Cause and Effect - Grade Nine by hzp22842

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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.




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                          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?




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                         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:




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                          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?”



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                          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.




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                         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




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                          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.


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                          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

								
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