Evaluating energy efficiency claims


This (or other) energy efficient light bulb package(s).

Energy Efficient Bulb 20-75 w

So many opportunities here, depending on how targeted you want to be. Or, if you prefer, what kind of problem you plan to facilitate. There’s a clear nod to systems of linear equations (when one compares the time of payoff). There’s also an opportunity for some simple, linear equation building: evaluate the truth behind the $44 claim.

I’m even thinking of a 101qs video in which a perplexed customer at a hardware store is comparing this light bulb, and, say, one of these, though, these existence of incandescent bulbs is probably not long for this world. And, being Easter, hardware stores are closed today (fun fact: also, retailers really don’t like it when you take photos and videos in their stores). But that brings up a whole other can of worms: how much energy will countries save by switching to energy efficient bulbs? Like I said, lets of ways to go about this, depending on whether you want to be targeted or more exploratory.

Suggested questions

  • Is that $44 claim reasonable or bogus when you compare it against a bulb that uses 75 watts?
  • How does this compare with other energy efficient bulbs at the old hardware store?
  • What would happen if you switched every bulb in your house/school/neighborhood to energy efficient ones?
  • How much does a kilowatt-hour cost in our town? And what exactly is a kilowatt-hour?

Potential Activities

  • Take some predictions: does $44 savings sound about right over 5 years? Is that too high? Too low?
  • Collect some data on how much your lights are actually on in your house.
  • Plot five years of bulb use and see what happens.
  • Go around your house and count the number of bulb outlets you have. That data may be nice to have on hand.
  • Tables, graphs, equations, the usual bit.

Potential Solutions

Not sure what electricity costs in your particular neck of the woods, but Planet Money suggests a US average of $0.12 per KW-hr. These 20 watt bulbs usually cost around $12 per bulb, give or take. So our function looks like:

cost=$12+(20 W)*(1 KW/1000 W)*($0.12/KW-hr)*hours

Incandescent bulbs go for about $2, and comparing with a 75 watt bulb, our graphs look like this.

I actually get a savings over 8000 hours of $42.8:

(2+75/1000×0.12x 8000)-($12+20/1000 x 0.12 x 8000). That doesn’t take into account replacing incandescent bulbs more often. You could potentially get all stepwise functions if you consider the, perhaps 1000-2000 hour lifespan of an incandescent bulb.

(note the slightly different guesstimations of numbers in the planning form)

Final Word. Pretty much anything involving energy efficiency is going to allow for some systems problems. It’s all about tradeoffs, with higher initial costs gradually replaced by energy savings. Water heaters, A/C Units, automobiles, window insulation, you get what you pay for.

How does one provide the complex data of global warming to students?

Update (3/12/2013): An atmospheric scientist friend of mine, Katie, suggested a few edits to this post, primarily to clear up a few of the tools listed here. The edits are in bold.

My initial thesis on this post was originally going to be “why don’t teachers let students investigate global warming very often?” While this may not answer it here’s a terrifying google search for any teacher who is interested in having their students do some independent research on climate change. Google: “global warming raw data“.


So the first result is a good one. A legit one. There are lots of links to reputable sites maintained by reputable scientists. Then the second result is a yahoo! answers post. The the third (third!) google result for a simple query on raw data turns up World Net Daily, a website for conspiracy theorists and people that think they’re going to be put in FEMA camps any day now. That is not a reputable site. They provide the opposite of “raw data”.

This is not a post about the messy politics and confusion-campaigns around climate change. But this does point to a particular difficulty that you’d hope would be much simpler: where can we find raw temperature data that we can actually use? For the record, a google search of “raw temperature data” yields much more acceptable initial results. But still, many of those results can be extremely difficult for a secondary math or science teacher to pick up and use, let alone students. For one, climate data is often presented in a file format that requires heavy coding knowledge or special programs to process (such as NetCDF). Second, it’s hard to know where to start with temperature data. Do you start by geographic location? Do you take the annual mean across the globe? How would one do that, exactly?

So this is the problem, and maybe a fundamental problem of teaching science: data are messy. We have to rely on others to package it for us. Scientists are interested in providing the raw data because they want people to have access to true observations, but that raw data is so vast and difficult to process (but not that difficult to interpret!) you have to get at least a Master’s degree before you can even start to decipher it. And often, scientists aren’t interested in culling the data to make it more digestible for the public. They’d prefer to show you the graph. This is great for communication, but not great for independent research. And worse, they’re now fighting on the same plane as disingenuous charlatans who are paid to be as such. So let’s provide students of science the raw data in a way that anyone with Microsoft Excel and a genuine curiosity can begin to explore the very real phenomenon of climate change.

My favorite site that does that is this NASA’s GISS Surface Temperature Analysis. In terms of accurate, raw, commentary-free, accessible, customizable, and processable data, I haven’t found a better place to start. Bookmark that site. Tell your students to go to that site. Start locally.

To find specific historic local weather stations, Katie recommends using the map rather than the search function. The map appears to have better functionality. So click on your favorite vacation spot and go find that precious, precious raw data.



Once you have the ASCII data (shown here), it’s simply a matter of copying and pasting it into Excel, or if you’re incredibly ambitious (or teaching a Stats class perhaps), having students import it into R, one of the industry standards.

For the uninitiated, let me translate a few things: 

D-J-F= December-January-February average

M-A-M=March-April-May average

J-J-A, S-O-N = I think you get the idea….

The last column, metANN = annual mean temperature. This actually might be the best first place to start. 

Berkley also has a nice data set organized by country. However, the accessible to-layperson data is a bit more hidden.


If you’re not careful, you’ll end up downloading intense, non-accessible-to-the-layperson, NetCDF data. Which, again, is fantastic data, but difficult to work with yourself.

But now we’ve got two sites with data that can be tossed into Excel, R, or even those statistics packages designed for secondary students. Now that we have that data, we can do a lot with it.

Suggested Activities

  • Have students investigate the temperature trend in their area.
  • Create a linear model that predicts temperature as a function of year locally.
  • Assign each group or student a different region of the world to investigate and develop a linear model for.
  • Or what about this: develop a sinusoidal equation that describes monthly temperature. Get some trig in there.
  • Ask the question: is our town/state/country/planet heating up or not? Or is it too uncertain to tell?
  • Can you find local stations that DON’T show a warming trend? Katie suggests looking at weather stations closer to the poles to consider the potential impact of polar temperature trends. This might be a bit science-y, but it’s something I’d happily let students explore in a math class.

Once you have actual data, you can start to test it to assess that last, fundamental question (which then spurs thousands of other questions, like “should I have children?”). Is ß>0 under the general linear model? Once we have that answer, even if it’s just locally, we can start to talk about the implications.

Taxonomy of Problems (Part 2): Ways and what to assess

In my last post, I tossed out a loose taxonomy to name four different types of problems:

  • Content Learning Problems
  • Exploratory Problems
  • Conceptual Understanding Problems
  • Assessment Problems

I felt it necessary for myself. Up until now, I’d been labeling all problem equally: they’re problems! They’re tasks that are supposed to get students to learn stuff! But that implies a one-size-fits-all-ness that I don’t think is practical. The planning, time frame, facilitation, scaffolding, and – for our purposes in this post – assessment and wrap-up all look different, even if the task itself doesn’t look that different (after all, ideally we’re all using nonroutine problems with a low bar and a high ceiling regardless of whether it’s being used for formatively assessing student understanding or creating new knowledge).

It’s tough to throw out exact examples for assessment since we’re all working from different standards and tools. So I’m going to restrict it to the following universe of things to assess problems on: New Tech Network’s (where I work) most common Schoolwide Learning Outcomes (SWLOs) and the Common Core Standards of Mathematical Practice.

things to assess

Now, different teachers and different schools I’ve worked with utilize these different halmarks differently. In fact, many schools have difficulty even defining many of these indicators of student learning, let alone assessing. But nevertheless, we’re trying to get a general look and feel to what a problem rubric would look like, depending on what you’re actually trying to accomplish from said problem. We’re talking broad-brush here.

Content Learning Problems

Things to assess: Oral Communication, Professionalism/Work Ethic, Make sense of problems and persevere in solving them, Look for and make use of structure, Look for and express regularity in repeated reasoning

This might just be personal preference, but I’d be wary of assessing content knowledge in a learning opportunity for a student. If we are distinguishing between learning and confirmation problems, we might want to more rigorously assess content on the latter. Another one of my favorite wrap-up activities is this quick check-up as an exit ticket.

Exploratory Problems

Things to assess: Critical Thinking, Oral Communication, Collaboration, Model with Mathematics, Construct viable arguments and critique the reasoning of others, Use appropriate tools strategically

Assuming that the time-frame is a bit longer for an exploratory problem, and that the solutions and solution routes are varying, the wrap-up could consist of a formal presentation, followed by panel-style questioning.

Conceptual Understanding Problems

Things to assess: Critical Thinking, Collaboration, Written Communication, Reason abstractly and quantitatively, Construct viable arguments and critique the reasoning of others, Look for and make use of structure, Look for and express regularity in repeated reasoning

Here, I think it makes sense to have students reflect on and communicate what they’ve learned.

Assessment Problems

Things to assess: Critical Thinking, Written Communication, Reason abstractly and quantitatively, Use appropriate tools strategically, Attend to precision

In this case, one can easily envision a rubric that assesses the items above. Assuming these tasks are a bit more individualized, a written piece – almost like the free response section of an AP exam – might make sense. I’ll leave it up to the reader’s discretion whether or not to allot numerical point values.


With these self-recommendations in hand, we can more easily (hopefully!) pick and chose what would go in a rubric and where, if a rubric is one of the tools in your toolbox.

Again, the idea is to make things easier, not more complex. And to better target outcomes for each and every problem. From these recommendations we might be able to construct a loose, lean problem planning template that is directly tied to the indicators you’re trying to peg with a particular problem. Maybe even some planned facilitation and scaffolding moves as well.