Submitted by:

Julie Rape

Date:

Edited by:

Sarah Juarez-Farias

Date:

Unit Name: Team Geometry

Lesson Length:  90 minutes

Overview: In this lesson, students will explore the relationship between the diameter of a circle and its circumference. They will derive the formula for finding the circumference of a circle, and then use the formula to calculate the area of the circles on various playing fields.

DESIRED RESULTS

TEKS and SEs

6.6C /1 The student uses geometric vocabulary to describe angles, polygons, and circles.  The student is expected to describe the relationship between radius, diameter, and circumference of a circle.

Critical Vocabulary

radius, diameter, circumference, pi, perimeter, line of symmetry, chord

Enduring Understandings (Big Ideas)

Essential Questions

Learning Goals and Objectives

Materials Needed

Miras™, string, measuring tapes or rulers, diagrams of playing fields, circles or circular objects of different sizes, calculators

ASSESSMENT PLAN

Performance Tasks

Individual

1.  Students will identify the diameters/lines of symmetry of a given circle.
2. Students will calculate the circumference of circles on sports playing fields.

Other Evidence

Teacher Observation:

During the lesson, the teacher will monitor the partners’ work.  Each partnership needs to be correctly using rulers and accurately measuring the sides of the sample gardens.  The partnerships should be taking turns and working cooperatively to complete the tasks.

LEARNING PLAN

Engage: 

Have students look at different playing fields.  Ask the students to list all the shapes that they find on the fields.  Ask the students what information what they would need to know to be able to draw the lines for each of the fields. (how long the lines are, the perimeter) Draw out the answer perimeter if it is not suggested.  Review how to find the perimeter of polygons.  Ask the students what can we do for the circles since they do not have sides?  Tell students that we are going to explore the parts of circles and how they are related to each other and to the “perimeter” of the circles which is called circumference. 

Explore: 

Give each student a circle and a Mira™.  Have the students use the Mira™ to find a line of symmetry and draw it on the circle.  Ask the students how many lines of symmetry they think they could find on the circle.  Have them draw in several more if they do not see that there is an infinite number.  Share with the students that the lines of symmetry that they have drawn are called diameters.  A diameter is any line segment that passes through the center of the circle and has endpoints on the circle. Also make sure that they understand that there is an infinite number of diameter and lines of symmetry. Also share with the students that the distance from the center to the edge of the circle also has a special name, radius.  Ask the students to define the relationship between the two parts of the circle.

Explain:

Tell the students that these parts of the circle also have a relationship to the circumference that is the same no matter what size of circle.  That is what we will be working on next.  We need to know that relationship to be able to make our circles for the sports field the correct size. 

Have each student use the Mira to find and measure the diameter of a circle.  Next have them take a piece of string and measure the circumference of the same circle.  Using their calculators have the students divide the circumference by the diameter.  Have the students record their data on a class chart on the board or create a class spreadsheet.  Ask the class if they see any patterns in the results.  Ask them why if the relationship is always the same why we didn’t all get the same answers.  Discuss with them why the measurements were not all exactly the same.  Share with them that this relationship is called pi and this is equal to approximately 3.14. 

Elaborate:

Pose the question to the class: If I know what the diameter of a circle is, how can I use that to find its circumference.  Help the students come up with the formula for finding the circumference of the circle.

Evaluate:

Have the students determine the circumference of the circles on the various sports fields using only the radius or diameter.

 Time 

Engage: 5 min.

Explore: 10 min.

Explain: 35 min

Elaborate:  20 min

Evaluate: 20 min

Extension:

Have students practice drawing circles with a given circumference.

Modifications:

Have students use a program, such as Circle Tool.  In this program students can change the radius of circles and chart the resulting circumferences.