Teacher: Mr. Cochrane
Grade Level: Grade 8
Subject: General Mathematics
Class Length: 50 min.
Lesson: Exploring the Area of Circles
Unit: Geometry: Using Area and Volume
Lesson Day Number: 1
Objectives
Upon completion of this lesson, TSWBAT:
 Apply the circle area formula to compute the area of circular regions
(cognitive/application)
 Draw a circle with given dimensions (cognitive/synthesis)
 Discuss the cost savings of reducing a Frisbee’s diameter in terms of
cost per Frisbee (affective/responding)
 Assemble a parallelogram from wedges of a paper circle to discover
the circle area formula (psychomotor/manipulating)
Prerequisites
Students must know:
 The definition of a circle and associated terminology
 How to find the radius, diameter, and circumference of a circle
 How to calculate the area of a parallelogram
 How to calculate the cost of an item given the item’s area and the unit
cost of the material
Required Materials/Resources
1. Anticipatory set handouts (150)
2. Calculator
3. Scissors
4. Markers
5. Ruler
6. Circle activity sheets (150)
7. Chalkboard compass
Materials Acquisition
1. Teacher will provide anticipatory set handouts
2. Teacher will provide 5-function calculators to students/groups who do not
possess calculator(s)
3. Teacher will provide safety scissors
4. Teacher will provide markers
5. Teacher will provide rulers
6. Teacher will provide circle activity sheets
7. Chalkboard compass is classroom equipment
Resources
 Geometer’s Sketchpad ® software (for circle activity sheet)
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
Glencoe Mathematics Applications and Connections Course 3 (1999
Edition) textbook (for circle formula discovery ideas)
All other materials and ideas are teacher-created
Notes / Special Information
 Check to make sure the overhead projector functions correctly at least
one day prior to the lesson
Plan
:00 - :05 – Review of circle attributes
 Teacher and students will review circle terminology.
 Teacher and students will review the circumference formula.
:05 - :10 - Anticipatory set
 Teacher and students will read and discuss the anticipatory set sheet.
:10 - :25 – Discovery of circle area formula
 Teacher will construct a circle on the chalkboard with a compass and
label the circle’s center, radius, diameter, and circumference. Students
will observe.
 Teacher will ask the class what other information we may want to know
about the circle. Intended answer: its area. Teacher will ask the class
for reasons why. Students will respond with answers such as how
much pizza you are purchasing, how much material might be required
to make a custom car rim, and how much material a compact disc
requires.
 Teacher will pass around circle examples (compact discs). Students
will use the compact discs as concrete models.
 Teacher will explain that the drawn circle’s dimensions are close to that
of the compact disc’s dimensions. Teacher will ask the class for clever
ways to find the area of the circle. Students will respond with
suggestions. Teacher will ask the students to consider “slicing” the
circle up into sixteen slices (the number of slices is not important) and
placing the slices into the configuration of a parallelogram. Students
will take notes.
 Teacher will have a student helper pass out circle activity sheets while
a helper passes out scissors. Instruct the class to color half of the
circle one color, and the other half of the circle a much different color.
Teacher will instruct the students to cut the circle into the sixteen
required slices, and then arrange them on their desks according to the
pattern on the chalkboard.
 Teacher will draw the circle-slice “parallelogram” on the chalkboard:



Teacher and students will calculate the area of the parallelogram.
Teacher will explain that the area of the parallelogram is A   b  h  .
Teacher will also explain that the base is really the same as one-half of
the circumference of the circle, and that the height of the parallelogram
is the same length as the circle’s radius. Teacher will explain that the
1
parallelogram equation can be thought of as A     C  r  , since
2
1
b  C and h  r . Students will take notes. Teacher will ask the
2
students to consider the previously learned fact that the circle’s
1
circumference is equal to 2 r . So by substitution, A     2 r  r  .
2
Teacher will show that the 2s will cancel out and the r’s will be
multiplied together to form A   r 2 , which is the formula that will be
used for computing the area of circles.
Teacher will instruct the students, unless told differently, to use 3.14 as
an approximation for pi when computing the areas of circles.
Teacher and students will calculate the area of the CD using the
discovered formula.
:25 - :40 – Group activity
 Teacher will instruct the class to look at the anticipatory set questions.
Teacher will read the questions aloud. Teacher will break the class up
into groups of three or four.
 Students will complete the anticipatory set questions in groups.
:40 - :45 – Group reporting
 Groups will report their findings. Teacher will ask the class for
agreement after each group gives their answers.
:45 - 50 – Follow-up activity and homework
 Teacher will summarize the major points of the lesson
 Teacher will assign homework problems
Short-Term Assessment
 Teacher will assess student comprehension on homework exercises,
group activity reports, anticipatory sheet answers, and on the unit
exam.
Long-Term Assessment

Long-term assessment will be performed via the weekly quiz, the unit
exam, and mid-term exam, the final exam, and the SAT-10 normative
assessment exam.
Follow-up Activities
Homework Exercises:
1. Find the area of a circle with a radius of 3 inches.
2. Find the area of a circle if the circle’s circumference is 5 inches and
its radius is .5 inches.
3. Find the area of the given circle.
4. Find a circular object in your house and find its area. Be prepared to
discuss the object and how you found its radius in class. You may bring
the object to class, provided that it does not violate the student code of
conduct.
Challenge Problem. Find the area of a circle if the circle’s circumference is 18
inches.
Self Assessment
Discuss what worked well.
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Discuss what did not happen according to what I wanted to happen.
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Discuss how this lesson could be improved.
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HANDOUT
Area of Circles Anticipatory Set
What we need to recall...



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The parts of a circle (Chapter 7),
How to calculate the circumference of a circle (C=2πr),
How to solve one- and two-step equations
How to calculate the unit cost of an item.
The Problem...
You are the manager of a business that makes Frisbees. Your cost of
materials to make the Frisbees has recently gone up, and you are considering
saving money by making the Frisbees smaller, but still charging the same
price for them. The materials currently cost $0.50 per square inch and your
Frisbees currently have a diameter of 12 inches.
You must find out the cost savings per Frisbee if you reduce the diameter
by one inch, and then by two inches. You must show all equations and work to
avoid making mistakes that could be costly to your business!
At the end of this lesson you will...


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Be able to calculate the surface area of a circle,
Compare the cost savings of reducing the Frisbee’s surface area,
Answer the following questions.
1. What is your savings per Frisbee if you reduce the Frisbee’s diameter by
one inch? Is this a good idea? Show your equation and work!
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2. What is your savings per Frisbee if you reduce the Frisbee’s diameter by
two inches? Is this better than reducing its diameter by just one inch? Why?
Show your equation and work!
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TRANSPARENCY