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This lesson provided by:
Author: Sara Wheeler
System: Calhoun County
School: Alexandria High School
General Lesson Information
Lesson Plan ID:
26202
Title:
Discovering Pi
Overview/Annotation:
This lesson allows students to discover the number Pi. By measuring real life objects, students will get to see where the number Pi comes from as well as how the circumference formula is derived.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Associated Standards and Objectives
Content Standard(s):
MA2015 (6) 13. Write, read, and evaluate expressions in which letters stand for numbers. [6EE2]
a. Write expressions that record operations with numbers and with letters standing for numbers. [6EE2a]
Example: Express the calculation, "Subtract y from 5," as 5  y .
b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient ); view one or more parts of an expression as a single entity. [6EE2b]
Example: Describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in realworld problems. Perform arithmetic operations, including those involving wholenumber exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). [6EE2c]
Example: Use the formulas V = s ^{3} and A = 6s ^{2} to find the volume and surface area of a cube with sides of length s = ^{1} /_{2} .
MA2015 (7) 14. Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [7G4]
Local/National Standards:
NCTM
Measurement 68
Understand both metric and customary systems of measurement.
Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.
Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of morecomplex shapes.
Primary Learning Objective(s):
The student will be able to obtain measurements of various objects and record the data in a table. The student will be able to analyze results by performing computations on the data acquired. The student will understand the number Pi and the derivation of the circumference formula.
Additional Learning Objective(s):
Preparation Information
Total Duration:
31 to 60 Minutes
Materials and Resources:
A variety of round objects (plates, buttons, cups, etc.), tape measures (1 for each group), Discovering Pi Worksheet  attached (1 for each group), paper, pencil, calculator, chart paper, cookies and napkins (optional), circle cutouts for grouping purposes (see step 2 in procedures)
Technology Resources Needed:
Computer with Internet access connected to a television or LCD projector
Background/Preparation:
Students should already be familiar with parts of a circle and the terminology associated. Click here to view an interactive site that shows parts of a circle.
Procedures/Activities:
1. Prior to the lesson, ask students to bring in several flat, round objects to measure.
2. Divide students into groups of two (or three, depending on class size). Before class, cut out enough circles for each student in the class. Write two of each number and have them find their partner by matching up numbers. For example, if you have 20 students, write 2 of each number 1 through 10 on each circle. Mix them up and hand each student one circle as they walk in the room. Distribute one tape measure to each group and make sure that each group has at least 5 round objects to measure (including a cookie and napkin). If not, use some that you brought from home. Distribute 1 copy of the Discovering Pi worksheet to each group.
3. For each object, have the students fill in the table by measuring with the tape provided. They may have a hard time finding the distance around. Let them troubleshoot to discover an efficient method. If hints are needed, have one person hold the object and the end of the tape while the other wraps the tape around.
4. Once the table is complete, have each group compute an average for the last column ("Distance Around ÷ Distance Across"). I allow my students to eat the cookie when they finish filling out their table. They LOVE this part!
5. While students are working, create a table on a piece of chart paper with a line for each group to record their results. See Sample Table worksheet attached. Have students come and write down their average for the class to see.
7. Ask students if they see a relationship in the results and if the numbers look familiar. The "Distance Around" (circumference, C) divided by the "Distance Across" (diameter, d) is approximately equal to Pi!
8. To derive the circumference formula, write out C/d = ∏. See if a student can solve this formula for C. (Multiply both sides by d and you get C = ∏×d, which is the circumference formula.
Attachments: **Some files will display in a new window. Others will prompt you to download.
Assessment
Assessment Strategies
Informal assessment can be performed while students are working. Check for student understanding on measurement, recording data, and calculating results.
For drill and practice problems, use this link to have students work out the problems on paper and turn them in before they leave. Allow them to remain in the cooperative groups and work together if needed.
Acceleration:
For those students that would like to explore the number Pi further, have them access this link . It will take them to a worksheet that gives many different approximations of Pi. Have them use their calculator to verify each approximation.
Intervention: