A Piece of Pi
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This lesson provided by:
Author: Connie Wheeler
System: Shelby County
School: Shelby County High School

General Lesson Information
Lesson Plan ID:
26249
Title:

A Piece of Pi
Overview/Annotation:

This lesson uses graphing to help students understand that pi is a constant and is the slope of the line graphed on a circumference vs. diameter graph.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMS-U Project.

Associated Standards and Objectives
Content Standard(s):
MA2015 (9-12) Algebra 22. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). [A-REI10]

MA2015 (9-12) Algebra 45. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [S-ID6]

a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [S-ID6a]

b. Informally assess the fit of a function by plotting and analyzing residuals. [S-ID6b]

c. Fit a linear function for a scatter plot that suggests a linear association. [S-ID6c]

Local/National Standards:

(NCTM)

1. Understand patterns, relations, and functions

• analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior;

• interpret representations of functions of two variables

2. Represent and analyze mathematical situations and structures using algebraic symbols

• use symbolic algebra to represent and explain mathematical relationships

3. Use mathematical models to represent and understand quantitative relationships

• identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships

Primary Learning Objective(s):

The students will graph data points on a graph and draw the "best fit line". The students will calculate the slope of the line.

Additional Learning Objective(s):

The students will develop the concept that the slope of the line graphed will be pi.

Preparation Information
Total Duration:

31 to 60 Minutes

Materials and Resources:

Graph paper , pencils, various round objects, measuring tape, paper

Technology Resources Needed:

OPTIONAL presentations

document camera could be used for presentation

LCD projector could be used for presentation of graph paper

Background/Preparation:

Teacher will need to gather materials together and have plenty available for measurements along with other materials.

Students will need graphing skills and knowledge of best-fit line and slope.

Procedures/Activities:
1. Students should be placed into cooperative groups.

2. Each group should be supplied with several round objects to measure and a measuring tape.

3. The students should perform the measurements and record each (worksheet Graphing CvsD Activity)

4. Graph the data collected on a circumference vs diameter graph.

5. Draw a line of best fit.

6. Use the line of best fit and calculate the slope.

7. Draw conclusions based on the value obtained for the slope. Write an equation for the line.

Attachments: **Some files will display in a new window. Others will prompt you to download.

Assessment
Assessment Strategies

The worksheet can be graded for accuracy and use the rubric c vs d attached for group participation and graph.

Acceleration:

Students can graph circumference vs radius to determine changes in the graph. Graph paper would be needed.

Intervention:

Each area below is a direct link to general teaching strategies/classroom
accommodations
for students with identified learning and/or behavior problems such as: reading
or math performance below grade level; test or classroom assignments/quizzes at
a failing level; failure to complete assignments independently; difficulty with
short-term memory, abstract concepts, staying on task, or following directions;
poor peer interaction or temper tantrums, and other learning or behavior problems.

Be sure to check the student's IEP for specific accommodations.