Grade level: 9-12     Subject: Algebra for the Technologies

Core Curriculum Objectives:

Given a set of data, how do you find the mean, median and mode? (AT2-A)

How do you use statistical techniques such as frequency tables, stem-and-leaf plots, bar and line graphs, and box and whisker plots, to display data? (AT2-B)

How do you apply your knowledge of data and statistics to solve problems and make informed decisions. (AT2-C)

Overview:

In this unit, measures of central tendency and methods of displaying data will be explored in detail. The lessons include diverse cooperative learning activities, teacher-guided discussions and graphic organizers. The teacher may choose to administer an end of the unit test and/or assign an interactive project that allows for school and community involvement. Emphasis will be placed on the application of skills learned in real-world problems and student created graphs. Every effort should be made by the teacher to use data sets that are student centered or based on school events or issues. At the conclusion of the unit, the learner will be able to determine and apply measures of central tendency, display data in a number of ways and determine which graphs are appropriate for specific data sets and its use.

Purpose/Essential Question(s):

Given a set of data, how do you find the mean, median and mode? How do you use statistical techniques such as frequency tables, stem-and-leaf plots, bar and line graphs, and box and whisker plots, to display data? How do you apply your knowledge of data and statistics to solve problems and make informed decisions?

Time Frame: 7 - 90 minute blocks

Resources and Instructional Materials:

Data sets to use in class examples (info obtained by teacher)

Line graphs examples (extra samples for class activity - sample provided)

Overhead graphic organizer template

Mid-chapter review sheet - Click for printable form. Requires Acrobat Reader

Newspaper sports pages (samples for each class member)

Cord Video--Unit 4 or 19

Cord Video Problem Sheet - Click for printable form. Requires Acrobat Reader

Data Project Rubric

Parental Response Sheet - Click for printable form. Requires Acrobat Reader

Data Gathering Activity Sheet

Teacher created Chapter Review Worksheet - Chapter Test (if needed)

Enter Here Video--Production Scientist (available through School-to-Career

Advisors

Correct and incorrect examples of all graphs for teacher-led lectures (these items must be provided by the teacher.)

Blank Overhead transparencies for group presentations

*Teachers may decide to use the graphing calculator to facilitate a graphing exercise, but emphasis should be placed on student created graphs.

Culminating Assessment:

Students will complete a data project based on the measures of central tendency and various graphing methods covered. Each student will either be given a data set or they may use their own data set if a parent who can attest to its validity signs it. Each data set must have a minimum of 20 items in the data set. An example of a student data set would be # hours spent studying/day, time volunteering at church/week, # hours practicing violin/day, etc. Students will use their data set to find the measures of central tendency and create each one of the graphs listed below. The display should be colorful, creative and reflect the data's theme. Students will be judged by the rubric created using their graphic organizers. The teacher will lead the rubric formation using the guidelines below. Students will be given a Parental Reflection Sheet to be submitted on the project due date. This will allow parents the opportunity to comment on their child's project prior to submission. The teacher may count this as a part of the project grade or as bonus. The final project will be hung either in the hallway or displayed at the school's next PTA meeting.

Items (Graphs) to Include

Measures of Central Tendency (mean, median mode)

Frequency Tables  

Bar and Histograms  

Box-and-Whisker plots

Stem-and-Lean plots  Line Graphs

Rubric Formation:

On day 6 the teacher will display the rubric template and list the major elements of the project. Students will then suggest the most important elements of the measures of central tendencies and the various features of graphing options. Students will then take these elements and, in groups, of two, write what would be unacceptable (needs improvement) and exemplary for each element. Students should use their graphic organizers to assist in identifying the most important elements of the measures of central tendency. (On the rubric template, the first element is provided as an example.) Groups will be randomly selected to report to the class the exemplary and unacceptable elements for the graphs and the measures of central tendency. The teacher will begin to form the project rubric with student input.

Students, before submitting the project, must have their parents comment on areas that they thought were good and areas they thought needed improvement using the Parental Response Sheet.

Instructional Activities:

Cooperative Learning Roles

During many of the following exercises, cooperative learning groups will be referred to. The following roles are appropriate for use during these exercises:

Transcriber: Writes or translates for the group. If work is to be submitted it is the job of the transcriber to neatly submit it.

Communicator: Helps to further explain topics to the group. The communicator is also the only one who can address the teacher.

Problem Solver: Suggests alternate ways of addressing problems. The problem solver must lead the group as solutions are sought.

Manager: The manager ensures that everyone contributes to the group discussion. The manager also reviews the final product to ensure adherence to project guidelines.

Graphic Organizer

According to the lesson plan, students will periodically record elements of each graph studied on the graphic organizer template provided. For instance, line graph might record equal increments on axis, labeled axis, etc. On the back, students will define each graph and give one real-world use.

Homework Problem Set

The teacher will assign their own homework set based on material covered in class and skills needing reinforcement.

Prior to beginning the unit, the teacher will post a blank project rubric on the wall and allow students to periodically contribute exemplary and unsatisfactory characteristics of graphing elements.

Day 1

Essential Question:

Given a set of data, how do you find the mean, median and mode?

Launch Activity:

Divide students into groups of three, each with a cooperative learning role. Distribute different data sets to each group and assign a measure of central tendency to each group. Data sets should reflect various careers (i.e. numbers of male and female nurses in the U.S., number of gold medals won in the Olympics last year, free throw percentages per game of a popular player on the school team, etc). Post the definitions of mean, median and mode and have groups determine their measure of central tendency based on the group's data set. Students must extract mathematical meaning from the definitions. A representative from each group will report the group's findings to the class, focusing on their thought processes. The teacher should post group findings and thought processes in the class and refer to them as the formulas are introduced. The teacher should summarize the launch activity by discussing the misuses of statistics.

Interesting data sets can be retrieved from the following web site:

www.espn.go.com\mlb\ (click on statistics in left column)

Class Activities: Finding the mean, median and mode.

Cognitive Teaching Strategies:

1. The teacher will lead the class in appropriately defining the measures of central tendency and discussing how they apply to statistics. The teacher will provide examples of finding the mean, median and mode as well as the effect of outliers on data sets. Connections should be made to the students' launch activity.

2. The teacher will guide additional examples, allowing students time to work on the first portion of the problem and pausing to allow students to correct and modify prior work before completing the problem. The following data sets may be used: the week's high temperatures, an anonymous student's test scores, or weekly salaries of students in the class.

(Note: The teacher must gather this data from members of the class. This will grab the student's attention and increase retention.)

3. Students will determine the mean, median and mode of each data set. Examples should be given until student's can successfully determine the mean, median and mode.

Examples of data sets are as follows.

**Number of staff members/department

**Number of women staff members/department

**Number of food offerings/food group

**Types of cars in student parking lot

The time sheet has a sample tally sheet on the top to guide students. The actual tally must be done on the tally sheet. The time that each piece of data was collected must be recorded so that time is not wasted.

4. Before the students are allowed to leave the classroom, the teacher must establish a clear standard of behavior and academic integrity for the assignment. All students must be aware of consequences and clearly understand the assignment. Be certain to emphasize that students must gather authentic data that can be verified.

5. Once students return from gathering data, they will then find the mean, median and mode of the individual data sets. Each group must provide feedback (at least 1 success and 1 difficulty) to the teacher in writing and post both the feedback and data collected in the classroom. The teacher should circulate around the classroom and gather thoughts from students immediately and troubleshoot, where necessary.

5. The teacher will answer all questions concerning the objective and assign the homework problem set.

HOMEWORK PROBLEM SET

_______________________________________

Summarizing Strategy:

1. 3-2-1 Strategy

Each student must write a response to each of the following and submit prior to leaving.

3--List measures of central tendency

2--Ways you could use what you learned today

1--Conclusion you've drawn about the effect of outliers on a data set

Day 2

Essential Question:

How do you use statistical techniques such as frequency tables, bar graphs and histograms to display data?

Activator:

Have students begin to construct the graphic organizer using the measures of central tendency (Day 1) on the template provided. Students must define each measure on the back of the graphic organizer and tell how it can be used in the real world. After students have completed their graphic organizer, they will identify the most important elements of each measure of central tendency and begin to fill in the project rubric posted in the classroom.

Class Activities: Creating frequency tables, bar graphs and histograms

Cognitive Teaching Strategies:

1. Display an exemplary and unsatisfactory 3-2-1 activity from Day 1 summarizing strategies. The teacher will offer all students the opportunity to suggest ways to improve each entry. This exercise will allow students to appropriately create an effective 3-2-1 activity.

2. Review homework set.

3. Teacher will define and show examples of frequency tables.

4. Students will then create a data set using information from their classmates on the board. (Topic example: number of birthday's in each month.)

Each student will create a frequency table using the data. Students will take turns discussing ways the data can be used.

5. The teacher will then explain the difference between a bar graph and a histogram and show examples of each. The teacher must emphasize the importance of horizontal and vertical axis and the intervals for each graph. The teacher will show incorrect examples of bar and histograms and students will help identify mistakes in the example graphs.

6. Students, in groups of two with assigned roles, will then create a bar graph and a histogram using the birthday data. Students must discuss the differences between frequency tables, bar and histograms and instances in which each would be most beneficial with their group. Each group must report one difference and a real-world use to the class. The teacher will post group responses on an overhead transparency for use during the student review session and ask groups to post graphs on board for other groups to check their graphs.

7. The teacher will answer all questions concerning the objective and assign the homework problem set.

HOMEWORK PROBLEM SET

_______________________________________

Summarizing Strategy:

1. 3-2-1 Strategy

Each student must write a response to each of the following.

3--Measures of central tendency

2--Ways to display data and a sketch of each

1--Difference between a bar graph and a histogram

Day 3

Essential Question:

How do you use statistical techniques, such as stem-and-leaf plots, to display data?

Activator:

1. Have students continue to construct the graphic organizer using frequency table, bar graph and histograms on the template provided. Students must, on the back of the graphic organizer, define each and tell how each may be used in real-world situations.

2. Students will watch the Enter Here video--Production Scientist and write at least 3 skills they would have to master to be successful in this particular job. (This video features acquiring and evaluating, interpreting and communicating and organizing and maintaining information.)

Class Activities: Creating stem-and-leaf plots

Cognitive Teaching Strategies:

1. Review homework set.

2. The teacher will prepare students to complete the graded Mid-Chapter review by asking them to count the number of times they blink their eye in 2 minutes. The eye-blank data will be used on the Mid-Chapter review sheet. This data should be put on the board prior to distributing the Mid-Chapter review. Students will then complete the Mid-Chapter review. Allow students to work individually on this graded activity.

3. The teacher will have students list the date of their birthday on the board when they pass in their graded activity. Once each student has completed the assignment, the teacher will explain the uses of a stem and leaf-plot and take students through an example using their birthdays.

4. The teacher will guide students through another stem-and-leaf plot, answering questions when posed by the students.

5. Cooperative learning roles will be assigned and students will be placed in groups of two. Each group will be given a page out of the newspaper sports section. Students will create a stem-and-leaf plot for the sports data provided (batting averages, field goal %, etc).

6. The teacher, prior to groups completing the task, will show an example of stem-and-leaf plot using the sports page. All students must suspend work on their own assignment and participate in the discussion. Adequate time for each group to correct or modify their assignment will then be provided. All group work will be posted in the classroom. The teacher will circulate around the room ensuring that student graphs are correct.

7. Groups will then circulate around the room with post-it notes. Students will draw conclusions based on each group's graph and attach it. Once all groups have drawn conclusions on all graphs, each group will claim their original graph and critique the conclusions or, if necessary, modify the graph.

8. The teacher will answer all questions concerning the objective and assign the homework problem set.

HOMEWORK PROBLEM SET:

____________________________________________

Summarizing Activity:

1. Have students continue to construct the graphic organizer using stem-and-leaf projects on the template provided. Students must, on the back of the graphic organizer, define stem-and-leaf plots and tell how it may be used in real-world situations.

2. Students will continue to work in groups and take the stem-and-leaf plot from the class example (birthdays) and find the mean, median and mode of the data set as well as create a histogram for the data set. The teacher will circulate around the room and suggest revisions prior to completion.

Day 4

Essential Question:

How do you use the box and whisker plots to display data?

Activator:

1. The teacher will lead students as they contribute exemplary and unacceptable elements of frequency tables, bar graphs, histograms and stem-and-leaf plots to the project rubric. Students should use their graphic organizers as a reference.

2. Teacher will show the Cord Applied Mathematics unit 4 or 19 video. Students will complete the problem at the end of the video and submit it. A video problem worksheet is provided.

Class Activities: Creating box and whisker plots

Cognitive Teaching Strategies:

1. Teacher will review homework problem set.

2. **Only for Project Class** Encourage students to begin thinking about a data set they may like to use on the project. Encourage them to bring in the data set for prior approval.

3. The discussion will begin with a review focusing on how to find the median. Several examples should be provided.

4. Students will then be asked to look at a data set, like the one below, and individually determine the median.

115, 108, 112, 120, 110, 104, 108, 102

5. The teacher will give detailed instructions on the box-and-whisker construction process and the parts of the box-and-whisker plot. The teacher will then lead students through a sample the box-and-whisker plot, focusing on the quartiles.

6. Pre-established box-and-whisker plots, like the one below, will then be displayed, and students will answer teacher directed questions about the pieces of the plot and the quartiles.

Data Set - 35, 42, 48, 43, 51, 39, 57

7. Students will then work in groups of two, with assigned roles, on the following box-and-whisker plots. Each group will receive a tally of the 1,2 or 3 point baskets scored by school basketball players during a season.

8. From this data, they will create a box and whisker plot using the data. Each group should only get one point type. For instance, group 1 will receive Player A's 1 point baskets scored during each game, group 2 will get Player A's 2 point baskets scored during each game, and so on. Each group will complete the plot and submit for display.

9. **This data should be displayed in a prominent area of the gym, preferably in an area frequented by basketball players.**

10. The teacher will then ask the students what the strengths and weaknesses of the box-and-whisker plots are and in what situations it can and cannot be appropriately used. Through the discussion, the teacher will discuss application pitfalls.

11. The teacher will answer all questions concerning the objective and assign the homework problem set.

HOMEWORK PROBLEM SET: 

STUDENTS WILL FINALIZE THEIR DATA SETS FOR THE PROJECT. THE DATA SET MUST BE TURNED IN ON DAY 5. Students will also be assigned box and whisker plots problems.

Summarizing Activity

1. Students will be asked to add box-and-whisker plots and stem-and-leaf plots to the graphic organizer with the appropriate support information.

2. Students will be shown examples of line graphs and will be asked to bring in examples of line graphs the following class period.

3. Ticket to Leave Activity

Each student must respond to the following statement.

Describe the steps to form a box and whisker plot. Make sure to address parts of the plot, use the data set below, and write in complete sentences.

8,16, 23, 24, 13, 7,1,19, 24

Day 5

Essential Question:

How do you use line graphs to display data?

Activator:

1. The teacher will lead students as they list the characteristics of line graphs, histograms, box-and-whisker plots and stem-and-leaf plots on their graphic organizer. Students should be reminded that various ways of displaying data are being explored in the unit and that line graphs are yet another way to display data.

2. Have students take out the example of line graphs that they've brought. (The teacher should also have several examples ready for students who don't have one.) Place students in groups of four. Have them list the common elements of the line graphs in their group on their individual graphic organizer under Line Graphs. Call on several groups to read their list. Students should begin to realize that the same elements continue to emerge.

Class Activities: Creating line graphs

Cognitive Teaching Strategies:

1. Review homework set.

2. **Only for Project Class** Students will submit data sets for approval.

3. While in groups of four, students will be assigned roles and asked to create their own data set for today's activity. (Note: The students will create their own data set using information from their group members-- hourly wage of group members over past two years, number of credits earned over high school career (9th, 10th, 11th, etc.)

4. The teacher will circulate around the room ensuring that students are choosing appropriate data sets and that group data is being gathered.

5. The teacher will then re-emphasize the importance of correctly drawn axis and appropriate intervals by showing examples of incorrect line graphs. Several examples should be thoroughly discussed.

6. Students will then take their group data and begin to construct their line graphs. The teacher will circulate around the room to uncover any mistakes being made by the group prior to submission.

7. The teacher will answer all questions concerning the objective and assign the homework problem set.

HOMEWORK PROBLEM SET

_______________________________________

Summarizing Strategy

Students will complete their graphic organizer and submit for teacher approval.

NOTE: The teacher may choose to give the chapter test either before or after the project is due. Because the project contains all elements of the chapter, the teacher may also choose to grade the project rather than administer the test.

Day 6 - Project Workday or Test Review Day

Essential Questions:

Given a set of data, how do you find the mean, median, and mode? How do you use statistical techniques such as frequency tables, stem-and-leaf plots, bar and line graphs, and box and whisker plots, to display data?

Launch Activity:

Students will be introduced to the four-step problem-solving plan. These steps will be given application problems from the text involving line graphs. As students complete their line graphs they will be asked to identify the steps of the problem-solving plan they used.

Test Cognitive Teaching Strategies

1. The teacher will review, through guided lecture, the important aspect of each graph type and display examples of each. All student questions concerning graph types will be answered.

2. Students will complete a Chapter Review worksheet created by the teacher. Students should be allowed to work individually and then be paired with a partner to check the work.

3. Student groups will then take turns explaining a problem to the class. Each group will draw a number from a hat to determine which question they will explain. They must answer all class questions. One student must explain the group's answer and the other must tell at least two benefits of the graph type involved.

4. The teacher will act as facilitator and focus student learning, discussions and behavior.

Test Summarizing Activity

1. Students will submit the 3-2-1 activity below (no notes or text)

3--important aspects (rules, parts) of the graph type of your choice

2--important aspects of another graph type of your choice

1--list of the measures of central tendency

Project Cognitive Teaching Strategies

1. Students will follow the teacher as the project rubric is completed using the guidelines under Culminating Assessment. The teacher will make every effort to ensure that all students know what is expected of them and how their project will be graded. The teacher will then type the rubric and copies of the rubric will be distributed to all students the next day, with the project due on the following day.

2. Students will then each be given a different set of data. If students can bring in their own legitimate data set, they may be allowed to use it if a parent who can attest to its validity signs it. Each graph type previously covered must be created using their data set and neatly presented on poster board. Students will be judged using the rubric created using their graphic organizers. The teacher will guide its production. The display should be colorful and creative. The resulting product should be hung either in the hallway or displayed at the school's next PTA meeting.

Items to Include

Measure of Central Tendency (mean, median mode)

Frequency Tables

Stem-and-Lean plots

Box-and-Whisker plots

Bar and Histograms

Line Graphs

3. Students will be given the remainder of the class period to work on their project. The teacher will serve as a facilitator and monitor graph creation as well as behavior.

Project Summarizing Strategy