Title: Calculating the Area of a Circle
Sunshine State Standard Benchmark MA.6.G.4.1: Understand the concept
of π, know common estimates of π (3.14; 22/7) and use these
values to estimate and calculate the circumference and the area of circles
Write the Objective
Given six diagrams of circles in which either the diameter or radius
is specified, students will determine the area of the circles using the
formula Area=πR2. Students must show their work and solve
at least five of the problems correctly.
Introduce the Lesson
- Gain Student Attention: Show two Frisbees™ of different sizes.
Ask students if they have ever played Frisbee™ and thought about
how the size of the Frisbee™ might affect how far it will go when
thrown? Tell them that a Frisbee™ or disk is really a circle,
and the surface is called the area. In this lesson, they will learn
how to determine the area of a circle.
- Explain the Objective: Today they are going to learn how to determine
the area of a circle. They will learn how to find the area when they
know the radius of the circle and when they know the diameter. Use the
Frisbee™ to point out the area, radius, and diameter.
- Relate to Prior Knowledge: Use prompting questions and statements
to remind students of the following:
- vocabulary for the parts of a circle: circumference, diameter,
radius (Draw and label the parts on the board.)
- the definition and value of π (π = 3.14 or 22/7)
- the formula for the circumference of a circle (Circumference=πD)
Present the Content
- Knowledge and Skills in Lesson: Students already know vocabulary for
the parts of a circle and the formula for the circumference of a circle.
The lesson content will focus on calculating the area of a circle.
- Teacher and Student Learning Activities:
- Write the formula for the area of a circle on the board and explain
it (Area=πR2). Model and describe several examples,
step by step, using the formula when the radius is known. Use the
Frisbee™ as the first circle.
- Draw circle diagrams and write the problem-solving steps on
a transparency as you explain the examples. Then, have the students
work two problems together with you. Ask prompting questions to guide
learning at each step in the process.
- Repeat the process described above to teach how to determine the
area of a circle when the diameter is known, adding in the extra step
required (dividing the diameter by 2) to find the radius.
- Activity Organization and Support:
- Media Selection: Gather two different-sized Frisbees™.
Secure an overhead projector and transparencies. Prepare two different
worksheets with four circles printed on them for guided and independent
practice. Prepare an assessment including six diagrams of circles,
three with the diameter specified and three with the radius specified.
- Student grouping: The introduction and the content are presented
to the whole class. Guided practice is a small group activity.
Provide Practice and Feedback
- Guided practice: Have students work in groups of four to determine
the area of four circles printed on paper, where either the radius or
the diameter is given. Ask students to follow the problem-solving
steps demonstrated in the lesson, showing their work on the back of
the sheet of paper. After the first problem is solved, have one person
in each group present the steps to the solution discuss it with the
group, After the second problem is solved, have a different group member
present the solution. Continue until all four problems are solved, and
each group member has had a turn presenting the solution. Rotate among
groups to coach students where needed and provide feedback on their
performance. Next, go over all of the problems together with the class,
showing each step in the problem-solving process on overhead transparencies.
Provide feedback on why responses are right or wrong. If needed, provide
additional examples and additional opportunities for practice and feedback.
- Independent practice: Assign a homework exercise for independent practice.
Give each student four circles printed on paper with different areas
than those used in the guided practice activity. Have students determine
the area of the four circles, where either the radius or the diameter
is given. Ask students to show the steps in their work on the back of
the page. Check the homework with the class the next day in the same
manner described for guided practice.
- Judicious review: Preview the remaining lessons in the unit and determine
appropriate places to include a short review of calculating the area
of a circle.
Summarize the Lesson
Remind students they have learned how to find the area of a circle.
Ask them to state the formula used and tell the extra step that must be
taken first if only the diameter is known. Point out that this skill could
be applied to finding the area of any circle, for example, the area of
the top of a round table, etc. Write an additional circle problem on the
board, have students solve it, and discuss responses.
Assess student learning
Determine the procedures: give students a worksheet including six diagrams of circles, three with
the diameter specified and three with the radius specified. The directions
tell students to determine the area of each circle using the formula Area
= πR2 and show the steps in their work.
Describe how to judge performance: students must
solve five out of six problems correctly to demonstrate mastery. The solutions
must include the steps and the correct answer.
For a student who has difficulty maintaining attention and working with
other students in small groups, the accommodations listed below could
- Provide Practice and Feedback: Within the small group, pair the student
with a trained peer who can help keep his or her work on track.
- Monitor the group’s interactions and provide positive reinforcement
to the student for appropriate behaviors.
For a student with poor functional vision the accommodations listed below
could be provided.
- Introduce the Lesson and Present the Content: Make sure the student
can see the visual aids for the lesson by making markings on the worksheets
dark and legible. If needed, provide a large print handout with formulas
and other key points for the student to read at his or her desk.
For a student who has poor fine motor control and writes very large,
the accommodations listed below could be provided.
- Assess Student Learning: Provide extra sheets of paper for the student
to show the steps in the problem solutions so the solution does not
have to fit into small spaces. Let the student use a word processor
to complete the assessment.
in Lesson Design
Access Points (Different Objectives)
for Individual Students
Students working on access points have different learning goals and
objectives for the lesson. The SSS Access Points specify learning goals
at the Independent, Supported, and Participatory levels.
For students working on the access points, the following modifications
could be made:
Independent Level Access Point: MA.6.G.4.ln.a Compare the distance around
the outside of circles (circumference) and areas using physical or visual
- Write the Objective: Given six diagrams of circles of different sizes,
in which either the circumference or area is specified, the student
will correctly Identify the circles with the largest and smallest circumferences
and the circles with the largest and smallest areas. (Note: The student
is not expected to calculate the area of a circle; he or she is learning
a prerequisite skill.
Supported Level access point: MA.6.G.4.Su.a Identify the distance around the outside of circles (circumference) and compare areas of circles using physical models.
- Write the Objective: Given six circles of different sizes, the student will correctly identify the distance around each one and correctly compare the circles with the largest and smallest areas.
Partcipatory Level Access Point: MA.6.G.4.Pa.a Recognize the outside (circumference)
and inside (area) of a circle.
Write the Objective: Given six circles of different sizes, the student
will correctly recognize the inside (area) of at least five circles.
(Note: The student confirms the "inside" of each circle
as indicated by the teacher–"Is this the inside of the
circle?" The student is not expected to know the term in parentheses–area.)
Go to sample lessons: Elementary
Science | Elementary Language Arts
Write Objective | Introduce | Present Content | Practice & Feedback | Summarize | Assess