## The Guise of a Graph Gumshoe

### Lisa Ove GibsonBay District Schools

#### Description

Students practice constructing bar, circle, and box-and-whisker graphs. Students also practice reading and interpreting data displays and explore how different displays of data can lead to different interpretations.

#### Objectives

The student collects, organizes, and displays data in a variety of forms, including tables, line graphs, charts, bar graphs, to determine how different ways of presenting data can lead to different interpretations.

The student understands and applies the concepts of range and central tendency (mean, median, and mode).

The student reads and interprets data displayed in a variety of forms including histograms.

The student constructs and interprets displays of data, (including circle, line, bar, and box-and-whisker graphs) and explains how different displays of data can lead to different interpretations.

The student finds the mean, median, and mode of a set of data using raw data, tables, charts, or graphs.

#### Materials

-Summary Sheet of Instruction for The Guise of a Graph Gumshoe (See page 1 of Associated File)
-How to Construct a Box-and-Whisker Graph (See page 2 of Associated File)
-Box-and-Whisker Graph Construction (See page 3 of Associated File)
-Data for Displays (See page 4 of Associated File)
-Bar Graph Construction (See page 5 of Associated File)
-Circle Graph Construction (See page 6 of Associated File)
-Data Display Practice (See pages 7-10 of Associated File)
-Vocabulary for Statistical Sleuths (See Unit Plan Associated File; further information is available in Extensions)
-Key for Graph Construction (See pages 11-13 of Associated File)
-Key for Data Display Practice (See pages 14-17 of Associated File)
-Data Detective Diary (used throughout the Unit Plan: Statistical Sleuths)
-Classroom display board (Examples: overhead projector, chart paper, or chalk board)
-Corresponding writing device (example-Vis-à-Vis)
-Blank transparency film for copy machines or printers
-Access to a computer lab or a single computer with presentation capabilities and Internet access
-[The American Heritage College Dictionary, Third Edition], Boston, New York: Houghton Mifflin Company, 2000, page 644
-Optional: Calculators for student use
-The following site is a Student Web Lesson found on the Beacon Learning Center Website. Using it is optional.
The Party Comedian
http://www.beaconlearningcenter.com/search/details.asp?item=3097

#### Preparations

1. Read the information in Vocabulary for Statistical Sleuths. (See Unit Plan Associated File. Further information is available in Extensions.) The reason for reviewing the information is to understand the definitions for the concepts that will be taught during today’s lesson.

2. Prepare a large writing space, preferably an overhead projector, in the front of the classroom to record:
(a) Detective diary entries (#7, #8, Follow-up for #7 and #8 and
(b) Comments/ideas generated during today's discussion. (Obtain appropriate writing tools.)

3. Make sure that students' Detective Diaries are available for today’s assignment.

4. Create copies of How to Construct a Box-and-Whisker Graph on page 2, Box-and-Whisker Graph Construction on page 3, Data for Displays on page 4, Bar Graph Construction on page 5, Circle Graph Construction on page 6, and Data Display Practice on pages 7-10. (See Associated File.) Special Note: Pages 2–9 will be administered during Part I of this lesson, and page 10 will be administered during Part II of this lesson for each student.

5. Create an overhead transparency of Box-and-Whisker Graph Construction from page 2, Data for Displays from page 4, Bar Graph Construction from page 5, and Circle Graph Construction from page 6 to be used for whole class instruction. (See Associated File.)

6. Review Key for Graph Construction to understand the best responses for each of these activities prior to modeling in instruction. (See pages 11-13 of Associated File.)

7. Review Student Web Lessons prior to instruction if used with this lesson.

8. Set up a presentation cart (with computer/television) and/or a computer lab to accommodate the online Student Web Lessons referenced in the Weblinks and Materials section of this lesson.

9. Optional: Create a transparency of graph paper for modeling box-and-whisker graphs. (See Weblinks.)

#### Procedures

Disclaimer: The student will not use the different types of sampling techniques in this unit. The student will identify random and systematic sampling techniques. If the teacher wishes to include the use of sampling techniques to collect data, they may integrate the necessary instruction to do so. The student will not read and interpret data displayed in a variety of ways. They will only read and interpret data displayed in a table. The student will not construct and interpret a line graph. The student will, however, construct a bar, circle, and box-and-whisker graph. The student will find the median of a set of data; however, they will not find the mean and mode in this lesson.

Prerequisite: The student understands fractions (parts to the whole) and how to convert a fraction to a percentage. These concepts will be utilized in the construction a circle graph.

Part I:
1. REVIEW from previous lesson Sampling Snoops, Detective Diaries through entry #6. Feedback included in the Detective Diary should help students that do not completely understand how to read and interpret a histogram. Also, review how to formulate a hypothesis and how to infer and draw conclusions based on statistical results as necessary.

2. NEW MATERIAL: In order to draw conclusions based on statistical results, we first have to organize the information into manageable sections. There are several ways to do this. Create a table, bar, circle, and/or box-and-whisker graph. By creating these data displays, we can see the spread of the data. Each display has a specific way that it presents the data:
(a) Tables help to organize data into meaningful sections.
(b) Bar graphs help to show comparison.
(c) Circle graphs do a better job of showing percentages and relationships of the part to the whole.
(d) Line graphs display data that changes over time. (This display will not be used in this lesson.)
(e) Box-and-whisker graphs show the median, quartiles, and range of the data set. By looking at the spread of the data, box-and-whisker graphs help summarize large amounts of data into an easily read diagram.

3. Explain the importance of using data displays to organize data collected. Also, explain that displays make reading and interpreting data an easier process. Ask students to make note in their Detective Diary of important information provided in the discussion of data organization (#2 of Procedures).

4. Use overhead transparency of Data for Displays. (See page 4 of Associated File.) For whole class instruction, write the completed table on the overhead, and then model reading and interpreting a table for students by using the table. Most students have successfully read and interpreted tables for several years. Use your own discretion to determine your individual students' needs. The purpose of reviewing the elements of a table is to be able to take the data organized in one and convert the data into a bar, circle, and box-and-whisker graph. After students have constructed each of these graphs, they should better understand how different displays of data can lead to different interpretations.

5. Use transparency of Bar Graph Construction for whole class instruction .(See page 5 of Associated File.) Use an overhead projector to model the steps necessary to complete this activity. To construct the bar graph use the data from table in Data for Displays. (See page 4 of Associated File.) During each modeling process, entertain students' questions about how to read and interpret data displays (table) and how to construct a data display (bar, circle and box-and-whisker graphs). Activities modeled for the class can be student directed depending on the proficiency of your students. Based on the standards, students have been constructing tables, bar and circle graphs for several years. The newest data display for students is the construction of a box-and-whisker graph.

6. Construct a K-W-L chart for Bar Graphs on a large display for all students to see. The topic for the K-W-L is how to construct a bar graph. Special Note: Usually KWLs are used to illustrate what students want to Know. In this case, KWLs are used to explain what students need to know. Also, they are answering Why a bar graph is used. Facilitate a discussion about the process necessary to construct a bar graph. As students respond, record statements made on the chart. When the K and W of the chart are complete, check for validity of comments. Make corrections as necessary. (For more information about KWLs, see the Weblinks section.)

7. For the K section of the K-W-L, students need to know the following: A bar graph helps to show a comparison between two or more things. Make sure the bar graph includes the following:
(1) A title.
(2) Labels for the axes.
(3) Appropriate and consistent scales.
(4) Accurate data.

A correct and complete response includes a correct bar graph similar to the one provided in the Key for Graph Construction. (See pages 11-13 of Associated File.)

8. Explain practical reasons why statisticians use bar graphs. This explanation leads to how different displays can lead to different interpretations of the data.

9. Write this entry in an area that all students can see, Detective Diary Entry #7: Record the information from the large display of the Bar Graph K-W in your diary.

Students will complete the L portion of the chart after constructing their own bar graph in the activity, Data Display Practice, during Part II, #16 of these Procedures.

10. Use transparency of Circle Graph Construction for whole class instruction. (See page 6 of Associated File.) Model the steps necessary to complete the activity.

11. Construct a K-W-L chart for Circle Graphs on a large display for all students to see. The topic for the K-W-L is how to construct a circle graph. Facilitate a discussion about the process necessary to construct a circle graph. As students respond, record statements made on the chart. When the K and W of the chart are complete, check for validity of comments. Make corrections as necessary.

12. For the K section of the K-W-L, students need to know the following: A circle graph does a better job of showing percentages and relationships of the part to the whole. To construct a circle graph, use the data from Data for Displays. Make sure the bar graph includes the following:
(1) A title.
(2) Labels for each section with the name of the appropriate book and the percent of students who prefer each book.

A correct and complete response includes a correct circle graph similar to the one provided in the Key for Graph Construction. (See pages 11-13 of Associated File.)

13. Explain practical reasons why statisticians use circle graphs. This explanation leads to how different displays can lead to different interpretations of the data.

14. Write this entry in an area that all students can see, Detective Diary Entry #8. Record the information from the large display of the Circle Graph K-W in your diary.

Students will complete the L portion of the chart after constructing their own circle graph in the activity, Data Display Practice, during Part II, #16 of these Procedures.

Part II:
15. Review any misconceptions that students might have from yesterday’s instruction of how to read and interpret a table, and how to construct and interpret bar and circle graphs.

16. Provide each student with a copy of the activity, Data Display Practice. (See pages 7-10 of Associated File.) Students complete this activity. Use the Key for Data Display Practice to formatively assess student work. (See pages 14-17 of Associated File.) This serves as the formative assessment.

17. Write this entry in an area that all students can see, Follow-up for Detective Diary Entry #7 and 8: Complete the L section of your K-W-L for Detective Diary #7 and Detective Diary #8. The L section will be different for each student because they will be paraphrasing instruction from the teacher. Make sure that students have the gist of these concepts. Provide formative feedback for students who appear to have any difficulty with these entries. Offer additional practice for students as necessary using material from you textbook or some other source. (This is formative assessment which is explains how different displays of data can lead to different interpretations.)

18. NEW MATERIAL: Show students an example of how a box-and-whisker graph looks. (Use examples available in the Weblinks section of this document.) Explain to students that they will learn how to create this kind of graph. Consider using a transparency of graph paper to draw the box-and-whisker graph for modeling purposes. An electronic version of a blank graph is available in the Weblinks section.

19. Distribute copies of How to Construct a Box-and-Whisker Graph to each student. (See page 2 of Associated File.) Ask students to read the steps listed. (Some variation in the order in which these steps are taken per teacher discretion.)

20. Use transparency of Box-and-Whisker Construction for whole class instruction. Model the steps necessary to complete the activity Box-and-Whisker Construction, using the steps from How to Construct a Box-and-Whisker Graph. (See pages 2-3 of Associated File.)

21. Special Note: Spend extra instructional time explaining how to find the median from a set of data. If students need additional practice, use the Student Web Lesson: The Party Comedian where students practice finding and using the median of a set of data. (See Weblinks section of this document for the URL address.) Suggestion: Use this lesson as a whole class by displaying the Student Web Lesson on a television that is connected to a computer with Internet capability or use Internet capable computers in your room for a more individual approach.

22. Provide each student with a copy of the activity, Data Display Practice. (See page 10 of Associated File.) Students complete this activity.

23. Assess students' completed box-and-whisker graphs with the Key for Data Display Practice. (See pages 14-17 of Associated File.) This serves as the formative assessment. The median or second quartile of this box-and-whisker graph serves as the formative assessment.

24. Return assessed activities to students. Explain that these materials will be used to review for the summative assessment in a few days.

#### Assessments

Formative assessment: Students read and interpret data presented in a table Data Display Practice by converting the data into another data display (bar, circle, and box-and-whisker graph). (See pages 7-10 of Associated File.)

Formative assessment: Students construct and interpret displays of data (including circle, bar, and box-and-whisker graphs) and explain how different displays of data can lead to different interpretations in the activity Data Display Practice. See Key for Data Display Practice for possible responses. (See pages 7-10 and 14-17 of Associated File.)

Formative assessment: Students find the median of a set of data when they construct a box-and-whisker graph in the activity, Data Display Practice. (See page 10 of Associated File.) Students do not find the mean and mode of the data in this lesson.

#### Extensions

1. The student will only read and interpret a single histogram in this lesson.

2. The Beacon Unit Plan associated with this lesson can be viewed by clicking on the link located at the top of this page or by using the following URL: http://www.beaconlearningcenter.com/search/details.asp?item=2958. Once you select the unit’s link, scroll to the bottom of the Unit Plan page to find the section, Associated Files. This section contains links to the Unit Plan Overview, Diagnostic and Summative Assessments, and other associated files (if any).

3. The Guise of a Graph Gumshoe is the third lesson plan in the Unit Plan: Statistical Sleuths.

4. Allow students to peer–assess each other’s diary entries if they are at a point where they can assess the content accurately enough to provide effective feedback.

This site offers interactive information and an opportunity for students to practice finding and using the median of a set of data.
The Party Comedian

This site offers a description and graphic for KWLs.

This site offers a more animated tool for creating circle graphs with parts to the whole and percentages.
Circle Graphs

This site offers an electronic version of graph paper.
Graph Paper

This site offers an electronic version of graph paper.
Free Online Graph Paper PDFs

This site offers a listing of activities that correlate to the Sunshine State Standards from the AIMS Education Foundation.
Florida Correlation Documents

This site offers a more extensive definition and an example for box-and-whisker plots.
Box-and-Whisker Diagrams

This site offers a more extensive definition and an example for mean, median, and mode.
Introduction to Statistics: Mean, Median, and Mode

This site offers information about Websites for collecting data for use with mathematics, social studies, and science.
Websites for Collecting Data for Use with Mathematics, Social Studies, and Science

This site offers comparisons and contrasts between histograms and bar graphs.
Histograms vs. Bar Graphs Discussion

This site offers quite an extensive list of assignments on mean, median, and mode.
AAA Math

#### Attached Files

The Guise of a Graph Gumshoe Associated File     File Extension: pdf