## Opening the Case

### Lisa Ove GibsonBay District Schools

#### Description

This is an introduction to the unit Data, Detectives and Decisions. Students are taught how to design an experiment and use graphs and statistics to help solve a problem.

#### 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 knows which types of graphs are appropriate for different kinds of data (for example, bar graphs, line, or circle graphs).

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.

#### Materials

The following sites are Student Web Lessons found on the Beacon site. Using them is optional.

Students find and use the mode of a set of data.
Party Mode
http://www.beaconlearningcenter.com/search/details.asp?item=3096

Students find and use the median of a set of data.
The Party Comedian
http://www.beaconlearningcenter.com/search/details.asp?item=3097

Students explore how to use pictographs to find the average for sets of data.
A Party In Review
http://www.beaconlearningcenter.com/search/details.asp?item=3103

Students use an Online calculator to find and use the average, or mean, of a set of data.
The Mean Green Machine
http://www.beaconlearningcenter.com/search/details.asp?item=3104

-Access to a computer lab or a single computer with presentation capabilities and Internet access
-Short-Answer Question Rubric (see associated file – Pg. 1)
-Student Activity Sheet for Opening the Case (see associated file – Pgs. 2 - 3)
-Vocabulary for Data, Detectives and Decisions (see associated file – Pgs. 4 - 7)
-Compiled List of Detective Diaries for the Entire Unit (see associated file – Pgs. 8 - 9)
-Instruction for Stem-and-Leaf Plot (see associated file – Pgs. 10 - 12)
-Student’s Data Detective Diary (used throughout the unit Data, Detectives, and Decisions – the teacher decides what kind of Diary he or she would like for students)
-Chart paper/writing device
-Classroom text and/or mock survey results

#### Preparations

1. Review Vocabulary for Data, Detectives, and Decisions prior to this lesson to familiarize yourself with the key terms and how they will be used throughout the unit (see associated file).

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

3. Decide how you will use the Student Activity Sheet for Opening the Case (see associated file). For example, will students complete the Student Activity Sheet OR will you use the sheet as a checking device during the lesson.

4. Prepare mini-lesson on stem-and-leaf plots, range, and measures of central tendency to review the purpose and the method to construct a stem-and-leaf plot see Instruction for Stem-and-Leaf Plots.

5. Prepare second mini-lesson on bar, line, and circle graphs showing which graphs reveal range, mean, median, and mode best. One way that this can be done is by reviewing the correct answers to Diagnostic Assessment #2 from the unit Data, Detectives, and Decisions with the entire class.

6. Select appropriate pages out of your classroom text or create mock results from another survey to allow students more practice with stem-and-leaf plots OR use the suggestions contained in Instruction for Stem-and-Leaf Plot.

7. Conduct an actual survey of 4th and 5th grade teachers in your school asking, How much time should the average 5th grade student spend on homework to make good grades? Collect the results and prepare 2 stem-and-leaf plots illustrating the responses. This information must be completed before the next lesson titled, Observing the Evidence.

8. OPTIONAL: 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.

9. OPTIONAL: Review Student Web Lessons prior to instruction, if used with this lesson.

10. If using the unit Data, Detectives, and Decisions, collect and secure each student's Detective Diary after EACH lesson. The Detective Diary will be returned to students after the summative assessments for the unit are completed.

#### Procedures

1. Pose the question to the class: How much time should the average fifth-grade student spend on homework to make good grades? Ask students to explain their responses.

2. Conduct a class survey of answers to the question. Ask each student for a response to this question (share possible answers for the survey if students appear to be stuck. Some answers might be: 2 hours because it takes 30 minutes for each subject; 40 minutes - there is not a test tomorrow; etc.)

3. List students' responses to the class question on the board, overhead, or chart paper for everyone to observe. Arrange responses so that girls' answers are separate from boys'.

4. Organize the results of the girls' portion of the class survey in a stem-and-leaf plot.

5. Provide a mini-lesson on the differences between range, mean, median, and mode. 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. For suggestions see Instruction for Stem-and-Leaf Plot in the associated file.

6. Use the girls' results in the stem-and-leaf plot and identify the range, mean, mode, and median of the data on the board. Make sure students understand how a stem-and-leaf organizes the information to help easily identify the range and measures of central tendency. Offer additional examples if students have any difficulty with these concepts.

7. Assign Detective Diary Entry #2: Given the boys' results from our class survey, use a stem-and-leaf plot to organize the information. Determine the range and measures of central tendency from the plotted data. In 2 or 3 sentences, explain how the stem-and-leaf plot helps identify the range, mean, median, and mode from a set of data. Ask students to record their responses in their Data Detective Diary. This entry follows the diagnostic assessment - entry #1- that is described in the unit plan titled, Data, Detectives, and Decisions.

9. Provide proper feedback for students by conferring with them in an individual conference or through a whole class discussion. Make sure they 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.)

10. Provide mini-lessons on bar, line and circle graphs with students. After reviewing the unique purposes for line, bar, and circle graphs, then show students which graphs reveal range, mean, median, and mode best. (Note: Bar graphs help to show comparison, while circle graphs do a better job of showing percentages and the relationships of the part to the whole. Line graphs are usually used to display data that changes over time.)

11. Assign DD Entry #3, Explain the relationship among the graphs and the measures of central tendency.

12. As a class, students self- and peer- assess journal entries #2 and #3 using the criteria listed on the Short- Answer Question Rubric (see associated file).

13. For homework, students practice-using stem-and-leaf plots to find the range, mean, median, and mode. Use appropriate pages out of your classroom text or create mock results from another survey and ask students to analyze the information and display the results in a stem-and-leaf plot. (This assignment should be used as a form of practice or formative assessment for the student and is not graded.)

#### Assessments

First students respond to the prompt (E#2), Given the boys' results from our class survey, use a stem-and-leaf plot to organize the information. Determine the range and measures of central tendency from the plotted data. In 2 or 3 sentences, explain how the stem-and-leaf plot helps identify the range, mean, median, and mode from a set of data. Make sure students understand these concepts and provide help if students are struggling before moving on to the next diary entry.

Students respond to a second prompt (E#3), Explain the relationship between different types of graphs and the measures of central tendency. After responding in their Detective Diaries (entries #2 and #3), students self- and peer- assess these entries using the criteria listed on the Short-Answer Question Rubric. Provide proper feedback for students to make sure they comprehend the relationships between stem-and-leaf plots, range, and measures of central tendency and which types of graphs reveal range and measures of central tendency best.

#### Extensions

This is the first 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 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).

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

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

This site offers an online math dictionary for educators and students. You want to check this out!
A Maths Dictionary for Kids

#### Attached Files

Opening the Case Associated Files     File Extension: pdf