Parts of a Circle
Developed by Paul Hartzer, Spring 2012
Topic: Honors Geometry (10th Grade)
Purpose: This is the second lesson in a unit on the parts and relationships within a circle. The basic textbook is Glencoe’s Geometry, Michigan Edition.
Objectives and Materials
Learn the terms for line segments within a circle: Radius, diameter, chord.
Understand how the radii/diameters of overlapping circles overlap.Identify the pattern of the perimeters of polygons of increasing numbers of sides.
G1.6.2 Solve problems and justify arguments about chords and lines tangent to circles.
Resources and Materials Needed
A ruler with a piece of sticky tack, a pencil, and a fine point white board marker (makeshift compass).
Basic or graphing calculators, one for each student
Introduction and Lesson
Begin by having students consider the skeeball question (“Nested Circles”). This is meant to demonstrate the use of circles in a real world environment most of the students are likely to be familiar with (skee-ball is popular at Chuck E. Cheese’s, for instance).
Once the introductory exercise has been discussed, introduce the basic terminology for line segments (“chord”, “diameter”, “radius”). Make sure that students understand that a diameter is a special kind of chord. To reinforce the concept of equidistance of points in a circle, use the makeshift compass, as follows: Take a standard ruler with multiple holes. Place a piece of sticky tack behind one of the holes for friction and hold the ruler in place with a pencil through this hole. Place the marker through another hole and draw a circle.
Work with students to complete the exercises in the textbook involving radius calculation, overlapping circles, and the relationship between circumference, diameter and radius.
Practice and Closure
Have students complete the “Check for Understanding” practice exercises.
Review the material and assign some problems for homework.
Accommodations and Assessments
Accommodations and Adaptations
As with all material in geometry, use both visual representations and verbal explanations to reinforce concepts. This book is written at a higher register than most of the students can parse, so make sure to explain concepts in more straightforward (if perhaps less mathematically rigorous) terms.
Outcomes, Assessments, and Extensions
As students work on the introductory assignment and check for understanding, monitor for confusion. The students should be able to identify a chord, radius, and diameter, and be able to give at least one of the two formulas for circumference (2πr or πd). Students will be assessed formatively on their classwork and homework, and summatively on the chapter test.
Given how much emphasis is (rightly) placed in pedagogical courses on the importance of tying mathematics to real-world applications, I was very disappointed with the reactions to the skee ball exercise. Most of the students were aware of the game (“we played that last month at Chuck E. Cheese’s,” one informed me), but they were daunted and highly uncooperative with trying the problem. One obstacle was the amount of text: I debated in setting up the problem whether to put the numbers on the picture itself or to provide it as text, as I did. I don’t know whether putting the numbers on the picture would have led to higher complaince, but as it was, students indicated that they thought they were supposed to answer a bunch of questions. Those students didn’t understand that the bulleted list was meant to be background information. I used this feedback to make sure that other warm-ups had clearer scaffolding and objectives.
The rest of the class went smoothly. Students responded well to the material and, based on their work, understood the material.