Title – Analyzing Correlations: Climate Change Impacts and Renewable Solutions
By – Laura Roberts
Primary Subject – Mathematics/Pre-Algebra
Grade Level – 8
Description:
These lessons are focused on the importance of engineering, based on climate trends and the need to
focus on energy. The first lesson introduces correlations, and the math concepts continue on to linear
fit/trend lines. To make a relevant assessment, students will analyze trends in engineering. Their final
activity is a hands-on application relating to solar energy. Students will collect data and determine
correlation/whether or not there is a linear representation.
Why should our students learn about renewable energy and energy conservation?
Climate is arguable the most important global issue for this generation of students.
Goals/Objectives:

Students will be able to identify current trends in carbon emissions and their global implications.

Students will analyze trends in data related to climate change/engineering trends.

Students will be able to explain the importance of lowering emissions/investing in engineering.

Students will collect data to build scatter plots modeling solar power.

Students will analyze impacts of climate change on specific populations.
Tennessee 8th Grade Math Standards Addressed:
F.4: Construct a function to model a linear relationship between two quantities. Determine the rate of
change and initial value of the function from a description of a relationship or from two (x, y) values,
including reading these from a table or from a graph. Interpret the rate of change and initial value of a
linear function in terms of the situation it models, and in terms of its graph or a table of values.
SP.1: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of
association between two quantities. Describe patterns such as clustering, outliers, positive or negative
association, linear association, and nonlinear association.
SP.2: Know that straight lines are widely used to model relationships between two quantitative variables.
For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the
model fit by judging the closeness of the data points to the line.
SP.3: Use the equation of a linear model to solve problems in the context of bivariate measurement data,
interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a
slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an
additional 1.5 cm in mature plant height.
SP.4: Understand that patterns of association can also be seen in bivariate categorical data by displaying
frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table
summarizing data on two categorical variables collected from the same subjects. Use relative frequencies
calculated for rows or columns to describe possible association between the two variables. For example,
collect data from students in your class on whether or not they have a curfew on school nights and
whether or not they have assigned chores at home. Is there evidence that those who have a curfew also
tend to have chores?
Lesson 1:
Materials/Resources (30 students):


350.org “Do the Math” video https://www.youtube.com/watch?v=KuCGVwJIRd0
Smartboard to Display video
Step-by-Step Procedure:
Hook: Why is Energy a Global Problem?
 Introduce students to 9 of the top ten global problems (have them written on board). Ask
them why these are problems/how we can use energy to solve these problems. The nine
problems are: Water, Food, Environment, Poverty, Terrorism & War, Disease, Education,
Democracy, and population. Maybe include a quote for each?
 Ask students what they think the 10th global problem is (energy). Get student opinions on
why energy might be a global problem.
 Introduce student to 3 numbers: 2, 565, 2795. Have them guess what they might represent.
 Show clips from “Do the Math”. First, 2°C and 565 (565 billion gigatons of carbon is the max
we have agreed to let into the atmosphere.). Re-visit objective (scatter plot/correlation)
without the students knowing what the current amount of carbon is we have emitted.
 Provide direct instruction on constructing scatter plots/determining correlation. Have
students create a scatter plot for data concerning tons of carbon ppm in the atmosphere.
Data: ftp://aftp.cmdl.noaa.gov/products/trends/co2/co2_annmean_mlo.txt



Once students see the carbon in the atmosphere they can make guesses as to how many
tons have been released.
Show clip concluding the 565 and showing the last number. Students will see that we are
expected to hit 565 gigatons of carbon in the next 15 years and there are 2795 billion
gigatons of carbon currently in reserves.
Homework: Create scatter plots/determine correlation for major effects of climate change
(temperature, arctic ice, and sea levels)
Source:
Data for Lesson 1:
www.climate.nasa.gov
http://data.giss.nasa.gov/gistemp/tabledata_v3/GLB.Ts+dSST.txt
http://nsidc.org/arcticseaicenews/
http://nsidc.org/data/masie/
http://climate.nasa.gov/vital-signs/sea-level/
http://climate.nasa.gov/system/internal_resources/details/original/121_Global_Sea_Level_Data_File.txt
Lesson 2: Creating Trend Lines and Analyzing Climate Change Impacts for Specific Populations
Objectives:
Students will create trend lines to interpret data
Introduction: The teacher will have an informal discussion of the trends the students found from their
homework. Which had positive/which had negative?
The teacher picks one graph…rising sea levels
-What do you think the change will be in 2019?
-How did you get your answer?
-Why would we want to predict future numbers?
•
The objective of trend lines can now be introduced, and the teacher draws a trend line through the sea
level data. Not much direct instruction is included here, since the students still need to be hooked.
Potential questions to ask the students are:
-What does this line show?
-How does it help us?
-What do you think could be some implications of rising sea levels?
•
Hook: Video. This video is a trailer for a documentary about the president of the Republic of the Maldives,
which is a nation identified as being high-risk in regard to climate change.
http://theislandpresident.com/#!wp-video-lightbox[iframes]/0/
Now the students can receive more detailed direct instruction regarding trend lines, and part of this
instruction will involve creating a trend line for the Maldives sea level rises.
Students can work with a partner or individually to create trend lines for the scatter plots they completed
for homework.
Homework: Students will analyze data sets for different populations to see the different effects of climate
change. The selected populations/issues are as follows:
-Tanzania Temperatures/Coffee Production
-Southern Africa Temperatures/Maize Production (soil moisture)
-New York Temp Increase/Precipitation Increase
•
The homework will also ask the students to respond to the following quote by suggesting some possible
solutions to the climate change problem. This will help prepare them for the final lesson.
“Creativity is not just for artists…it's for engineers trying to solve a problem; it's for parents
who want their children to see the world in more than one way” - Twyla Tharp
http://www.brainyquote.com/quotes/keywords/engineers.html#bwwyXSbVuAqIWBUA.99
The following are some higher order thinking questions that can also be included in the students’
homework assignment.
-How does this data affect the populations of the respective countries? How do you think they are
responding to the data?
-Who should be the most concerned out of all the populations? Least concerned? Why?
-Do you think we are affected by the trends in different cities/countries? Explain your reasoning.
Data for Lesson 2:
Mӧrner, Nils-Axel. “The Maldives: A Measure of Sea Level Changes and Sea Level Ethics”.
Paleogeophysics and Geodynamics, Rӧsundavӓgen 17, 13336, Saltsjobaden, Sweden.
http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&ved=0CC8QFjAC&url=http%3A%
2F%2Fmyweb.wwu.edu%2Fdbunny%2Fpdfs%2FCh7Elsevier.pdf&ei=5QWIVYjiK8WoyATGyLzACQ&usg
=AFQjCNF69gdW4uqnTlv3QOvXaNdWCmiXOA&sig2=CbwIuZiWVUahTJoMeiyXbw
Tanzania Mean Temperature
Tanzania Arabica Production Trends
Craparo, A.C.W. et. al. “Coffea arabica yields decline in Tanzania due to climate change: Global
implications”. Agricultural and Forest Meteorology, Volume 207, 15 July 2015, pp 1-10
http://www.sciencedirect.com/science/article/pii/S0168192315000830
New York Mean Temperature Change and Precipitation Chang
New York City Panel on Climate Change, 2013: “Climate Risk Information 2013: Observations, Climate
Change Projections, and Maps.” C.Rosenzweig and W. Solecki (Editors), NPCC2. Prepared for use by
the City of New York Special Initiative on Rebuilding and Resiliancy, New York, New York.
http://www.nyc.gov/html/planyc2030/downloads/pdf/npcc_climate_risk_information_2013_report.pdf
South Africa Temperature Change
Hudson, D.A., and R.G. Jones. 2002. Regional climate model simulations of present day and future climates of Southern
Africa. Technical note 39. Bracknell, UK: Hadley Centre
http://www.scielo.org.za/scielo.php?pid=S1816-79502012000400001&script=sci_arttext
South Africa Soil Moisture
Jury, Mark R. “An Inter-comparison of Model-simulated East-west Climate Gradients over South Africa”.
“Water SA”,vol.38 n.4 Pretoria Jan. 2012. University of Zululand, KwaDlangezwa, 3886, South Africa
Physics Department, University of Puerto Rico Mayaguez, PR, USA 00681
http://necsi.edu/research/social/southafrica/
Other Useful Links:
http://www.climatehotmap.org/global-warming-locations/republic-of-maldives.html
http://s3.amazonaws.com/mmc-beta-production/assets/11709/maldives.jpg
http://news.nationalgeographic.com/2015/02/150213-tuvalu-sopoaga-kench-kiribati-maldivescyclone-marshall-islands/
http://www.sciencedirect.com/science/article/pii/S0168192315000830
http://www.reuters.com/article/2015/05/18/us-climate-change-tanzania-idUSKBN0O30TS20150518
http://thinkprogress.org/climate/2015/04/30/3652671/study-tanzania-coffee-climate-change/
http://news.nationalgeographic.com/news/2014/05/140531-coffee-rust-columbia-brazil-costproblems/
http://www.bloomberg.com/news/articles/2015-02-26/south-africa-s-withering-corn-cropthreatens-region-s-food-costs
http://www.businessinsider.com/new-york-city-global-warming-risk-2015-2?op=1
http://www.newrepublic.com/article/116887/does-climate-change-cause-extreme-weather-i-saidno-and-was-attacked
Lesson 3: Hands on Solar:
Objectives:
1.) Students will collect and analyze data modeling solar power throughout a simulated day
2.) Students will attempt to maximize power output of solar panel and document their data/determine their
effectiveness
Materials Needed: (8 of each if students are grouped by four)
-Lamp
-Solar Panel
-Multi-Meter
-Chair (or something that provides a moveable fixed height)
-Alligator Clips
-Tape
-Tape Measurer
Students will be introduced to the lesson with an informal discussion regarding the trends they found from
the homework assignment. They will then be hooked with a video showing a non-profit’s efforts to provide
solar panels for schools without electricity in underdeveloped nations.
 https://www.youtube.com/watch?v=6lpw8uc2vao
Students will then be introduced to their task for the day. They will be collecting data regarding voltage
provided by solar power by simulating a day. Before starting, students are asked to predict whether the
data will model a linear function.
Potential group assignments
Team Leader
Recorder
Multi-meter Manager
Chair Coordinator
Students will measure and mark tape according to certain hours of the day (8, 9, 10, 11, 12, 1, 2, 3, 4)
Alligator clips connect the solar panel to the multi-meter and the solar panel stays in a fixed place (12:00)
The chair is moved along designated times, stopping at each marked spot on the tape to record data
•
The data should model a quadratic function, since as the lamp moves closer to the solar panel, the more
voltage is produced.
Once students determine their correlation is not linear, they must work as a team on the following task:
You cannot lift the solar panel completely off the ground or move it outside it’s designated box.
How can we maximize the solar energy? Experiment!
st
Sample Data Sets: 1 is leaving solar panel flat, the second involves adjusting the angle of the solar
panel.
“Time”
8
9
10
11
12
1
2
3
4
Voltage
.848
.926
1.024
1.357
1.549
1.39
1.11
.93
.837
“Time”
8
9
10
11
12
1
2
3
4
Voltage
.879
.95
1.09
1.39
1.56
1.4
1.15
.96
.89
Follow-up Questions:
-Which hours would you expect to see the most difference in voltage? Why? Of your data, which
hours saw the most difference in voltage?
-Could this data ever represent a perfect line? Why or why not?
-Do you think solar panels’ angles change throughout the day? What would the advantage be?
Disadvantage?
Exit Slip:
Will the total amount of voltage collected throughout the day have a correlation? If so will it be weak or
strong? Is it possible for this to be a perfect line? Provide explanations for all your answers.
Homework:
Students will create a scatterplot comparing time and total voltage. They will then determine correlation
and draw a trend line if possible.
Assessment:
To keep the assessment relevant to the unit, students will analyze trends in engineering by plotting data,
assessing correlation and drawing trend lines.
Introduce the assessment with the following quote:
“I hope climate science becomes the big thing. And then what I want is electrical engineers to solve the
world's energy problems, energy distribution problems. I want mechanical engineers to make better
transportation systems. I want chemical engineers to develop better solar panels, and so on”-Bill Nye
Students will then analyze the following trends by creating scatter plots, determining correlation, and
drawing trend lines.
•
1.) Trends in engineering degrees (electrical, mechanical, chemical)
2.) Women in as a percentage of workers in science and engineering careers (specifically engineers)
3.) Graduate enrollment in engineering, by citizenship/race and ethnicity
Data for Assessment:
Trends in engineering degrees (electrical, mechanical, chemical)
http://www.nsf.gov/nsb/sei/edTool/data/engineering-01.html
Women in Engineering:
Graduate Enrollment Demographics
http://www.nsf.gov/nsb/sei/edTool/data/workforce-07.html
http://www.nsf.gov/statistics/seind04/c2/fig02-06.htm
Potential Project-Based Learning or Co-Curricular Opportunities:
-Debate importance of renewable energy (address the fact that climate change is in fact a debate: a
current weakness of these lesson plans)
-Analyze more biodiversity data to coincide closer with science standards
-Students choose diminishing species (plant or animal) and create a research project
•
-Have students come up with ideas to conserve energy/reduce waste. They can collect the data and
determine their success (e.g. negative correlation for time/weight of trash-steeper slope is better)
-Connect to political events (ex. Current Alaska pipeline debate)
-Students can write a persuasive letter or create a video taking a side and providing evidence to
back up their argument
-Convince high school students to enter engineering
-This can either be accomplished with a persuasive letter or have students present to an actual
audience of high-school students. If presenting, students can be themselves or be assigned the
role of a citizen of one of the populations they learned about when creating trend lines.