Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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## Circumference/Diameter

Video Overview

The class reviews the meaning of radius, diameter, center, and circumference. Students are asked to work in teams to find circular items throughout the room and to record the diameter and circumference of each item on a chart. They must understand the meaning of, and how to measure, these different parts of the circle. After they gather their data, each team selects one item to share with the entire class. These measurements are recorded on an overhead projector. Students are then challenged to find a relationship between the circumference and the diameter. Students determine the circumference of any circle is approximately equal to the diameter multiplied by 3. (However, the exact ratio *, which they have just estimated, is not introduced in this lesson.) After the groups find the relationship, the teacher writes down the equation and the groups compare it to the measurements on the chart.

Topics for Discussion

The following areas provide a focus for discussion after you view the video. You may want to customize these areas or focus on your own discussion ideas.

Discovering Geometric Relationships

1. What generalization or relationship was Ms. Scrivner hoping that students would discover? Describe Ms. Scrivner's techniques for letting students explore the relationship between circumference and diameter. What other techniques could you use?

2. Discuss the benefits of helping students develop an estimate for the relationship of the circumference to the diameter before they are introduced to the ratio of the circumference to the diameter.

3. In essence, students in this lesson were learning about *, the ratio of the circumference to the diameter. Compare how students in this class are learning with how you learned when you were in school.

4. Traditionally, students were told to memorize geometric relationships and generalizations, which turned the learning of geometry into a long list of vocabulary terms to remember. What other geometric relationships could students discover rather than just memorize?

Letting Students Make Choices

1. How did Ms. Scrivner have students develop ownership in the mathematical task in this lesson?

2. What choices were students given in this lesson? What decisions did students have to make as a group?

3. How can a student's understanding be assessed with this task?

4. In their desks, students had mathematics kits that contained various mathematical tools. What are the advantages and disadvantages of giving students mathematics kits as Ms. Scrivner did? What items would you include in a mathematics kit for students?

5. Identify the benefits of building student choices into all lessons; brainstorm ways to make this ideal a reality.

Extension

Developing Activities for Discovering Geometric Relationships

Formulas are nothing more than relationships that someone has already discovered. Investigate and develop activities that help students discover formulas and strategies for finding the areas of various figures, such as rectangles, squares, triangles, parallelograms, trapezoids, and circles. You can then investigate ways that help students discover formulas or strategies for finding the volumes of various solid shapes, such as rectangular prisms, pyramids, cylinders, and cones.

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