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Exploring Energy, Correlation, and Line of Best Fit Lesson Plan

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Exploring Energy, Correlation, and Line of Best Fit Lesson Plan Subject Areas: Math and Social Studies Grade Levels: The lesson can be adapted for grades 4 12 (ages 9 18). Time: At least one 50-minute
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Exploring Energy, Correlation, and Line of Best Fit Lesson Plan Subject Areas: Math and Social Studies Grade Levels: The lesson can be adapted for grades 4 12 (ages 9 18). Time: At least one 50-minute class period; time outside of class as necessary Lesson Objectives: Students will: Make conclusions based on data presented in tables and plots (graphs). Analyze relationships between fields of data including energy production and consumption. Learn to apply a line of best fit and analyze the relationship between plots and their correlation coefficients. Explain their findings in writing and visual slide shows. Standards: Common Core State Standards 1 : Common Core State Standards for Mathematics: Mathematical Practices Reason abstractly and quantitatively. Use appropriate tools strategically. Measurement and Data Represent and interpret data. Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. College and Career Readiness Anchor Standards for Writing: Standard 6. Use technology, including the Internet, to produce and publish writing and to interact and collaborate with others. National Council for the Social Studies Standards 2 : The Ten Themes of Social Studies Theme 7: Production, Distribution, and Consumption Social studies programs should include experiences that provide for the study of how people organize for the production, distribution, and consumption of goods and services. Theme 9: Global Connections Social studies programs should include experiences that provide for the study of global connections and interdependence. 1 Overview: In this lesson, students will use InspireData to analyze the relationship between energy production and consumption for a selection of countries. They will use axis plots to look for correlation between variables, apply a line of best fit, analyze the relationship between plots, and evaluate their correlation coefficients. Older or more advanced students can use the line of best fit to make predictions about future energy production and consumption. Possible investigations include: Are the largest producers of energy also the largest consumers of it? What role does population play in energy consumption? Students will also be asked to think about whether the energy production and consumption patterns are equitable, responsible, and sustainable, and if not, what can be done to alter the observed trends. Discoveries and ideas will be documented in annotated slide shows. Preparation: This lesson requires the InspireData software application published by Inspiration Software, Inc. You can download a 30-day trial at 2 Lesson: 1. Ask students if they think the largest producers of energy resources are also the largest consumers of it. Which countries do they think produce more than they consume, and vice versa? How would they expect a country s population and level of economic development to contribute to its energy use? Tell students that these are questions they will be investigating today with data on the world s energy production and consumption. 2. Open InspireData s Energy Use database located here: InspireData Starter Databases Mathematics Energy Use. 3. Read the table notes and discuss the contents of the table, examining field notes as necessary and defining any unknown terms, such as per capita. Point out that the database contains information on energy production and consumption for the world's 25 most populated countries, plus Canada, Australia, and New Zealand. If your country is not listed, add a new row to the table and input the data using the sources at the bottom of the table notes. 3 4. Point out the Possible Investigations in the table notes that students will be exploring today. As a demonstration, click the Plot View button on the Toolbar to switch to Plot View and analyze the data. Your demonstration should include how to select plot types via the buttons on the Toolbar. Point out the Axis plot button and tell students that axis plots will be especially useful for today s lesson. 5. Click the Axis plot button and demonstrate how to define the x/y axes. For example, click X Axis and choose Population for the x axis, and click Y Axis and choose Energy Use/Capita for the y axis. Ask students what they observe from the resulting plot. Discuss possible explanations for their observations, such as some countries using much more energy per capita than others. Students might also point out that most countries have populations of 300 million or below, but that two countries, India and China, have populations that are much higher. Demonstrate for students how they can label the countries with their names or abbreviations to help identify them. 4 Note: Use the InspireData handouts to help with plotting and analysis (Help Documentation Handouts or InspireData Starter Learn to Use Documentation Handouts). You may want to print one or more sets of handouts to make them available for students Ask students for suggestions of other plots that would help them answer the questions. Change either the x or y axis (or both) to create a new plot such as the one shown below. Tell students that a line of best fit can be added to help analyze the relationship between the data fields, such as energy use and population. Explain that the line of best fit is a straight line that best represents the data in an axis (or scatter) plot. Ask students to approximate where the line of best fit would fall. What direction and how steep would they expect it to be? Demonstrate how to add a line of best fit by selecting the Line Type button in the lower-left corner of the workspace and choosing Line of Best Fit from the menu that appears. What type of correlation does the line of best fit suggest (positive or negative)? Is this a strong correlation or a weak correlation? What does this mean with regard to energy consumption and population? 5 7. Explain that the correlation coefficient is also listed to help determine the relationship between the variables, in this case electricity production and population. The correlation coefficient, which is displayed in the upper-left corner of the workspace, gives a measure of the strength and direction of the linear relationship. The correlation coefficient always falls between -1 and 1. The farther the coefficient is from 0, the stronger the relationship. Ask students what a correlation coefficient of 0.56 indicates (a moderate, positive correlation between population and consumption of electricity). Discuss how the United States is an outlier and how its deviation from the general pattern impacts the correlation coefficient. Ask what a correlation coefficient of 1 would look like. Are there any variables that might have that close of a relationship? Why? 8. Discuss the difference between slope and correlation, or how a very steep line of best fit could have a very low correlation coefficient. Ask how the line of best fit can be used to predict energy consumption for countries with larger populations. Demonstrate how to use the Notes area to record an analysis for each plot. Click on in the lower right to open the area. Be sure to show students how to capture a slide for each plot, including their notes, by clicking the Slide Sorter button to open the Slide Sorter and then the Capture Slide button. 6 9. Divide students into pairs or as many groups as there are computers available. Ask them to explore at least six relationships between numeric fields, using the Possible Investigations in the table notes to help them. Point out the Sample Plots tab that they can refer to if they need ideas. 10. For each plot, direct students to do the following: Add a title. (Plot menu plot Title ) In the Notes area, record an analysis that includes a discussion of the general trend(s) shown by the plot, any outliers, and their meaning in the context of the situation. Are any observations surprising? Why do students think countries use differing amounts of energy? Add a line of best fit. Use the Notes area to add additional comments about the correlation coefficient and its meaning as it relates to the graph. Does the correlation coefficient provide any additional information to help explain the relationship between energy production, consumption, and population? Capture a slide. 11. Conclude the lesson by viewing a variety of the groups slides and having a class discussion about each plot, the line of best fit, and the correlation coefficient. What predictions can students make about future energy production and consumption using the lines of best fit? Is rapid economic development in countries like China and India likely to continue to affect their consumption of energy? Are any economic, environmental, or national security concerns likely to affect energy production and consumption in the United States and other countries around the world? Do students think the observed energy production and consumption patterns are equitable, responsible, and sustainable? If not, what could be done to alter the observed trends? Adaptations/Extensions: For older or more advanced students, have them add at least one prediction by extrapolating from the line of best fit (e.g., A country with a population of 1,600,000,000 might consume 3 billion kilotons of oil equivalent per year. ), and add it to the Notes area. Be sure to remind students to capture the slides and notes. 7 Students can enhance their plots by adding other InspireData features. For example, the Color by Field tool can be used to color icons by Level of Development or Region, as shown on the next page. Students can discuss the interaction of this third variable with variables plotted on the axes. Note: You can refer students to the InspireData handouts for help with plotting and analysis (Help Documentation Handouts Learn to Use Plots and Learn to Use Axis Plots . For younger students, consider analyzing more of the data as a whole class, at least until students understand the process. The entire lesson could also be conducted as a class. Have students research renewable forms of energy that are currently meeting only a small percentage of world energy needs but that might be more environmentally friendly and important in the future. Students can use InspireData to create another database to gather and analyze the data on the renewable energy production and consumption. One excellent source for this data is the U.S. Department of Energy at 1 Copyright Common Core State Standards. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Learn more online at 2 Copyright Themes of Social Studies. National Council for the Social Studies. All rights reserved. Learn more online at 8
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