathematics applied to sustainability and the design of the Opera House that teachers could use to help inspire the next generation of young people to learn mathematics and science.
Presented by Naomi Martin, Manager, Environmental Sustainability Sydney Opera House.

Published in: Education
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Connect with Maths ~ Discovering Sustainability & Maths in a World Heritage Icon

  1. 1. Australian Association of Mathematics Teachers Webinar . 14 October 2015Wednesday 14 October 2015 Discovering Sustainability & Maths in A World Heritage Icon Naomi Martin Manager, Environmental Sustainability
  2. 2. Source: Perception vs fact.com
  3. 3. Australian Association of Mathematics Teachers Webinar . 14 October 2015 Inspired by Nature
  4. 4. Australian Association of Mathematics Teachers Webinar . 14 October 2015 Sydney Opera House Opera House. Education sustainability Teachers. sustainability cross curriculum priority Engage students in maths. Students. Interest in sustainability What we have in common Give students motivation and tools to make their own changes towards a more sustainable future. Excite students by showing maths that can make a difference.
  5. 5. Australian Association of Mathematics Teachers Webinar . 14 October 2015 SUMMARY OF TALK • 2 sustainability stories: Energy & Carbon • Case study at Opera House • Applying the tools at school • 3 Opera House maths in design stories.
  6. 6. Australian Association of Mathematics Teachers Webinar . 14 October 2015 Sustainability Story #1 Concert Hall Lights: Energy saving calculations
  7. 7. Australian Association of Mathematics Teachers Webinar . 14 October 2015 Version v3_NM review Price $/Kwh1 Labour Rate/hr per person Current Operational Hours Proposed Operational Hours Days NGA Factor2 Project Cost $3 0.17$ 47.00$ 14 14 364 1.06 2,000,000.00$ Type Fitting Qty Watts Including Ballast Lamp Qty Lamp Life (Hours) Relamping Period Yrs6 Cost per lamp6 Install Time Hrs Crown Lights 64 575 1 300 0.06 35.00$ 2 Low level 194 200 1 1,000 0.20 25.00$ 2 High level 89 300 1 1,000 0.20 12.50$ 2 Work Lights 16 575 1 300 0.06 35.00$ 2 Type Fitting Qty Watts Including Ballast Lamp Qty Lamp Life (Hours) Relamping Period Yrs Cost per lamp3 Install Time Hrs LED crown lights 72 160 1 50,000 9.81 3,745.00$ 2 LED high level HS 89 100 1 50,000 9.81 2,445.00$ 2 LED low level HS 194 35 1 50,000 9.81 1,763.00$ 2 INPUT PROPOSED LIGHTING VARIABLES3 Project Description: Concert Hall crown and high level house lights Date: 29-June-2014 INPUT CONTROL VARIABLES INPUT CURRENT LIGHTING VARIABLES6
  8. 8. Australian Association of Mathematics Teachers Webinar . 14 October 2015 5,096 Hrs 5,096 Hrs 568,204 Kwh 138,662 Kwh 602 tCO2-e 147 tCO2-e 96,594.68$ 23,572.57$ 77,947.57$ 84,518.89$ 263,303.53$ 3,401.07$ 437,845.77$ 111,492.53$ 429,542 kWh 455 tCO2-e 73,022.11$ -$6,571.33 259,902.45$ 326,353.24$ 6.13 Years 76% CURRENT LIGHTING PROJECTIONS PROPOSED LIGHTING PROJECTIONS Total Hours used per year Total Hours used per year Energy Usage pa Energy Usage pa CO2 pa CO2 pa Energy Cost pa Energy Cost pa Cost of lamps per year Cost of lamps per year Cost of labour for relamping per year Cost of labour for relamping per year Total Annual Operational Costs Total Annual Costs PROJECTED PROJECT RESULTS Annual Energy Savings Annual CO2 Savings Annual cost savings energy Annual cost saving on lamps Annual labour costs savings for relamping Total annual cost savings over life of new lamp Payback period including energy & relamping cost savings % Reduction in energy use
  9. 9. Australian Association of Mathematics Teachers Webinar . 14 October 2015 At School You can choose energy efficient appliances to reduce power use. Maths gives you the tools to calculate energy and cost savings.
  10. 10. Australian Association of Mathematics Teachers Webinar . 14 October 2015 At School • Total Power (watt) • One classroom has 2 fluorescent tubes in each fixture, in 8 fixtures that draw 45W each tube. • What is the total power?
  11. 11. Australian Association of Mathematics Teachers Webinar . 14 October 2015 At School • Total Power (watt) • One classroom has 2 fluorescent tubes in each fixture, in 8 fixtures that draw 45W each tube. • What is the total power? • = 2 x 8 x 45W • = 720W
  12. 12. Australian Association of Mathematics Teachers Webinar . 14 October 2015 At School • Hours used • The lights are on 12 hrs per day, 5 days per week, 40 weeks per year. • What is the total time they are on?
  13. 13. Australian Association of Mathematics Teachers Webinar . 14 October 2015 At School • Hours used • The lights are on 12 hrs per day, 5 days per week, 40 weeks per year. • What is the total time they are on? • = 12 x 5 x 40 • = 2400hrs
  14. 14. Australian Association of Mathematics Teachers Webinar . 14 October 2015 At School • Energy = Power (W) x time (hr) • Power (W) = 720 • Hours (hr) = 2400. • What is the Energy used per year in kWhs? • = 720 x 2400 • = 1,728,000 Wh (/1000) • = 1728 kWh
  15. 15. Australian Association of Mathematics Teachers Webinar . 14 October 2015 Current: T8 LED tube & motion sensors Power (Watts) 45 W 20 W Bulbs 2 2 Number of fixtures 8 8 Total Power multiply above 720 W 320 W Hours/Day 12 hr 8 hr Days/week 5 days 5 days Weeks 40 weeks 40 weeks Total Hours hrs x days x wks 2,400 hrs 1,600 hrs Energy use (Wh) W x hrs 1,728,000 Wh 512,000 Wh Energy use kWh W / 1000 1,728 kWh 512 kWh Cost per kWh 0.3 $/KWh 0.3 $/KWh Annual cost cost x energy use (kWh) 518.4 153.6 Energy saving compared to T8 (%) ((old -new )/old) x 100 70% Cost Saving compared to T8($) annual cost T8 - annual cost LED 364.80$
  16. 16. Australian Association of Mathematics Teachers Webinar . 14 October 2015 At School You can choose energy efficient appliances to reduce power use. Maths gives you the tools to calculate energy and cost savings. Tools • Spreadsheets, forumulas • Units of measurement • Equations for energy/power.
  17. 17. Australian Association of Mathematics Teachers Webinar . 14 October 2015 • Sustainability - Cross Curriculum Priority • OH Education –beyond arts students Sustainability Story #2: Carbon and Events
  18. 18. Australian Association of Mathematics Teachers Webinar . 14 October 2015 Carbon & Events
  19. 19. Australian Association of Mathematics Teachers Webinar . 14 October 2015 VIVID15_Party_Slides_23
  20. 20. Australian Association of Mathematics Teachers Webinar . 14 October 2015 Carbon 101
  21. 21. Australian Association of Mathematics Teachers Webinar . 14 October 2015 1) Concentration of CO2 increasing. http://www.csiro.au/greenhouse-gases/ 2015-1976 = 39 years
  22. 22. Australian Association of Mathematics Teachers Webinar . 14 October 2015 1) Concentration of CO2 increasing. http://www.csiro.au/greenhouse-gases/ Rise in CO2 (ppm) = 395.569-329.653 =65.91 ppm 2015-1976 = 39 years Rise in CO2 (ppm) = 398-330 = 68ppm http://www.csiro.au/greenhouse-gases/
  23. 23. Australian Association of Mathematics Teachers Webinar . 14 October 2015 1) Concentration of CO2 increasing. http://www.csiro.au/greenhouse-gases/ Rise in CO2 (ppm) = 395.569-329.653 =65.91 ppm 2015-1976 = 39 years Rise in CO2 (ppm) = 398-330 = 68ppm Rate of change = 68ppm/39yr = = 1.75ppm/yr http://www.csiro.au/greenhouse-gases/
  24. 24. Australian Association of Mathematics Teachers Webinar . 14 October 2015 • CO2 is 0.039% of the atmosphere • 0.05% alcohol blood limit 2) Increase in CO2 has big impacts
  25. 25. Australian Association of Mathematics Teachers Webinar . 14 October 2015 http://www.theguardian.com/environment/interactive/2013/sep/27/climate-change-how-hot-lifetime-interactive 2) Increased CO2 has big impacts - Temperature
  26. 26. Australian Association of Mathematics Teachers Webinar . 14 October 2015 2) Increased CO2 has big impacts - Temperature
  27. 27. Australian Association of Mathematics Teachers Webinar . 14 October 2015 2) Increased CO2 has impacts - Sydney
  28. 28. Australian Association of Mathematics Teachers Webinar . 14 October 2015 Why - impacts 400ppm
  29. 29. Australian Association of Mathematics Teachers Webinar . 14 October 2015 2) Increased CO2 has impacts - Sydney Opera House
  30. 30. Australian Association of Mathematics Teachers Webinar . 14 October 2015 Kids • What has STEM got to do with me. http://www.environment.gov.au/system/files/resources/b24f8db4-e55a-4deb-a0b3- 32cf763a5dab/files/national-greenhouse-accounts-factors-2014.pdf 3) We can make a difference by understanding carbon emissions
  31. 31. Australian Association of Mathematics Teachers Webinar . 14 October 2015 Case Studies (content).3) We can make a difference by understanding carbon emissions • Carbon emitted = volume of fuel or activity x emission factor. Activity Emissions Factor Unit Reference Electricity (NSW) 0.99 kg CO2-e / kWh NGA Factors Unleaded Petrol 2.80 T CO2-e / kL NGA Factors Flight - medium haul 0.18 kg CO2-e/km/personEPA Victoria Meat and meat products 5.83 kg CO2-e/$ EPA Victoria Vegetable and fruit growing, hay, plant nurseries, flowers 0.92 kg CO2-e/$ EPA Victoria
  32. 32. Australian Association of Mathematics Teachers Webinar . 14 October 2015 3) We can make a difference by understanding carbon emissions • Carbon Calculators http://www.epa.vic.gov.au/agc/home.html
  33. 33. Australian Association of Mathematics Teachers Webinar . 14 October 2015 CARBON 101 SUMMARY 1) CO2 is increasing 2) Continuing to increase CO2 in atmosphere has impacts we would like to avoid 3) By understanding carbon emissions, you can make a difference
  34. 34. Australian Association of Mathematics Teachers Webinar . 14 October 2015 Back to the case study..
  35. 35. Australian Association of Mathematics Teachers Webinar . 14 October 2015 Case Studies (content). 0.00 200.00 400.00 600.00 800.00 1000.00 1200.00 1400.00 TonnesCO2equivalent Sources of Greenhouse Gas Emissions Vivid 2011 1609 T CO2-e Vivid 2012 1067 T CO2-e Sustainability Story #2: Vivid Live Carbon Footprint
  36. 36. Australian Association of Mathematics Teachers Webinar . 14 October 2015 Insert carbon counter
  37. 37. Band 1 - Rider = more than one car over a year Carbon STEM Academy, University of Sydney. Wednesday 25 November 2014
  38. 38. Band 2 - Rider = half a scooter over one year STEM Academy, University of Sydney. Wednesday 25 November 2014
  39. 39. Australian Association of Mathematics Teachers Webinar . 14 October 2015 At School Here are some eg. calculations What would you do to reduce your carbon? Activity Unit Emissions Factor Unit Tonnes CO2-e Electricity for a 4 person home in Sydney for one year 7492 kWh 0.99 kg CO2-e / kWh 7.42 Car for 1 year with 12L/100km, driving 15,000km 1.80 kL 2.80 T CO2-e / kL 5.04 Return flight to Melbourne (713km 1 way) 1426 km 0.18 kg CO2- e/km/person 0.26 Cutting out one serve of red meat per week for 1 year (assume $10 steak) 520.00$ 4.44 kg CO2-e/$ 2.31
  40. 40. Australian Association of Mathematics Teachers Webinar . 14 October 2015 At School You can choose to reduce the carbon you emit. Maths gives you the tools Tools • Graphs, rates of change • Interpret pictograms • Units of measurement. • Formulas • Extrapolate
  41. 41. Australian Association of Mathematics Teachers Webinar . 14 October 2015 Sydney Opera House. Mathematics of Design
  42. 42. Australian Association of Mathematics Teachers Webinar . 14 October 2015
  43. 43. Australian Association of Mathematics Teachers Webinar . 14 October 2015
  44. 44. Australian Association of Mathematics Teachers Webinar . 14 October 2015 Spherical Solution
  45. 45. Australian Association of Mathematics Teachers Webinar . 14 October 2015
  46. 46. Australian Association of Mathematics Teachers Webinar . 14 October 2015 Case Studies (content).Spherical Solution After three years of intensive search for a basic geometry for the shell complex I arrived in October 1961 at the spherical solution shown here. I call this my ‘key to the shells’ because it solves all the problems of construction by opening up to mass production, precision in manufacture and simple erection and with this geometrical system I attain full harmony between all the shapes in this fantastic complex. Joern Utzon
  47. 47. Australian Association of Mathematics Teachers Webinar . 14 October 2015
  48. 48. Australian Association of Mathematics Teachers Webinar . 14 October 2015 • The geometry used in the Opera House isn’t hard, but it is so practical. • You can apply geometry in so many ways
  49. 49. Australian Association of Mathematics Teachers Webinar . 14 October 2015 • Terracycle • Green Lane Green Cross • Bookend Trust • Environmental Educators 22m 8m 23.4m 9m 12m How long does it take sound to travel? (2 x 23.4m)/340.29 m/s = 0.14 sec (2 x 12m)/340.29m/s = 0.07 sec Concert Hall Acoustics
  50. 50. Spherical Solution Spherical solution
  51. 51. Australian Association of Mathematics Teachers Webinar . 14 October 2015 Case Studies (content).
  52. 52. Australian Association of Mathematics Teachers Webinar . 14 October 2015 • Terracycle • Green Lane Green Cross • Bookend Trust • Environmental Educators
  53. 53. Australian Association of Mathematics Teachers Webinar . 14 October 2015 • Terracycle • Green Lane Green Cross • Bookend Trust • Environmental Educators
  54. 54. Australian Association of Mathematics Teachers Webinar . 14 October 2015 • Terracycle • Green Lane Green Cross • Bookend Trust • Environmental Educators
  55. 55. Australian Association of Mathematics Teachers Webinar . 14 October 2015 • The maths used in many designs isn’t hard, but it is so practical. • Understanding geometry helps you build things.
  56. 56. Collaborate with partners Feedback • How could this presentation and case studies be further developed to help you? • Format – online case studies? Digital tours? Onsite tours with tour guide or ‘do it yourself’ tours, activities around a show • What would Sydney Opera House need to provide you as materials? • Partnership Opportunities – how far we get depends on our resources
  57. 57. Cool Australia http://www.coolaustralia.org/

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