SISL > 2012 Sustainability in Math Workshop > Activities > Choosing Between Home Appliances: Benefits to the Planet and Your Wallet

# Choosing Between Home Appliances: Benefits to the Planet and Your Wallet

#### Summary

In this activity, students compare various options for purchasing new home appliances:

• refrigerators,
• washing machines,
• clothes dryers,
• dishwashers,
• microwave ovens,
• electric ranges, and
• window air conditioning units.

Students compare the energy usage of more efficient models to less energy efficient models, and calculate the "payback period" in cases for which the purchase price for the energy efficient model is higher, but the energy savings over time make it less expensive in the long run.

## Learning Goals

This activity helps students frame purchasing decisions with a focus not merely on purchase price, but on energy efficiency, which has implications for the planet AND for longer-term personal finances.

It engages students in analyses and communications that lead to more effective decision making.

The activity helps with critical thinking, quantitative reasoning, data analysis, and mathematical modeling.

The activity is an applied Fermi problem, giving students practice spelling out assumptions, working with unit conversions, calculating from daily usage to annual usage, to multi-year usage. Students can think about the effects of their own decisions and scale those up for community and societal effects.

## Context for Use

This applied Fermi problem helps students in basic math courses and quantitative reasoning courses with algebra, unit conversions, reading tables and graphs, making comparisons, and making decisions using mathematical evidence.

## Description and Teaching Materials

Each student is asked to select two of the following appliances to examine:
• refrigerators,
• washing machines,
• clothes dryers,
• dishwashers,
• microwave ovens,
• electric ranges,
• and window air conditioning units.

For each of the selected appliances, students are to compare two attractive options in terms of their purchase price, energy usage, expected longevity, and long-term costs.

For each appliance and for each option (e.g., "Energy Star Most Efficient" refrigerator and less energy efficient, but also less expensive, refrigerator), students are to consider the energy usage of the appliance on a daily or annual basis (or whatever is available) and estimate the annual energy cost savings of the more efficient model. Doing so has students working with units of energy and working with unit conversions.

Ultimately, students are to consider if and when the efficient model's energy savings offset the higher purchase price; i.e., what is the "payback period"? Does it take two years? Three years? Over the expected life of the appliance, what is the total cost savings to the consumer of the more energy efficient choice? If the more energy efficient option remains more expensive even over the long-run, is the purchaser willing to pay that higher price to save on energy consumption for sustainability reasons?

## Teaching Notes and Tips

For younger audiences, such as middle school or high school students, teachers might restrict the number of appliances from which to choose and direct students to specific Web sites for finding the data on energy usage. For college students, part of the project involves finding appropriate data and experiencing the culling of those data. The National Energy Education Development (NEED) Project presents a nice booklet on Plug Loads; pages 7-8 are especially helpful for making the relevant calculations. Some students can create Excel spreadsheets to perform these calculations. A simpler version of this project would have students using an Excel spreadsheet created by NEED.

## Assessment

• Are students able to make a choice and clearly articulate why one option is preferred to the other?
• Are they able to spell out their assumptions about how often the appliance is used, etc.?
• Are their calculations correct?
• Do they clearly show proper unit conversions?
• Can students communicate their findings and their decision-making process to share those with others who might make such real-world decisions?

## References and Resources

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## Choosing Between Home Appliances: Benefits to the Planet and Your Wallet -- Discussion

Hi Everyone. I'd be happy to get your feedback on how I can provide additional materials to make this usable in lots of different types of classrooms (high school and college)... I am thinking of providing an example of an analysis for another appliance not listed here to serve as an exemplar.

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Hi Corri,

I really like your learning activity. My students do student-selected project at the end of each semester and many students choose to do what you propose, and they get a lot out of the experience.

A couple of small things: (1) In your summary, you might want to reword the last sentence. Instead of "compare the energy savings", something like "compare the energy usage to determine savings"? (2) Unit conversion is something that is not part of standard mathematics curriculum. Unless students have had enough science, its likely to be new to them (and possibly their instructor). So, links to resources on the topic would be good.

Rikki

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Thanks, Rikki! I intend to make a handout explaining units dealing with energy and power and will provide an example showing some of these unit conversions. I will also include some instructor notes on unit conversions: how it is all about multiplying by equivalents of 1. I'd say about 1/4 of my incoming college students have not seen unit conversions this way and that lesson is a big "Aha!" moment for them. -- Corri

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BTW, I spoke with the fellow from the Alliance to Save Energy, and I think I'll take his suggestion of having students compare not only the \$\$\$ costs of the options, but also the carbon costs...

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