## Using Statistics to Uncover More Evidence

### Lisa Ove GibsonBay District Schools

#### Description

Students use statistics to interpret data collected from a representative sample.

#### Objectives

The student writes notes, comments, and observations that reflect comprehension of fifth-grade or higher level content and experiences from a variety of media.

The student analyzes and explains orally or in writing the implications of graphed data.

The student uses a stem-and-leaf plot from a set of data to identify the range, median, mean, and mode.

The student uses range and measures of central tendency in real-world situations.

The student interprets the results using statistics (range and measures of central tendency).

#### Materials

Students describe graphs in terms of range, measures of central tendency, and distribution.
All That Data Too!
http://www.beaconlearningcenter.com/search/details.asp?item=3106

-Access to a computer lab or a single computer with presentation capabilities and Internet access
-Teacher Quick Sheet (Procedures) – Using Statistics to Uncover More Evidence (see associated file – Pg. 1)
-Mock Survey Results (see associated file – Pg. 2)
-Teacher Answer Key for Mock Survey Results (see associated file – Pg. 3)
-Printable version of the SWL, All That Data, Too! (see associated file – Pgs. 4 – 8)
-Data Detective Diary (used throughout the unit Data, Detectives, and Decisions)
-Long Answer Question Rubric (see associated file – Pg. 9)
-Chart paper/writing device
-Results from the student conducted survey of 5th grade students asking, How much time should the average fifth-grade student spend on homework to make good grades? and data displays

#### Preparations

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

2. Review the Student Web Lesson, All That Data, Too! prior to instruction.

3. Prepare a large writing space in the front of the classroom to record comments/ideas generated during today's discussion (obtain appropriate writing tools).

4. Make copies of the Printable Version of the Student Web Lesson, All That Data, Too! (see associated file).

5. Collect and provide individual feedback to students regarding their answers to Printable Version of the SWL All That Data, Too! (see associated file).

6. Review Teacher Quick Sheet (Procedures) – Using Statistics to Uncover More Evidence (see associated file) and possibly use for a quick reference to what the crux of the instruction will be for this lesson.

7. Prepare a mini-lesson explaining how to use a data display to interpret results from a survey. Review stem-and-leaf plots, range, and measures of central tendency.

8. Display the responses gathered from the student-conducted survey of 5th graders asking, How much time should the average 5th grade student spend on homework to make good grades? Also look at the displays of graphed data which are both located in Lesson #3 - Looking for More Evidence.

9. Select appropriate pages out of your classroom text or use mock survey results to allow extra practice for creating bar and circle graphs, creating stem-and-leaf plots, and identifying range, mean, median, and mode.

#### Procedures

1. Review the correct answers from the previous days' lesson with students- Looking for More Clues.

2. Distribute copies of Printable Version of the SWL, All That Data, Too! for each student (see associate file). (Hint: If you need to conserve paper, make copies of both sides of the paper.)

3. Instruct students to write their responses on their copy of Printable Version of the SWL, All That Data, Too! BEFORE using it as an instructional model.

4. Use the Online Student Web Lesson titled, All That Data, Too! as an instructional model (see the Materials section of this document for the specific Web address). Demonstrate the use of the Web lesson page by page on an Internet accessible computer/TV presentation cart. In this lesson students review a group of committee members' survey results and how they displayed their data in order to identify the range, mean, median, and mode of their individual and collective data results.

5. Provide a class discussion at the end of each Web page. Come to a consensus about the best answer for each field during the discussion. Type in the most popular answers from the class discussion in each field of the Web lesson and further discuss as a whole class the computer's responses (the program will offer hints if the answer is not correct and it will offer congratulations if you are right).

6. After completing All That Data, Too! ask students to turn in their answers. Provide proper feedback for each student and offer more instruction to students who had difficulty with any part of this lesson.

7. Provide a mini-lesson on using a data display to interpret results from a survey. Review stem-and-leaf plots, range, and measures of central tendency (see Lesson 1 of this unit – Opening the Case). Make sure students comprehend the relationships between stem-and-leaf plots, range, and measures of central tendency (for more detailed information about stem-and-leaf plots see Web addresses in the WebLinks section of this document.) The range of a set of data tells us the distance, or area, covered from low value to high value. The mean allows us to summarize all the data with one number known also as the average; the median is the middle value in a set of ordered numbers (from least to greatest); and the mode is the item or value listed most often in a set of data.

8. As a class, review ALL of the responses gathered from the student-conducted survey (Lesson #2 - Observing the Evidence) of 5th graders asking, How much time should the average 5th grade student spend on homework to make good grades?). Also look at the displays of graphed data from Lesson #3 Looking for More Evidence.

9. Assign Data Detective Entry #7, Given the results from this survey and the displays of graphed data, how would a stem-and-leaf plot help to identify the range, mean, median, and mode? Ask students to create a stem-and-leaf plot for one set of data collected. For example, a student can create a stem-and-leaf plot for the number of hours that boys felt should be spent on Math homework to make good grades. For this example there would only be 15 pieces of data in the stem-and-leaf plot. Then ask students to label the range, mean, median, and mode for each stem-and-leaf plot. List 2-3 interpretations or statements that can be made based on the data displayed.

10. Provide individual feedback for each student upon his or her completion of diary entry #7.

11. Students reconvene in their small groups that were established during Lesson # 2 Observing the Evidence. While in these groups, students review previous work regarding their representative sample from the survey. Based on the data collected, students identify the range and measures of central tendency from their section of the representative sample. This information should be labeled on the data displays created in the Lesson #3 Looking for More Clues and stored in their Detective Diary entry #6.

12. Provide formative feedback for each group upon their completion of the activity in step 11. (Check to make sure that each group accurately displays data acquired during the survey conducted by students during Lesson #2 Observing the Evidence. Also check that they use the stem-and-leaf plot correctly and that they accurately identify the range and measures of central tendency of their representative samples.

13. Assign Detective Diary entry #8; Use a stem-and-leaf plot to display the data of the representative sample collected by the small groups. Identify the range and measures of central tendency of the representative sample. List 2 - 3 interpretations and/or statements that can be made based on the data displayed.

14. As a class, students' peer-assess diary entry #7 and #8 using the criteria listed on the Long-Answer Question Rubric (see associated file).

15. If students need additional assistance or practice, an optional homework assignment would be to use appropriate pages out of your classroom text OR use mock Survey Results (see associated file). The mock Survey Results can be used for practice of data analysis and display. For specific directions on how to use the Survey Results see the Extensions section of this lesson plan.

#### Assessments

Formative assessments:

1) Based on yesterday's homework assignment (text pages) check each students' answers.

2) After collecting students' work for the Student Web Lesson, All That Data Too! provide individual feedback to students regarding their answers.

3) Provide individual feedback for each student upon his or her completion of diary entry #7.

4) Provide formative feedback for each group upon completion of their review of survey results and review of data displays from Lessons #2 and #3.

5) Students' peer-assess diary entry #7 and #8 using the criteria listed on the Long-Answer Question Rubric.

#### Extensions

This is the fourth lesson of the unit Data, Detectives and Decisions. 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=2942 . Once you select the unit’s link, scroll tot 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).

Lesson 1 – Opening the Case
Lesson 2 – Observing the Evidence
Lesson 3 – Looking for More Clues

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A Maths Dictionary for Kids

This site offers an online math dictionary for educators and students. You want to check this out!
Harcout Math Glossary

This site offers an excellent illustration of a stem-and-leaf plot and allows for interactive practice finding the mean, median, and mode of data using an Online stem-and-leaf plot.
Making Stem and Leaf Plots

This site is ABSOLUTELY awesome!! It allows students the opportunity to practice using data in a stem-and-leaf plot to find the mean, median, and mode.
Stem – and – Leaf Plotter

This site offers a demonstration lesson for teachers using stem-and-leaf plots.
Stem-and-Leaf Plots

#### Attached Files

Using Statistics to Uncover More Evidence Associated Files     File Extension: pdf