Ohio Resource Center
Lessons
Pi Line
Discipline
Mathematics
8, 9, 10
Professional Commentary
This lesson is a nicely creative extension of a lesson in which students measure the diameter and circumference of several circular objects to arrive at an approximation of pi. In this lesson, students use strips of masking tape to measure the diameter and circumference of various circular objects, create a graph using the strips of tape, and relate the slope of the line to pi, the ratio of circumference to diameter. An activity packet, overheads, graphing tools, discussion questions, suggestions for assessment, extensions of the lesson, and prompts for teacher reflection are included. (author/sw/js)
21st Century Transformative Skill:

The method of plotting points on a diameter-circumference graph is so unique that students will necessarily come away with a different and deeper perspective on the meaning of pi. (sw)

Common Core State Standards for Mathematics
Expressions and Equations
Understand the connections between proportional relationships, lines, and linear equations.
8.EE.B.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
Functions
Use functions to model relationships between quantities.
8.F.B.4
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
High School - Functions
Interpreting Functions
Interpret functions that arise in applications in terms of the context
HSF-IF.B.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
Construct and compare linear, quadratic, and exponential models and solve problems
HSF-LE.A.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Interpret expressions for functions in terms of the situation they model
HSF-LE.B.5
Interpret the parameters in a linear or exponential function in terms of a context.
Ohio Mathematics Academic Content Standards (2001)
Patterns, Functions and Algebra Standard
Benchmarks (8–10)
E.
Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros.
J.
Describe and interpret rates of change from graphical and numerical data.