## Closing the Case

### Lisa Ove GibsonBay District Schools

#### Description

Students review the steps for data collection and how to prepare data displays using statistical information from a survey.

#### Objectives

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 creates an appropriate graph to display data, including titles, labels, scales, and intervals.

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

#### Materials

-Data Detective Diary (used throughout the unit Data, Detectives, and Decisions)
-Chart paper/writing device
-Compiled data set -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? THE TEACHER SHOULD PREPARE THIS BEFORE TODAY'S LESSON (the results from the survey were also used in yesterday's lesson plan)
-Teacher's Observation from theUnit Review (see associated file – Pg. 1)
-Steps for Data Collection (see associate file – Pg. 2)
-Short Answer Question Rubric (see associated file – Pg. 3)
-Activity for Closing the Case (see associated file – Pgs. 4 – 9)

#### Preparations

1. Combine and organize the small group representative samples from (Lesson #3 Looking for More Clues) to form one complete set of data results (like the committee members did in the Student Web Lesson, All That Data!). This must be completed by the teacher prior to this day, organized on a worksheet, and given to each student. Illustrate these data results in some way and administer one copy to each student.

2. Provide a mini-lesson explaining the steps for data collection for a survey of a representative sample (see associated file).

3. Create a mini-lesson of all concepts covered during the unit Data, Detectives, and Decisions for a summative review.

#### Procedures

1. Special note: Teachers may need to produce handouts for students to practice due to the variety of data, which can be collected.

2. Review the steps involved in data collection: Generating Questions and Designing a Survey (Lesson #1 - Opening the Case), Selecting a Representative Sample and Collecting/ Organizing Data (Lesson #2 - Observing the Evidence), Displaying Data (Lesson #3 - Looking for More Clues), and Interpreting Data (Lesson #4 - Using Statistics to Uncover More Evidence). See Data, Detectives, and Decisions in the Unit Plans section of the Beacon Learning Center Website.

3. Provide a copy of Steps for Data Collection (see associated file) for each student. These steps serve as a reminder for students.

4. As a class, identify how each of the steps were followed as you sought to answer the question, How much time should an average 5th grade student spend on homework to make good grades? Generally speaking, the steps for data collection can be summarized in the following way:
1) Design a survey with questions that require more than a yes or no response.
2) Use a stem-and-leaf plot to organize the data collected from the survey.
3) Identify the range, mean, median, and mode (also known as the measures of central tendency) of the data.
4) Acquire a representative sample for your survey.
5) Display the data collected from the survey in a line, double bar, and/or circle graph (depending on the kind of information that you collected) (see associated file). As you review the steps for data collection with students, ask them to write their own notes on the associated file, Steps for Data Collection.

5. Combine all of the small group representative samples to form one complete set of data results, which was originally collected during group work in Lesson #2 - Observing the Evidence. This must be completed by the teacher PRIOR to this day, organized on a worksheet, and given to each student (see associated file).

6. Provide each student with a worksheet containing the complete set of data results.

7. Provide each student with a copy of the Activity for Closing the Case (see associated file).

8. As a class look at the distribution of the data. Organize the data in two different stem-and-leaf plots (one for girls' responses and one for boys') and identify the range, mean, mode, and median of each group. Make sure students understand how a stem-and-leaf organizes the information to help easily identify the range and measures of central tendency. (This is the last opportunity to help students understand any misconceptions. The summative assessment for the unit is scheduled for tomorrow.)

9. Students write the stem-and-leaf plots on their own paper, one plot is for the girls' portion and another is for the boys' portion of the survey –this is not a diary entry. Students also identify the range, mean, median, and mode for each stem-and-leaf plot. Use the Preparation for the Summative Assessment-Checklist to individually assess each student on his or her work (see associated file).

10. Provide proper feedback for students to 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.) Assess student work by walking from desk to desk to observe their answers.

11. After completing the stem-and-leaf plots, students (while still in their small groups) display the data results in both a double bar and a circle graph. Based the results that were collected, what comparisons can be made between students' responses? Summarize the relationships that are noticed in each type of graph. Write at least two comparative statements after each graph (in sentence form). Remember to display the data using appropriate titles, labels, scales, and intervals.

12. Use the criteria listed on the Short-Answer Question Rubric to assess the validity of each statement made (see associated file) – this is not a diary entry.

13. Use the Preparation for the Summative Assessment-Checklist to record each student’s progress completing the graphs (see associated file). Make sure you provide formative feedback for each student before the end of the class period since the summative assessment is tomorrow.

14. For the benefit of the class, record the results of the graphs on a larger scale (on the chalkboard or on the overhead projector) - reviewing the correct answers with the students.

15. Discuss the range, mean, median, mode and distribution of data. Review the interpretations that can be made based on the data results.

16. Following this days’ lesson is a summative assessment. See the Extensions section of this lesson for the location of this assessment.

#### Assessments

Formative assessments:

1) Students create two stem-and-leaf plots (one for girls' responses and another for the boys') based on the complete set of data organized by the teacher.
2) Based on the stem-and-leaf plots students correctly identify the range, mean, median, and mode for each plot.
3) Students create a double bar graph (comparing girls' to boys' responses) and two different circle graphs (boys and girls versions).
4) Summarize the relationships that are noticed in each type of graph. Write at least two comparative statements after each graph (in sentence form).

These formative assessments are the last practice opportunities for students before they must show mastery of the specified standards. If students appear to struggles with any of the content, individual tutoring sessions with the student should be established before the summative is administered.

#### Extensions

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
Lesson 4 – Using Statistics to Uncover More Evidence

Directions for using the associated files attached:
1. Page 1 titled Teacher's Observation from the Unit Review should be given to every student. This is the checklist that the teacher will use to assess if the student is prepared for the summative assessment.
2. Page 2 titled Steps for Data Collection serves as a guide for the student and the teacher. This page should be given to each student to help remind them of the steps for data collection and display. This worksheet can also be used to record student's notes from today's class discussion.
3. Page 4 - 9 Activity for Closing the Case allows students the opportunity to practice the concepts taught in this unit. If students have difficulty completing any of the information in this activity, offer additional instruction as needed.

#### Web Links

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

Closing the Case Associated Files     File Extension: pdf