Ohio Resource Center
Lessons
Exploring c/d = pi
Discipline
Mathematics
5, 6, 7
Professional Commentary

Students measure circular objects to collect data to investigate the relationship between the circumference of a circle and its diameter. They find that, regardless of the size of the object or the size of the measuring unit, it always takes a little more than three times the length of the diameter to measure the circumference. Students then plot the ordered pairs (diameter, circumference) on a coordinate graph and analyze the results. Guiding questions, summary questions, assessment tasks, and lesson extensions are included. (author/sw)

Common Core State Standards for Mathematics
Standards for Mathematical Practice
CCSS.Math.Practice.MP5
Use appropriate tools strategically.
CCSS.Math.Practice.MP6
Attend to precision.
Geometry
Graph points on the coordinate plane to solve real-world and mathematical problems.
5.G.A.2
Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
Ratios and Proportional Relationships
Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
1. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
2. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
3. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
4. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Geometry
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
7.G.B.4
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.
Ohio Mathematics Academic Content Standards (2001)
Measurement Standard
Benchmarks (5–7)
C.
Identify appropriate tools and apply appropriate techniques for measuring angles, perimeter or circumference and area of triangles, quadrilaterals, circles and composite shapes, and surface area and volume of prisms and cylinders.
3.
Estimate perimeter or circumference and area for circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by: a. estimating lengths using string or links, areas using tiles or grid, and volumes using cubes; and b. measuring attributes (diameter, side lengths, or heights) and using established formulas for circles, triangles, rectangles, parallelograms and rectangular prisms.
Geometry and Spatial Sense Standard
Benchmarks (5–7)
B.
Draw circles, and identify and determine the relationships among the radius, diameter, center and circumference.
1.
Draw circles, and identify and determine relationships among the radius, diameter, center and circumference; e.g., radius is half the diameter, the ratio of the circumference of a circle to its diameter is an approximation of .
Patterns, Functions and Algebra Standard
Benchmarks (5–7)
F.
Use representations, such as tables, graphs and equations, to model situations and to solve problems, especially those that involve linear relationships.
5.
Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions.