Gale Schools - Lesson Plans - Secondary

Math / English > PI Day

Title: PI Day

Author: Rene Ribant-Amthor and Andrew Renaud

Grade Level: 9

Subject/Content: English and Integrated/Applied Mathematics

Summary of Lesson: Through the application of math concepts (listed above), the purpose of the investigation is to examine direct variation, the history of PI, circle circumference and arc length, area and sector area in order to develop an understanding of how these concepts apply to a the PI day project.

Focus Question: How will an understanding of direct variation, the history of PI, circle circumference and arc length, area and sector area play an important role in the development of the project?

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

Procedures:

Materials needed: PI Day handouts, Scientific Calculator, meter sticks, tape measures, PI Day supplies (forks, knives, napkins, pies, pop, paper towel), art supplies (markers, colored pencils, glitter, glue, etc.) clip board, loose leaf paper, pencils
After our general review of the prerequisites: direct variation, the history of PI, circle circumference and arc length, area and sector area, students are asked to participate in the activity in groups of four.
Each person in the group will participate in the PI Day handout activities.
Students will participate in the PI Part 2 activity.
Students will explain answers to follow-up questions appropriately.

Steps/Activities by student(s):

Anticipatory Set: Students will view appropriate clips from the movie PI or one the History of PI. If an appropriate video cannot be obtained, clips or information to motivate can be found at http://www.joyofpi.com/pilinks.html#history
Key terms/skills: Students will review the prerequisites including these math ideas: PI Day handouts, Scientific Calculator, meter sticks, tape measures, PI Day supplies (forks, knives, napkins, pies, pop, paper towel), art supplies (markers, colored pencils, glitter, glue, etc.) clip board, loose leaf paper, pencils.
PI Day directions and worksheets are attached.
Students should view and discuss information obtained at the Gale website in order to complete this lesson:
1. Academic ASAP: Keyword search "PI (number)." Under Magazines & Journals, Let Pi be 3 by Robert N. Anderson, So that's why 22/7 is used for PI! by Maurice J. Burke, and Perimeters, patterns and PI by Sue Barnes
2. Infotrac: Student Edition K12 Graphic Interface: Keyword search "circle" by the Columbia Encyclopedia, "area measurement" by Columbia Encyclopedia, "Pi" by Columbia Encyclopedia, under periodicals, Squaring the circle is no piece of S by Bruce Watson and Spying Pi in the Sky by Science News
3. Student Resource Center: Keyword search "Pi." Math & Mathematicians: The History of Math Discoveries Around the World and Gale Encyclopedia of Science, "circle" U·X·L Encyclopedia of Science, "Archimedes" DISCovering Biography and, under the Magazines and Journals tab, Pi by the billions by Science News
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. PI Day worksheets (attached.)
2. PI Part 2. On a white sheet of paper, create a classified advertisement using PI. You must include illustrations with your ad. Be creative.
3. Students answer follow-up questions related to the project.
Recap – What did we learn? Explain verbally the important math skills that you utilized. What are ideas/skills needed in order to create an accurate timeline?
H.Home link – Students answer these basic questions: Why is a sound understanding of direct variation, the history of PI, circle circumference and arc length, area and sector area important for this lesson? What is the major significance of direct variation utilized? Why would you consider this to be an applied mathematics lesson? What does math have to do with anything that is 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 direct variation, the history of PI, circle circumference and arc length, area and sector area that exists in the context of a PI Day project.

Related Activities: H.O.T.S. (Higher Order Thinking Skills) --Stresses Bloom's Syntheses and Evaluation levels. Students create a "PI Passion Play." They can use poetry, song, or art within their play. They could research historical information on the internet, in books, magazines, journals, and newspapers to demonstrate the importance of PI. They could use these sources as rationale for what things will be like in if there was no PI. They could present all that they learned (and the math utilized during the process.)

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
3.1 Analyze characteristics and properties or two- and three- dimensional geometric objects
3.4 Use visualization and spatial reasoning to solve problems both within and outside mathematics
4.1 Understands attributes, units, and systems of measurement
4.2 Apply a variety of techniques, tools, and formulas for determining measurements
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
7.2 Make and investigate mathematical conjectures
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 direct variation, the history of PI, circle circumference and arc length, area and sector area to the PI day project.

Performance Indicators:

At Level 1, the student is able to:
- Write (show basic knowledge for) about the meaning of these: direct variation, the history of PI, circle circumference and arc length, area and sector area.
At Level 2, the student is able to:
- Comprehend and Apply these concepts: direct variation, the history of PI, circle circumference and arc length, area and sector area.
At Level 3, the student is able to:
- Synthesize new ideas related to and Evaluate concepts: direct variation, the history of PI, circle circumference and arc length, area and sector area.

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