Area of Circles

This lesson is based from the textbook Holt Middle School Math:  Course 2.
Bennet, J.M., Chard, D.J., Jackson, A., Milgram, J., Scheer, J.K., Waits, B.K.  (2004).  Holt middle school math:  Course 2.  Orlando:  A Harcourt Education Company.

Lesson Title:  Finding Areas
Grade Level:  7th grade                                    
Course Title:  Compacted Math
Time Allotted:  1 class period                     
Number of Students:
  24-34 students                             
Extra Information About Students: 
None
Day 5


Goals and Objectives:

According to the NCTM Principles and Standards of Mathematics, the following standards are met in this lesson:
1.   To understand measurable attributes of objects and the units, systems, and processes of measurement.

2.   To apply appropriate techniques, tools, and formulas to determine measurements.

According to the NCSCOS, the following standards are met in this lesson:

1.   Competency Goal 2:  The learner will demonstrate an understanding and use of the properties and relationships in geometry, and standard units of metric and customary measurement.

Goals:


Materials Needed and/or Use of Space:

Math Fact of the Day:

What do you call a crushed angle?
       A rect-angle


Problem of the Day:

A 16 in. pizza sells for $11.99.  A 10 in. pizza sells for $5.99.  Which size gives you more pizza per penny?  Explain.


*NOTE:  Throughout this lesson, I use pi to symbolize 3.14 and the ^ sign is used to show that something is raise to a power.  For example, r^2 means "r squared".

Motivational Activity:

The students will learn about how to find the area of circles today.

Lesson Procedure:

Yesterday we learned how to find the area of triangles and trapezoids.  Today we are going to discuss how to find the area of circles.  We are going to do this first by deriving the formula for the area of a circle ourselves.

This activity was found at http://www.education-world.com/a_tsl/archives/00-2/area_of_circle_doc.shtml.

The objective of this activity is for students to form a rectangle by partitioning a circle and relate A = bh to A = pi r^2.

Here is a chart similar to those we looked at the past two days to help you understand how to find the area of a circle, along with a picture to help you learn.

AREA OF A CIRCLE

The area A of a circle
is the product of
pi and the square
of the circle's radius r.


A=pi*r^2
f

*Make sure that the students are reminded that the variable r in this formula works as a placeholder for the actual value of the radius.  Since r is squared, you must also square the value.  We cannot forget to square our value r.

Example 1:  Find the area of the circle.

*NOTE:  Remind the students that pi is approximatley 3.14, thus, we will substitute 3.14 for pi when calculating the area for circles.

f

We use the formula and substitute for r.
A=pi*r^2
A=(3.14)(3 m^2)
A=(3.14)(9 square meters)
A= 28.26 square meters.

Thus, the area of the circle is 28.26 square meters..

Example 2:  Find the area of the circle.

c

*NOTE:  Be careful - we are given the diameter, not the radius.

Since the radius is 1/2 of the diameter, we can find the radius by r=d/2.
So, r=10/2=5 cm
Now let's find the area of the circle.

A=pi*r^2
A=(3.14)(5^2)
A=(3.14)(25)
A=78.5 square centimeters.

Thus, the area of our circle is 78.5 square centimeters.

Example 3:  There are circular fields located in the Wadi Rum Desert in Jordan.  On these fields, crops are grown on circular patches of irrigated land.  If the radius of one irrigated field is 60 feet, what is the area of the field?  Round your answer to the nearest whole number.

So, we know that r=60 feet.  Let's find the area!

A=pi*r^2
A=(3.14)(60^2)
A=11,304 square feet.

Thus, the area of the field is is about 11,304 square feet.

Extension:

If an extension activity is needed, the students can think and write responses to the following questions:

Closure:

As you can see, we have learned how to find the area of circles.  We first derived this formula by starting with a circle and manipulating the circle to see how we could find the area of the circle.  We discussed at the beginning of class the example with the pizza and how we could find the better buy simply by finding the area of each pizza and comparing the prices.  This is something that you would use in your everyday lives.  Tomorrow we are going to discuss how we can apply the concepts that we have learned in the past week to the real world. 


Assessment:

 
Evaluation of Lesson Upon Completion:

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