1. Efficiency in Algebra: Lightbulbs and Linear Systems.
Laura Roberts
RET Summer 2016
Which Lightbulb Should I Buy?:
Students will collect data (temperature, wattage) to determine energy and cost efficiency of different
lightbulbs. They will create and graph linear equations to display, analyze and determine results.
Materials for Lab:
3 lightbulbs (halogen, fluorescent, led) Pencils/Pens
Infrared Thermometer Graphing Paper
Data Collection Worksheet KW Meter
Graphing calculator (TI-84) Lamp
Students review graphing linear equations and are asked the question “Which lightbulb is better?”. They will then collect data on wattage and heat emissions from 3 lightbulbs (incandescent, compact fluorescent and
LED). Students will finally create graphs and equations for heat and cost efficiency of each lightbulb.
Extension activities could include analyzing the efficiencies of different appliances or modeling scenarios
For varying energy usages during the day.
Which Lightbulb Should I Buy?: Part 2
Students are asked the same question, but now the teacher brings in the cost of each lightbulb.
-Which lightbulb should I buy?
-How much time will it take to start saving money (break even point)?
This lesson serves as an introduction to systems of equations and break – even point and will consist of more direct instruction than Lesson 1.
Students will work in partners on classwork problems to write equations for daily cost savings for each lightbulb pair (CFL vs. Incandescent, LED vs. CFL, LED vs. Incandescent). They will thn graph these lines and also graph the lines of the upfront cost of the lightbulb (break-even point is the solution to the system).
Extensions-Add in Modeling Scenarios similar to Lesson 1.
-add in different appliances
-Vary daily energy usage (model different scenarios)
Linear Systems in Energy and Engineering Trends:
Students will examine energy trends to explore why energy efficiency is an important current area of focus. They will also look at current trends in engineering domestically (demographics). They will use their systems to model different scenarios to alter trends.
The lesson will start with students watching a clip from 360.org called “Do the Math”. They will make predictions as to when carbon emissions will exceed 565 giga-tons, and then solve the system of equations to estimate the solution.
After discussing the importance of energy in a global context as opposed to personal cost-benefits, students will analyze demographic trends in the field of engineering. They will use systems to model different scenarios. Difficulty level can be adjusted depending on the level of the class.
Potential Student Questions:
How could we extend the prediction for meeting the carbon threshold by 5 years? 10? 15?
At current trends, will female salaries ever equal male? Why or why not?
What if we wanted an equal distribution in 5 years? 10 years? 20?
Resources
Systems Class Notes
“Investigating Lightbulbs”
“Lights Light Up Your Life” Data Sheet
“Do the Math” video
Distribution of Workers in S&E occupations, by race and ethnicity:
Median Annual Salary among S&E highest degree holders working full time by sex, race and ethnicity: 1995,2003, and 2013
Atmospheric CO2 at Mauna Loa Observatory
ftp://aftp.cmdl.noaa.gov/products/trends/co2/co2_annmean_mlo.txt
This work was supported primarily by the ERC Program
of the National Science Foundation and DOE under NSF Award Number EEC