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Cause and Effect? – Grade Nine Ohio Standards Lesson Summary: Students examine several data sets to Connection: explore the validity of various conclusions from a Data Analysis and correlation study. Through questioning and small group Probability discussions, students discover that correlation does not necessarily imply causation. This lesson involves frequent Benchmark F use of small group discussion in an effort to encourage Construct convincing students’ use of mathematical communication. If time is an arguments based on analysis of data and issue, place time limits on these discussions. In the post- interpretation of graphs. assessment activity, students find articles from magazines or newspapers, reporting about correlation studies and Indicator 6 evaluate the writer’s conclusion statements. Make inferences about relationships in bivariant data, and recognize the Estimated Duration: One hour and 40 minutes difference between evidence of relationship Commentary: (correlation) and causation. Cause and effect are familiar terms to students from Mathematical Processes relationships in reading/language arts, science and social Benchmarks studies. These terms are important in the mathematical world also. B. Apply mathematical knowledge and skills Change in variables produces change in data. In this lesson, routinely in other content areas and students understand that the correlation between two practical situations. variables does not necessarily indicate a cause and effect G. Write clearly and relationship. coherently about mathematical thinking Introduce students to unfamiliar terms, such as bivariate, as and ideas. they delve deeper into statistics. Be sure they are familiar H. Locate and interpret mathematical with terms such as outlier, scatterplot and line of best fit information from earlier studies with statistical data. accurately, and communicate ideas, Numerous activities in this lesson gather data and produce processes and needed graphs for interpretation. Students make inferences solutions in a complete as evidence in cause and effect correlation studies. and easily understood manner. Pre-Assessment: Instructional Tip: If this lesson follows the Grade Nine lesson from the IMS on the Web site, “Graphs and More,” covering Data Analysis and Probability Benchmark A, this pre-assessment may be unnecessary. 1 Cause and Effect? – Grade Nine • Distribute Plotting Points and A Line of Best Fit, Attachment A. Students will also need a piece of grid paper. If none is available, students can use a copy of Attachment G. • Students create a scatterplot (by hand or with technology) and find the line of best fit, given one set of bivariate data. Scoring Guidelines: Score informally. Circulate around the room monitoring student progress and providing assistance as needed. Post-Assessment: • Distribute a copy of Evaluation of a Correlation Study, Attachment B, to each student. Read aloud as students read along. Answer any questions students may have. • Have students find articles involving correlation studies from newspapers or magazines and evaluate the conclusions. Instructional Tip: If time permits, take the whole class could go to the library/media center to look for articles. At that time, help students find an article that describes a correlation study. With some prior notice, the media specialist at your school may help. In general, look for a situation in which two pieces of numeric data are gathered for each subject in the study. For example, a correlation study could compare the number of accidents that occur for each age group of driver, or it might compare how many hours a student sleeps with the student’s score on a test. Scoring Guidelines: Develop a rubric with the students. A sample rubric follows. 2 points Demonstrates an understanding that correlation does not imply causation. 1 point Demonstrates some understanding of correlation but does not clearly discuss the issue of causation. 0 points Did not select an article that describes a correlation study. OR Does not demonstrate an understanding of correlation. OR Did not include an evaluation of the article’s conclusion. Instructional Procedures: 1. Assign students to small discussion groups of three to five students. Give the groups chart paper and markers to record discussion points of the following questions: • What factors impact a student’s success in school? • Which factor is the most important? • Do any of these factors impact one another? If so, which ones? Why? 2 Cause and Effect? – Grade Nine 2. Ask groups to share a summary of their discussions. While each group is sharing, create a list of important factors on the chalkboard or a flip chart. Conduct a short discussion of the inter- relationships between the factors. 3. Distribute Attachment C, Data Set #1. and one piece of grid paper. They can use their own grid paper or a copy of Attachment G. Students create a scatterplot and draw the line of best fit for the NAEP scores by number of minutes of homework assigned each day. Students answer the following questions: • Do students with higher numbers of minutes of homework assigned tend to have higher or lower achievement scores? How can this be determined? • Describe the relationship between the number of minutes of homework that is assigned each day and a student’s success. Use your graph to justify your argument. • Does it make sense that assigning more homework causes students to be more or less successful? Why or why not? Instructional Tip: NAEP stands for the National Assessment of Educational Progress. The National Assessment of Educational Progress (NAEP), also known as "the Nation's Report Card," is the only nationally representative and continuing assessment of what America's students know and can do in various subject areas. In this activity, a student’s score on the NAEP is being used as a measure of that student’s academic success. 4. Instruct students to pair with someone sitting near them to discuss their answers to these questions. Then have a few pairs share their ideas with the class. If there is disagreement about the issue of causation, allow it to remain unresolved until later in the lesson. 5. Distribute Attachment D, Data Set #2, and one piece of grid paper. They can use their own grid paper or a copy of Attachment G. Students create a scatterplot and draw the line of best fit for the NAEP scores by number of hours of television watched each day. Students answer the following questions: • Do students with higher numbers of hours of television watched tend to have higher or lower achievement scores? How can this be determined? • Describe the relationship between the number of hours of television that is watched each day and student success. Use your graph to justify your argument. • Does it make sense that watching more television causes students to be more or less successful? Why or why not? 6. Instruct students to pair with someone sitting near them. (Ideally, each student will have a different partner for this pairing than in step 4 above.) Have them discuss their answers to these questions. Then have a few pairs share their ideas with the class. There may be some disagreement among class members at this point, which is fine. In the final discussion, students come to consensus. 7. Distribute Attachment E, Predicting Data, and one piece of grid paper. They can use their own grid paper or a copy of Attachment G. Students make their own predictions about the amount of time spent doing homework based on different amounts of time watching television. Then students answer the following questions: 3 Cause and Effect? – Grade Nine • Do you predict that students with higher numbers of minutes of homework assigned tend to spend higher or lower numbers of minutes spent doing homework? How can this be determined? Instructional Tip: Students may debate whether homework can be done while watching television. If so, lead students towards an understanding that these data are randomly selected from all students. Consequently, even if some students can do homework while watching television, the overall percents would still be affected by those who cannot. • Describe your prediction of the relationship between time spent watching television and time spent doing homework, as illustrated above. • Does it make sense that watching more television causes students to be more or less successful? Why or why not? Instructional Tip: By examining the relationship between time spent watching television and time spent doing homework, students should begin to question whether television has any direct impact on student success. In the next step, students discuss these ideas in small group before coming back to whole-class discussion. Move around the room and monitor their progress. 8. Put students back into discussion groups of three to five students. (These can be the same groups as in step #1, or students can be grouped with different students this time.) Instruct students to examine the two data sets and discuss the following questions: • How do Data Set #1 and Data Set #2 relate to one another? Use your predictions in Attachment E, “Predicting Data,” to illustrate your impression of this relationship. • Based on this relationship, is it fair to assume that watching television has any direct effect on student success? Why or why not? • Is it possible that watching television has no direct effect on student success? Why or why not? 9. Examine each student’s conclusions drawn in Data Set #2. Do any of the conclusions make assumptions about the cause for levels of student success? If so, is it fair to say that watching television causes more or less success for students? Could the graph in Data Set #2 really be impacted by the amount of time these students spend studying? Instructional Tip: Ask leading questions to guide students toward a clearer understanding of correlation. For example, “If students who watch a lot of television have less time for studying, what does that say about the conclusions in Data Set #2?” 10. Conduct a final whole-class discussion. Start by having different groups share their conclusions. The goal of this discussion is to come to consensus on the answer to this question: “Can a scatterplot with its line of best fit (such as those used in a correlation study) be used to prove causation?” 4 Cause and Effect? – Grade Nine Instructional Tip: Students should conclude that correlation does not prove causation. Rather, a correlation between two variables simply provides evidence they are related. It cannot be assumed that one causes the other. For example, another factor could impact both variables, i.e., time spent doing homework might impact both the amount of time spent watching television and student achievement. 11. Distribute Attachment F, Draw Your Own Conclusions. Students need grid paper. They can use their own grid paper, or a copy of Attachment G. Have them write a possible conclusion for each graph shown. 12. Conduct a class discussion of the conclusions drawn by students. Ask clarifying questions such as, • Can we assume from this data that older students are braver than younger students? • Can we assume from this data that younger students are easier targets for violence? • What other factors might impact these results? Differentiated Instructional Support: Instruction is differentiated according to learner needs, to help all learners either meet the intent of the specified indicator(s) or, if the indicator is already met, to advance beyond the specified indicator(s). • Throughout the lesson, move around the room, providing support to students who need additional assistance. • Assess informally throughout the lesson to identify those students needing additional assistance. In the post-assessment, make accommodations for students who need help with verbal skills, such as writing. • Change the requirements slightly so articles illustrate an invalid conclusion. As part of the critique, the student must re-write the author’s conclusion so that it is valid. Extension: Students perform a correlation study and write an article for possible publication in the school newspaper or other publication. Home Connections: In the post-assessment, students select articles from magazines or newspapers that their parents have at home. If so, students could be encouraged to discuss their finding with their parents. Interdisciplinary Connections: Standard: Research Benchmark: B. Evaluate the usefulness and credibility of data and sources. Indicator: 3. Determine the accuracy of sources and the credibility of the author by analyzing the sources’ validity (e.g., authority, accuracy, objectivity, publication date and coverage, etc.). The post-assessment can be altered slightly to require students to find a correlation study reported in a textbook from another class, or from a journal related to a particular subject area. 5 Cause and Effect? – Grade Nine Materials and Resources: The inclusion of a specific resource in any lesson formulated by the Ohio Department of Education should not be interpreted as an endorsement of that particular resource, or any of its contents, by the Ohio Department of Education. The Ohio Department of Education does not endorse any particular resource. The Web addresses listed are for a given site’s main page, therefore, it may be necessary to search within that site to find the specific information required for a given lesson. Please note that information published on the Internet changes over time, therefore the links provided may no longer contain the specific information related to a given lesson. Teachers are advised to preview all sites before using them with students. For the teacher: Flip-chart paper and markers (optional) For the student: Attachments, graphing calculator, computer (optional) Vocabulary: • achievement scores • bivariate • causation • consensus • correlation • line of best fit • NAEP • scatterplot Technology Connections: • For the analysis and interpretation of the graphs and data, it is appropriate that students create the graphs using graphing calculators or computers. • Students can use the Internet to find articles for the post-assessment or other data sources, such as other government sources or national newspapers. Research Connections: "BSCS Science: An Inquiry Approach." BSCS Biological Sciences Curriculum Study. 23 Dec. 2003 <http://63.225.114.218/bscsdotorg/curriculum/InquiryFAQs.htm> Marzano, Robert J., Jane E. Pollock and Debra Pickering. Classroom Instruction that Works: Research-Based Strategies for Increasing Student Achievement, Alexandria, VA: Association for Supervision and Curriculum Development, 2001. Sousa, David A. How the Brain Learns: A Classroom Teacher’s Guide. Reston, VA: NASSP, 1995. 6 Cause and Effect? – Grade Nine Attachments: Attachment A, Pre-assessment, Plotting Points and a Line of Best Fit and Answer Key Attachment B, Post-assessment, Evaluation of a Correlation Study Attachment C, Data Set #1and Answer Key Attachment D, Data Set #2 and Answer Key Attachment E, Predicting Data and Answer Key Attachment F, Draw Your Own Conclusions and Answer Key Attachment G, Grid Paper 7 Cause and Effect? – Grade Nine Attachment A Plotting Points and a Line of Best Fit Create a scatterplot for these data and draw the line of best fit. x y 17 24 12 19 15 22.5 21 32 25 37.5 14 20 18 29 23 35 25 37.5 22 32 8 Cause and Effect? – Grade Nine Attachment A (continued) Answer Key for Pretest (Plotting Points and a Line of Best Fit) 9 Cause and Effect? – Grade Nine Attachment B Evaluation of a Correlation Study 1. Search through magazines and newspapers for an article that describes the results of a correlation study. 2. Read the article with a critical eye. Pay careful attention to the writer’s conclusions. For example, did the writer claim to show that one variable causes the other? 3. Write a paragraph or two evaluating the writer’s conclusions. Are the conclusions valid for a correlation study? Why or why not? 10 Cause and Effect? – Grade Nine Attachment C Data Set #1 Create a scatterplot for these data, and draw the line of best fit. # minutes of homework Average NAEP assigned each Score day 15 265 30 269 45 284 60 296 Data from the National Center for Education Statistics, 1990 K. Street, NW, Washington, D.C. 20006. http://nces.ed.gov/nationsreportcard/naepdata/ Questions for discussion: 1. Do students with higher numbers of minutes of homework assigned tend to have higher or lower achievement scores? 2. Describe the relationship between the number of minutes of homework that is assigned each day and a student’s success. Use your graph to justify your argument. 3. Does it make sense that assigning more homework causes students to be more or less successful? Why or why not? 11 Cause and Effect? – Grade Nine Attachment C (continued) Answer Key Create a scatterplot for these data, and draw the line of best fit. Questions for discussion: 1. Students with higher numbers of minutes of homework assigned tend to have higher achievement scores. 2. Answers will vary. 3. Answers will vary. 12 Cause and Effect? – Grade Nine Attachment D Data Set #2 Create a scatterplot for these data, and draw the line of best fit. # hours of television watched each Average NAEP day Score 1 290 2 288 3 282 4 278 5 275 6 259 Data from the National Center for Education Statistics, 1990 K. Street, NW, Washington, D.C. 20006. http://nces.ed.gov/nationsreportcard/naepdata/ Questions for discussion: 1. Do students with higher numbers of hours of television watched tend to have higher or lower achievement scores? 2. Describe the relationship between the number of hours of television watched each day and a student’s success. Use your graph to justify your argument. 3. Does it make sense that watching more television causes students to be more or less successful? Why or why not? 13 Cause and Effect? – Grade Nine Attachment D (continued) Answer Key for Data Set #2 Create a scatterplot for these data, and draw the line of best fit. Questions for discussion: 1. Do students with higher numbers of hours of television watched tend to have higher or lower achievement scores? Students with higher numbers of hours of television watched tend to have lower achievement scores. 2. Describe the relationship between the number of hours of television watched each day and a student’s success. Use your graph to justify your argument. Answers will vary. 3. Does it make sense that watching more television causes students to be more or less successful? Why or why not? Answers will vary. 14 Cause and Effect? – Grade Nine Attachment E Predicting Data In the table below, predict the number of minutes a student might spend doing homework with the given number of hours spent watching television. Create a scatterplot for these data, and draw the line of best fit. # hours of # minutes television doing watched each homework day each day 1 2 3 4 5 6 Questions for discussion: 1. Do you predict that students with higher numbers of minutes of homework assigned tend to spend higher or lower numbers of minutes spent doing homework? 2. Describe your prediction of the relationship between time spent watching television and time spent doing homework, as you have illustrated it above. 3. Does it make sense that watching more television causes students to be more or less successful? Why or why not? 15 Cause and Effect? – Grade Nine Attachment E (continued) Answer Key for Predicting Data In the table below, predict the number of minutes a student might spend doing homework with the given number of hours spent watching television. Create a scatterplot for these data, and draw the line of best fit. # hours of # minutes television doing watched each homework day each day 1 2 3 4 5 6 Data and graphs will vary. Questions for discussion: 1. Do you predict that students with higher numbers of minutes of homework assigned tend to spend higher or lower numbers of minutes spent doing homework? Answers will vary. Most will agree that students with higher numbers of minutes of homework tend to spend lower numbers of minutes doing homework. 2. Describe your prediction of the relationship between time spent watching television and time spent doing homework, as you have illustrated it above. Answers will vary. 3. Does it make sense that watching more television causes students to be more or less successful? Why or why not? Answers will vary. 16 Cause and Effect? – Grade Nine Attachment F Draw Your Own Conclusions Create a scatterplot and line of best fit for each set of data. Then, write a valid conclusion that can be drawn from each graph. 1. This table lists the percent of students in each grade who reported feeling that school was too unsafe to attend on one or more days in a 30-day period. % who Grade felt unsafe 9 8.8 10 6.3 11 5.9 12 4.4 Source: U.S. Dept. of Health and Human Services, Centers for Disease Control and Prevention, CDC Surveillance Summaries Conclusion: 2. This table lists the percent of students in each grade who reported being actually threatened or injured with a weapon on school property over a 30-day period. % who Grade were threatened 9 12.7 10 9.1 11 6.9 12 5.3 Source: U.S. Dept. of Health and Human Services, Centers for Disease Control and Prevention, CDC Surveillance Summaries Conclusion: 17 Cause and Effect? – Grade Nine Attachment F (continued) Answer Key for “Draw Your Own Conclusions” Create a scatterplot and line of best fit for each set of data. Then, write a valid conclusion that can be drawn from each graph. 1. Conclusion: Answers will vary: Conclusions should indicate a relationship between the grade of the students and the percent who report feeling unsafe. However, there should not be any statements that imply that being in a higher grade causes students to feel more safe. 2. Conclusion: Answers will vary: Conclusions should indicate a relationship between the grade of the students and the percent who report being threatened. However, there should not be any statements that imply that being in a higher grade causes students to be threatened less often. 18 Cause and Effect? – Grade Nine Attachment G Grid Paper 19