Summary:

Students in Kathy Scribner's fourth grade class at the Castle Elementary School in Bakersfield, California are asked to try and discover a numeric relationship between the circumference and diameter of circular items in their classroom. After reviewing the meaning of radius (radii), diameter, compass, and center, and after recalling how a circle can be constructed using string and chalk, the students set about the task of gathering data on the circumferences and diameters of "round" things in their classroom. During their search, the teacher assesses if students understand what constitutes a circle. Some students understand that circles are closed figures, but many miss that, for an object to be a circle, every point on its curved plane must be equidistant from a given, fixed center point. Students measure items using appropriate centimeter units, and in a few instances record circumference and diameter dimensions that are accurate enough to approximate pi.

Standard Connection:

(Practice Standard)—In this lesson, Common Core Practice Standard #6—attend to precision—can be detected in two important instances. First, students learn that precision is important in measurements if they are to have any hope of getting close to an approximation of "pi." Second, students begin to understand that precision is needed to communicate relationships found between circles and their parts. Knowing that a circle has one fixed center point from which all other of its points are equidistant endpoints of radii is essential to understanding "circleness." Using language in context and allowing students to debate what is and is not a circle establishes a need for a precise definition for a "circle." Using student-generated data on measurements of circumferences and diameters demonstrates the need for precision to get a reasonably close approximation of pi (π).

(Content Standard)—The domain that captures the mathematics content in this lesson is—Geometry 5.G. Students are being primed to understand the precise definitions of geometric terms and that "attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category." Specifically, in this clip, students are poised to learn, "if circle centers are all placed on one center, all will be instances of concentric circles differing only by radii lengths."

Questions to Consider:

What additional preparation might the teacher do to insure that students understand the definition of a "circle"? What strategies could be used to move students toward greater accuracy and precision in gathering measurement data and in calculating quotients (i.e. C/d = π)?

6. Attend to precision

5.G Geometry