Day 19 - Saving at the Pump?

The Problem...

The price of gas is going up tomorrow.  Should I go fill up my tank?

Why?

• Illustrate the human factor that complicates apparently simple math problems
• Discussion of sustainability in transportation
• Practical application of linear relations, unit conversions
• Facilitates critical thinking

This is the dilemma: 

You are at home in the evening and you hear on the news that the price in gas is going up 5 cents over night.  You know you will need to fill up soon anyways.  You are faced with a choice:  Go out now to fill up or just go on the way into school/work tomorrow morning.  You know if you go now, there will probably be a line at the pumps.  How much will you save if you go tonight?  Is it worth the inconvenience?

from:http://www.energyblogs.com/blackswanblog/index.cfm/2013/5/14/The-Black-Swan-Blog-No-soft-landing-for-the-PV-Solar-Industry 

I know most high school students don't drive so it might not be a great question for them.    Or maybe its a calculation they can share with their parents.  Regardless, it's a question I have wondered whenever I hear gas prices are going up and I see line ups of cars at gas stations.

From my calculations, I would save about $2.00 to fill up 50L by driving out to the gas station.  Assumptions listed below and will vary by model of car and other factors:

• Fuel Efficiency = 10L/100km (from the dashboard display on my parents' car)
• Distance to Gas Station = 1.5 km
• Idling consumption = 0.1 L /10 minutes (I found this on one site. Very unsure about the accuracy)
• Assume a 10 minute line up for gas (idling) before the price goes up
• Assume a fill up is 50 L

In a class...

Because most likely a lot of students won't have vehicles of their own, I would probably present them with the above scenario and results.  Really, the point of this would be to start a deeper discussion about how we often oversimplify decisions like this.  This activity could really be done in any Science class.  It's a valuable lesson on how complicated Real-World Problem Solving and decision making can be.

I would pose this question to them:

Given the fact that you will save $2.00 if you fill up tonight (instead of tomorrow), will you go fill up?The first instinct may be to be purely economical and say yes of course.  Maybe students could look at trends in gas prices over the year and see how often big price drops/increases occur to try to predict how much they would save over a whole year.

Challenge the Assumptions

I would expect students to inquire about how I got the $2.00.  I would then explain my method to them and they could further critically analyze the assumptions I used to arrive at the answer.  Something that may come up is the gas consumption unit of L/100 km (or MPG in the States).  Where does that measure break down? Idling!  When you are idling, the gas consumption should theoretically be infinity L/100 km because you aren't going anywhere but are still using gas but most cars that report 'instantaneous' fuel consumption in the console will show 0 L/100 km.  If you calculate the average fuel consumption using the instantaneous values, the average will be biased downwards because of this.  So what do car companies report when they advertise efficiency?  I don't know.  Something to discuss!

Time is Money

I would then challenge them a bit and ask how much them how much their time is worth to them.  This is something they would not think about if they don't have a job.  Say it takes 25 minutes to drive to the station, wait in line, fill up, and return home.  Is it still worth it?  Quantifying how much a persons time is worth is an interesting topic (engineers use it when optimizing public transit routes and schedules).  For a high school student, would they consider minimum wage ($10.25) to be how much their time is worth? If so, the 25 minutes it takes is not worth it!  It also depends on how busy they are.  Do they have an exam coming up the next day?  Or are they not doing anything anyways?  The Human Factor can complicate things.

Internalize the Externalities

What about the environmental implications of going out to fill up?  How much carbon dioxide is released during the trip and while idling?  Idling is actually very inefficient on gas and produces a relatively large amount of CO2 for not moving anywhere.  This is a good way to get into discussions about the impacts of elevated greenhouse gases and the carbon tax debate.  We pay for water, electricity and gas.  If we are using up clean air by polluting it, why aren't we paying for that as well?


According to Wikipedia, the Energy Density of Gasoline is 36 MJ/L.  I calculated 0.4 L of gas for the trip to the gas station and back.  Thats 14.4 MJ or 4 kWh - the equivalent of leaving a 40 W lightbulb on for about 4 days.  In terms of energy used, it's not insignificant (though it would only cost about 40 cents of electricity because our electricity is ridiculously cheap).  This highlights how much energy transportation actually uses.  Remember, that the 14.4 MJ is only for driving 3 km and idling for 10 minutes. 

21C...

Students could weigh all these options and come to conclusions which they can share with the class or discuss in a discussion board.  The topic can be used as a jumping off point for a whole host of STSE issues as well.

Okay so maybe this is a bit of a mundane way to illustrate the complexity of problem-solving and decision making that doesn't demonstrate 21C all that well.  There are probably much better examples of cost-benefit analysis (such as the Exploding Ford Pinto Debacle), but I was curious about filling up the tank before the price goes up so that's what I decided to write about.

2. Knowledge Construction: entry - adoption - adaptation - infusion - transformation
3. Real-World Problem Solving & Innovation: entry - adoption - adaptation - infusion - transformation

Future lesson topics...

• Ethics in Engineering and problem solving/decision making
• Optimal vehicle speed for fuel efficiency/GHG emissions

Day 17 - Canoe Trip Physics

The Problem...

How can you use an understanding of physics to make a canoe trip more enjoyable and less work?

Why?

• Opportunity for students to use physics concepts to help plan for a canoe trip
• Opportunity to bring sustainability discussions into a Physics class
• Interdisciplinary math, science, biology, physics, ecology, geography

Check out this blog entry from a few years ago by @emnose.  Canoe tripping is awesome.  The planning, driving, paddling and portaging all pay off when your alone on a lake in the middle of Ontario enjoying the silence and the stars.

In a class...

I would only use this activity in a class if right opportunity presented itself:  if students were actually going on a canoe trip (I know a bunch of high schools that regular do canoe trips). Students working on their Duke of Edinburgh are actually required to do a trip so it would be a good opportunity for them to earn some of the requirements.  

The Physics...

Believe it or not, there is actually a ton of physics that can be found in canoe tripping.  Here are some examples:

1. Buoyancy and hydrodynamics

• What canoe shape, size, depth is appropriate for the trip.  Can study the drag/friction of the canoe in the water.
• Optimal weight and number of people per canoe.  Too heavy and the canoe will sit too low in the water and be inefficient to paddle!
• Number of canoes needed for the trip.
• Optimal paddle length and shape.  There is some statics involved in the best paddle length.  The shape has to do with hydrodynamics.
• This site has a whole bunch of canoe recommendations and images including the one below.  A good question may be which one would be most appropriate canoe profile for the trip.

2. Distance-time relationships

• Best route to a destination (connections to contours in geography and optimization in math).  Students would have to develop some criteria for what 'best' route entails.  Easiest? Quickest? Shortest travel time?  In the picture below, what would be the best route from the Three Legged Lake Access Point to Clear Lake? 

Map is of Massassauga Provincial Park.

Clear Lake is a route we've done a few times.

3. Statics

• What is the best way to pack a hiking pack in terms of physics.  Would it be better to pack the heavier stuff closer or further away from your body?  This can be interpreted as a simple statics problem (see below).  How does your body adapt if the centre of gravity of your pack is further away from your back.

Drawn in Penultimate

• Carrying a canoe - In terms of statics, is it better to carry a canoe with two people or one?  What are some advantages and disadvantages of each.  I've never had a problem with 1 person...

Canoes are designed to be carried by one

 person but at first it doesn't seem to make 

sense from a physics standpoint.

These are just a few examples of how to look at canoe tripping through a physics lens.  I'm sure there are plenty more though.

Transformative Environmental Education

As a Scout leader, I have the opportunity to fairly regularly organize and participate in trips with groups of Scouts.  It's something I think every high school student in Toronto should have a chance to experience.  We talk about Environmental Sustainability but sometimes we forget what we're actually trying to sustain.  Living in the city all year, I sometimes forget about my connection and dependance on nature.  

In an article I read at OISE for my cohort class (Global Citizenship and Sustainable Development), Julie Johnston stresses the importance of stepping outside the curriculum box by practicing Transformative Environmental Education.  She presents education as the primary source of social reproduction and thus where we must start the cycle of understanding, caring for and protecting our environment.  Two examples of Transformative Environmental Education she provides (that I could utilized in this Canoe Tripping activity) are:

• Sky Awareness - promoting the importance of just looking up! Talking about how the sun tracks across the sky and how you could navigate by the stars.  This is easily tied to physics (astronomy).
• Bioregion-Based Education - understanding your connection to your immediate environment.  Understanding the ecosystem in which you live.  This ties nicely into biology and ecology concepts.

21st Century...

Students will be using Real-World Problem Solving and Innovation to help them plan their trip.  Concepts from Physics and other courses can help make an actual trip more enjoyable and less laborious.  

The activity also has the potential to be fairly long term and Self-Regulated by students, culminating in the actual trip.  Journals kept by students during the trip could be used to self-assess the effectiveness of their plans.

Lastly, there would be few more interdependent activities than a canoe trip, which basically forces everyone to do their part in order for the group to get to a destination.  It's an excellent opportunity to demonstrate Collaboration.

1. Collaboration: entry - adoption - adaptation - infusion - transformation
3. Real-World Problem Solving & Innovation: entry - adoption - adaptation - infusion - transformation
5. Self-Regulation: entry - adoption - adaptation - infusion - transformation

Day 3 - How Many Lightbulbs?

The Problem...

How much energy do you regularly use?  How much of an impact will you have if you reduce your energy use?

Why?

• Students examine and visualize the extent of their regular energy use to get an intuitive sense of what energy really is
• Bring big sustainability topics into science classes

Visualizing Energy...

This is a video I found a while ago on TED-Ed:

This video is full of important Science, Math and Sustainable Development topics.  It helps students visualize energy use (hard to visualize by itself) in terms of lightbulbs (easier to visualize).  He discusses the fact that we need more substantial, systemic change than just 'eliminating plastic bags' to really make a difference in the world.  

The video has been flipped on TED-Ed, meaning that in addition to the video, it has questions and extra resources for students.  It is a good place to start a conversation on difficult topics such as sustainable power generation and personal energy use.  Today I will focus on the personal energy use aspect.  Flipped to a class, the questions given on TED-Ed can act as a homework check for a teacher as well as a formative assessment about their current understanding of the topic.

Personal Energy Audit

Watching the video, I was reminded of a project from third year where I had to perform a Personal Energy Audit by tracking my energy use over the course of a week.  We then had to analyze our results and create a plan to reduce our energy consumption.  Here are some of my results from that project:

The hardest part about collecting the data is figuring out the rate of consumption of each item.  Most of them require the application of Ohm's Law (V=I/R) to find out the current.  The natural gas can be found from utility bills and transportation can be approximated by mileage and gas consumption.  This is where a Google Spreadsheet would come in handy.  Each student could be assigned a different item and figure out how much energy it consumes for each hour/kilometre/month in operation and record the value and any assumptions. They could record their findings on the spreadsheet so the rest of the class would be able to see it.  They could then use their classmates' values to Collaboratively calculate their total energy consumption by just keeping track of approximately how long each appliance is running and multiplying it by the consumption.  The collaborative aspect of the task makes it much less laborious for each student while emphasizing the need for authentic and necessary collaboration. 

Be Critical...

After performing the analysis, they would be responsible for creating an Action Plan that they can use to figure out how to reduce their energy consumption which they will put into practice.  They should then compare their results to the number of lightbulbs given by the presenter in the video and critically analyze his assumptions.  As an extension, the whole class can look at the total energy consumption and find out how many lightbulbs that equates to.  Group discussions can be used to develop strategies for reducing power consumption as a school/community and educate their peers on the issue.

The investigation gives the students a great feel for the scale of their impact compared to the assumptions in the video.  They can validate the speakers assumptions based on their own data and determine whether their personal impact is worth the effort it may require.

Curriculum connections...

In terms of curriculum, the assignment requires appropriate research, unit conversions, energy conversions, record keeping and data management, and basic electricity and energy calculations.  Based on these expectations, Grade 11 or 12 Science would probably be appropriate.  I think an interesting application would be for students to start the project in Grade 9 (or earlier) and track their energy use until Grade 12.  This way they can evaluate and improve their own plans for reducing their energy consumption. 

On the 21st Century Continuum...

Depending on how far a teacher wants to go with this project, I think it has the potential to be transformative in all dimensions of the 21C framework.  The best part of it is that they can put self-constructed knowledge to good use with their Action Plans and set a good example for friends and family members by implementing them.


1. Collaboration: entry - adoption - adaptation - infusion - transformation
2. Knowledge Construction: entry - adoption - adaptation - infusion - transformation
3. Real-World Problem Solving & Innovation: entry - adoption - adaptation - infusion - transformation


4. Skilled Communication: entry - adoption - adaptation - infusion - transformation
5. Self-Regulation: entry - adoption - adaptation - infusion - transformation
6. Use of ICT for Learning: entry - adoption - adaptation - infusion - transformation





D2L

Today I attended a D2L training session.  D2L would provide students doing an Energy Audit with the tools to collect the data, discuss the results and share the results with each other.  They would also be able to share their results across schools and boards and track their progress over the years.  

Future Lesson Ideas

• Nuclear Power Generation and Energy Return on Investment (EROI)
• Analyse carbon footprint/GHG emissions
• Embodied energy and life-cycle analysis