Gale Schools - Lesson Plans - Secondary - Math - Statistics/Sampling Patterns

Culture

Title: Populations Lab - Cultures Lesson: Statistics / Sampling Patterns

Grade Level: 9

Subject/Content: Integrated/Applied Mathematics

Summary of Lesson: Through the application of math concepts, the purpose of the investigation is to examine the application of statistical sampling, data collection, analysis, and representation that exists in schooling and teenage lifestyles in Japan and the United States, in order to develop an understanding of how cultural differences and similarities exist.

Focus Question: How are the cultural differences and similarities that exist in Japan and United States teenage lifestyles important to a high school student?

Databases(s): Infotrac: Student Edition K12 Graphic Interface, Student Resource Center

Procedures:

Materials needed: Schooling and Teenage Lifestyles handouts, graph paper (5 division/inch) , TI-83 PlusGraphing Calculator, ruler, clip board, loose leaf paper, pencils
After our general review of the prerequisites: statistical sampling, data collection, analysis, and representation, students are randomly placed into groups of four
Each person in the group will participate in the handout activities
Students will participate in a Jigsaw activity
Students will give create questionnaires, collect data, analyze the results, and present these results appropriately
This data will be visually represented using Microsoft Excel chart wizard and the TI-83 graphing calculator
Students will explain answers to follow-up questions appropriately

Steps/Activities by student(s):

Anticipatory Set: Students listen to current popular Japanese musical audio clips. Some can be found at
http://dir.yahoo.com/regional/countries/japan/entertainment/
music/artists/by_genre/rock_and_pop?o=a
Key terms/skills: Students will review the prerequisites including these math ideas: statistical sampling, data collection, analysis, and representation. Sampling types can be found at http://www.csm.uwe.ac.uk/~pwhite/SURVEY1/node26.html
Students should view and discuss information obtained at the Gale Web site in order to complete this lesson:
1. Infotrac: Student edition K-12 Graphic Interface: Keyword search "statistics." View three Encyclopedia excerpts, one book reference on statistics, two periodicals – Statistics never lie... by Nancy Tague, Be careful what you ask for by Daniel Melnick, and Lie, damned lies... by Peter Francese
2. Student Resource Center: Keyword search "statistics." Math & Mathematicians: The History of Math Discoveries Around the World, Gale Encyclopedia of Science. "Sample" Gale Encyclopedia of Science. "Correlation" U·X·L Encyclopedia of Science. "Percent" Gale Encyclopedia of Science. "Japan" Worldmark Encyclopedia of the Nations. "japan culture", under the Magazines & Journals tab, Japan: its people and culture and our and theirs: redefining Japanese pop music
Modeling: Students listen to teacher describe the lesson. Students take notes. Teachers can generate the needed handout from the information provided below
Student Test for Understanding: Students will follow this list of procedures with teacher support.
1. Students participate in the general directions. Students, within their groups, will be assigned questions from the list below. Each student will survey and record at least 10 responses, 5 male and 5 female, from a population of high school teenagers. The ages and genders for each response should be carefully recorded
2. After collecting the data, the results will need to be tallied appropriately. Students should be prepared to share group results in raw numbers as well as percentages
3. Once the group has tallied the data and converted it to percentages, the following will need to be discussed.
  1. What is the sampling type(s) that were used?
  2. Why is it important to know this?
  3. What is the validity level of this survey?
  4. How do you know this?
4. Survey questions:
  1. What is your school's calendar? How long are your Winter, Spring, and Summer breaks? How many days do you attend school each year?
  2. What do you and your classmates do at home after school? What are the most popular after school activities?
  3. How many courses and how many electives do you have each year at school? What is the average class size at your school?
  4. Does you school have a students dress code? What is it? How do you feel about it?
  5. What are the most common reasons students get into trouble at you school? What do you think is the most common juvenile crime in your area?
  6. How many students in your class have jobs? About what percent of upper-class students at your school have jobs? What is your state's minimum age for working?
  7. What is the minimum age to obtain a driver's permit in your state? A license? How many students in your class drive a car?
  8. What percent of students own the following items: watch, bicycle, radio/CD player, air conditioner, stereo, camera, television, video, camera, video game set, piano, motorbike, computer, automobile, ski equipment?
  9. What percentage of students in your school plan to attend college? How many do you think actually will be successful in attending college? How many will graduate?
  10. What athletic teams, clubs, and extracurricular activities are there in you school? Which are you involved with?
  11. How much do students in your class talk about their parents?
  12. What is the average daily schedule for a student in you school?
  13. What role do students have in your school in keeping the building and the grounds clean?
  14. Which do you think is more important to academic success: innate (inborn) or effort?
  15. Does you school have a song, motto, emblem, school code? Are students aware of these?
  16. What are the favorite types of music listened to?
5. In small groups students complete the jigsaw activity. Article information can be found at http://www.cybercypher.com/japan/main.htm and, for U.S. teens, http://www.marketresearch.com/map/cat/1446.html. Each student read, organize, and hare what they found out from their articles. Each student will complete a comparison note page (two column format) with titles Japan teens and U.S. teens
6. Students will answer the following question in essay format – What can these statistics tell us about the different values and way of life of these two groups? How can statistics be helpful in studying culture? What types of things can't statistics help us to discover about a culture?
7. Students will use Microsoft Excel chart wizard in order to create some graphical representations for the data collected in the survey
8. Students will use the TI-Graphing calculator and view screen to display line or histogram plots for data collected.
If students do not have access to the calculators described above, data can be displayed by hand using graph paper
Recap – What did we learn? Explain verbally the important math skills that you utilized. What are important group skills (communication, cooperation, collaboration) used?
Home link – Students answer these basic questions: Why is a sounds understanding of statistical sampling, data collection, analysis, and representation important for this lesson? What is the significance of four sampling techniques? What is the significance of data display types? What does statistics have to do with the cultural comparisons in the lesson? What does Teenage lifestyles in the context of this lesson mean in the context of math in general? Why is this stuff important for you and your life?
Follow-up – Class presentation of the results. Students type a three paragraph summary in proper (Type III format - proper grammar, punctuation, spelling, 5-7 sentences per paragraph, at least ten word per sentence, no sentence starts with the same word in a paragraph.) Paragraph One explains what the lesson was about. Paragraph Two describes what the student learned. Paragraph Three explains how this applied to the individual's own current or future life. The highlights of paragraph three are verbally shared with the class by each student

Outcome: Through the application of math concepts (listed above), the students gain at least an application level understanding of statistical sampling, data collection, analysis, and representation that exists in the context of a cultural comparison.

Related Activities: H.O.T.S. (Higher Order Thinking Skills) --Stresses Bloom's Syntheses and Evaluation levels. Students create an outrageous statistic using cultural data that misleads. Students can create valid questionnaires and data displays in a way that misleads. The following websites might be helpful http://www.bbc.co.uk/dna/h2g2/A1091350 and http://hoa.aavso.org/mathtalk.htm

Standard Date: October, 1998

Content Standard(s):

1.1 Understanding numbers, ways of representing numbers
1.2 Understanding the meaning of operations and how they relate to each other
1.3 Use computational tools and strategies fluently and estimate appropriately
2.1 Understand various types of patterns and functional relationships
2.2 Use symbolic forms to represent and analyze mathematical situations and structures
2.3 Use mathematical models and analyze change in both real and abstract contexts
5.1 Pose questions and collect, organize, and represent data to answer those questions
5.2 Interpret data using methods of exploratory data analysis
5.3 Develop and evaluate inferences, predictions, and arguments that are based on data
6.1 Build new mathematical knowledge through their work with problems
6.2 Develop a disposition to formulate, represent, abstract, and generalize in situations within and outside mathematics
6.3 Apply a wide variety of strategies to solve problems and adapt the strategies to new situations
6.4 Monitor and reflect on their mathematical thinking in solving problems
8.1 Organize and consolidate their mathematical thinking to communicate with others
8.2 Express mathematical ideas coherently and clearly to peers, teachers and others
8.3 Extend their mathematical knowledge by considering the thinking and strategies of others
8.4 Use the language of mathematics as a precise means of mathematical expression
9.1 recognize and use connections among different mathematical ideas
9.2 Understand how mathematical ideas build on one another to build a coherent whole
9.3 Recognize, use, and learn about mathematics in contexts outside mathematics
10.1 Create and use representations to organize, record, and communicate mathematical ideas
10.2 Develop a repertoire of mathematical representations that can be used purposefully, flexibly, and appropriately
10.3 Use representations to model and interpret physical, social and mathematical phenomena

Learning Expectation: Students will apply understanding of concepts related to statistical sampling, data collection, analysis, and representation within the context of Cultures.

Performance Indicators:

At Level 1, the student is able to:
- Write (show basic knowledge for) about the meaning of these: statistical sampling, data collection, analysis, and representation
At Level 2, the student is able to:
- Comprehend and Apply these concepts: statistical sampling, data collection, analysis, and representation
At Level 3, the student is able to:
- Synthesize new ideas related to and Evaluate concepts: statistical sampling, data collection, analysis, and representation

Computer Literacy and Usage Standards 9-12:

Students demonstrate a sound understanding of the nature and operation of technology systems
Students are proficient in the use of technology
Students understand the ethical, cultural, and societal issues related to technology
Students practice responsible use of technology systems, information, and software
Students develop positive attitudes toward technology uses that support lifelong learning, collaboration, personal pursuits, and productivity
Students use technology tools to enhance learning, increase productivity, and promote creativity
Students use productivity tools to collaborate in constructing technology-enhanced models, prepare publications, and produce other creative works
Students use technology tools to process data and report results
Students use technology resources for solving problems and making informed decisions
Students employ technology in the development of strategies for solving problems in the real world

ISTE NETS for Students

Identify capabilities and limitations of contemporary and emerging technology resources and assess the potential of these systems and services to address personal lifelong learning, and workplace needs
Make informed choices among technology systems, resources, and services
Select and apply technology tools for research, information analysis, problem solving, and decision making in content learning
Collaborate with peers, experts, and others to contribute to a content-related knowledge base by using technology to compile, synthesize, produce, and disseminate information, models, and other creative works

Information Power; Information Literacy Standards 1-4:

The student who is information literate accesses information efficiently and effectively
The student who is information literate evaluates information critically and competently
The student who is information literate uses information accurately and creatively
The student who is an independent learner is information literate and pursues information related to personal interests
The student who is and independent learner is information literate and strives for excellence in information seeking and knowledge generation
The student who contributes positively to the learning community and to society is information literate and practices ethical behavior in regard to information and information technology