## Search for the Missing Pi

### Brenda YorkBay District Schools

#### Description

Students actively investigate measuring circular objects, recording data accurately to derive the formula for the relationship known as [pi].

#### Objectives

The student uses concrete and graphic models to discover an approximation for ( and creates a formula for finding circumference.

#### Materials

-[Sir Cumference] by Marilyn Burns or [Sir Cumference and Dragon of Pi] by Cindy Neuschwander

-Tape measures provided for each group of two or three students

-Charts for each student for recording data located in associated files

-Rubrics for each student located in associated files

-Written assessment prepared and duplicated by the teacher for each student based upon level of students

-Ample pies for slicing or moon pies for each student for the culmination activity

#### Preparations

1. Duplicate investigation charts, rubrics, and written test for students.

2. Select circular objects to be measured.

3. Duplicate paper tape measures if measuring tapes are not available by using a transparency for duplication.

4. Locate the book to be read aloud to students.

5. Select and duplicate additional teaching tools and materials to be used as support and practice.

6. Be aware of students' prior skills and make accommodations according to knowledge of measurement, decimals, and finding the mean.

#### Procedures

1. The teacher will share the rubric in the attachments with students. Students will then work in groups of two to three students with measuring tapes, finding the circumference and diameter of teacher-selected circular items. For students who may experience difficulties using a tape, the students may cut string to fit the circumference, measuring the string with the tape afterwards.

2. Students will record data of measurements for the circumference and diameter of all items measured on the chart provided in the attachments.

3. Student groups will discuss the results of their findings to infer the relationship between the circumference and diameter known as [pi].

4. Students will examine data for outliers to determine values that may adversely affect investigation results. It should be discussed with students that adverse information may have been the result of a faulty measurement.

5. Students will use calculators and data on their charts to divide the circumference by the diameter for each measured item, recording results to the nearest hundredth or desired rounding place on the chart from their investigation.

6. Students will find the mean for all relationships on their chart. Students should notice that their mean should closely approximate [pi], 3.14. Have each student group find the difference between their investigation mean and [pi]. The student group that worked the most carefully will be the closest to [pi] and may be awarded a reward for the most careful work in solving the mystery of [pi] used in the circumference formula.

7. The class will discuss the activity, applying the information in the formula for the circumference of a circle.

8. A class dicussion will focus on the role of circles in our daily lives and the need for finding the circumference of circles. Students may use the Internet to locate further uses and needs for finding the circumference in daily living. Students who search and find the most examples, may be named the Princes or Princesses of Pi.

9. Students will choose a circular object not used in the investigation, measuring only the diameter of the object.

10. Students will find the circumference of the object applying the formula for the object measured, validating the circumference for accurate work with a tape. All students should bring in their objects for the class to measure. The class will then try to correctly solve which item matches the value of the circumferences provided by each of the students. The teacher may wish to compile a list of items and circumferences previous to the activity. Students who match the most objects correctly with the circumferences have solved the mystery of the phantom [pi].

11. The teacher or a student will read the book [Sir Cumference] by Marilyn Burns or [Sir Cumference and Dragon of Pi] by Cindy Neuschwander to the class.

12. The teacher will provide practice activities, selected materials, and teaching tools to facilitate learner needs.

13. Students may practice online with a quiz at www.mathgoodies.com/lessons/
vol2/circumference.html.

14. Students make a home connection by sharing the investigation of [pi] with their family. Paper tapes may be made.

15. Family involvement can also be provided through the www.harcourtschool.com/
activities/family_involvement/pdf/G06C25NA.PDF.

16. The teacher will hold individual conferences with each student discussing how the student worked cooperatively in groups for a goal.

17. The teacher will complete the provided rubric for each student.

18. The students will complete the written examination with selected problems finding the circumference. The written assessment should be compiled by the teacher to reflect expected learner knowledge and level of the learner.

19. As the search for the missing [pi] comes to a close, students may be rewarded with a piece of pie or a moon pie. Of course, the students will find the circumference of the pie before consuming.

#### Assessments

A rubric assesses the problem-solving process (formative); a written set of problems assesses the application of the formula for circumference using [pi](summative); and the teacher-student conference evaluates the ability to work cooperatively in a group. All materials are located in the associated files.

#### Extensions

Modification in the level of problems can be made, such as rounding to the nearest tenth; older students/parents may be used to assist students needing additional assistance.

As an extension, a historical study of Archimedes may be explored since legend has it that he died while cutting circles, and mathematician Sophia Germaine was inspired by Archimedes and his circles.

Art may be created using compasses, drawing designs with circles. Students will find the sum of the circumference of the circles after art completion. Circles should be drawn in different colors to facilitate measurement.

Students may integrate science energy principles creating balloon vehicles with a specified circumference upon inflation for a path contest.

Students may use sketch pads to do circumference activities.

#### Attached Files

All Around the Circle Rubric.     File Extension:  pdf

All Around the Circle Data Chart.     File Extension:  pdf