Circles in Action
Jennifer Moore
Johnson City Schools
th
6 Grade
Lesson Title:
Circles in Action
Grade:
6
Alignment with State Standards: GLE 0606.4.3 Develop and use formulas to
determine the circumference and area of circles, and the area of trapezoids, and
develop strategies to find the area of composite shapes.
Math Goals:
1. The students will solve contextual problems involving area and circumference of
circles through the use of literature, media, and hands on experimentation.
2. The students will calculate with circumferences and areas of circles.
Students’ Needs: The students must be able to define and label the parts of a circle;
including a chord, arc, radius, diameter, circumference, and area of a circle. Having the
basic geometry and measurement vocabulary is critical to the success of this lesson.
See “Parts of a Circle” handout. Also see
http://www.brainpop.com/math/geometryandmeasurement/circles/ for an introductory
lesson on circles and http://www.brainpop.com//math/numbersandoperations/pi/activity/
for a hands-on activity that includes graphing on a coordinate plane to build an
understanding of circumference and pi. These activities would be beneficial to use prior
to this lesson.
Materials:
Literature- Sir Cumference and the Dragon of Pi A Math Adventure by Cindy
Neuschwander, illustrated by Wayne Geehan
Media1. Pi BrainPOP Video describing both Pi and circumference (running time is about
2 ½ minutes)
http://www.brainpop.com/math/numbersandoperations/pi/
2. Pi BrainPOP Quiz, great assessment to check students’ understanding. Can be
used formally or informally.
http://www.brainpop.com/math/numbersandoperations/pi/quiz/
3. Brainingcamp, wonderful site that walks you through a circumference lesson. It
is both interactive so students can deepen their understanding of the skill and
has questions at the end that will test students’ knowledge of the concept.
http://www.brainingcamp.com/content/concepts/circumference/lesson.php
4. Teacher Tube Video, excellent song to help students remember the formulas for
finding area and circumference.
http://www.teachertube.com/viewVideo.php?video_id=38335&title=Circle_Song_2
Note: If you are not a subscriber of BrainPOP or Brainingcamp, you can sign up for a free trial.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Other MaterialsParts of a Circle Handout (use prior to lesson)
Circumference Graphic Organizer (Versions 1 & 2)
Bubble Experiment Data Sheet
Pi & Circumference Extended Practice Page
Pi BrainPOP Quiz
Ticket Out the Door
13 bottles of bubbles with wands
Black construction paper
Yarn
Rulers
Dry erase boards and dry erase markers
Lesson Plan:
Before
Note: This lesson can take several days depending upon how much time you have in a
math block. If you only teach math, the room can remain set up until the lesson is
completed.
PART I- Leading up to the lesson.
The room will be set up before students arrive. The handouts (in packet form), black
construction paper, bubbles, rulers, yarn, dry erase boards, and dry erase markers will
be placed at each pair of desks. Students will be asked to not touch anything until they
have been given the signal to begin. Having the room ready before the students walk
in will encourage their curiosity and build excitement while saving class time by being
organized and well prepared. Before diving into the lesson, I will have the Parts of a
Circle handout projected on the board. Together, we will review the parts of the circle.
One student at a time will come to the board and label the parts of the circle. Once the
circle and formulas are labeled (except the circumference formula), I will ask the
students to brainstorm ways we can find the circumference of any circular object. This
will be discussed within partner groups, and then I will ask the groups to share with the
class. We will record our ideas on the board.
Next, the students will turn to their Pi BrainPOP Quiz located in their packet. A few
minutes will be given for them to look over the questions. They should already be able
to answer many of the questions since Pi has been taught. I will play the Pi BrainPOP
quiz as a quick review, and the students can answer questions as the clip plays. If they
do not finish, they can finish at the end of class or take it home for homework. This is
being used as an assessment of the skills retained up to this point in the unit. It will be
collected for a grade.
PART II- Activating Strategy
I will read the book, Sir Cumference and the Dragon of Pi A Math Adventure. As I read,
I will ask the class the following questions:
-
-
When measuring the middle of the circle, what exactly are you measuring?
Page 13
How do you measure around a circle? What strategies could be used?
What is the distance around a circle called? Page 13
Why do you think the poem said to divide so a number can be found?
Page 13
How many strips of dough went around the pie? What do you think that
represents? Pages 16 & 17
What did Radius find when he measured the outside edge of the wheel by
the inches across the middle? What is another name for the quotient he
found? Page 19
Was Radius’s conclusion reasonable? Could the distance around the
dragon circle really be three and one seventh times the distance across it?
Does that make sense? Page 24
The book not only serves as a review of the prior lessons taught but also gets the
students thinking about how Pi and circumference relate. Also, the very last set of
questions I listed from page 24, can help students discover the formula for finding the
circumference of a circle. Once this discovery is made, students should add the formula
to their Circumference Graphic Organizer. Version 1 does not have the formulas, but
Version 2 does. Version 2 may be used with students that have special needs. You
may even choose to call on a student that is using Version 2 and allow them to give the
formula to the rest of the class. This usually boosts their confidence and gets them to
participate on a regular basis that they may not have other wise. The graphic organizer
has three ways to write the formula. The formula using the diameter was given in Sir
Circumference and the Dragon of Pi. Lead the class into discovering a way to write the
formula when the radius is given. You may ask, “How does the radius compare to the
diameter?” They should tell you the radius is half of the diameter. Then push them to
writing a formula for this. They should be collaborating with their partners. I will walk
around the room, and if a group is struggling, remind them that the radius is two times
the diameter. This should get them to say two times the radius, times pi.
Asking questions throughout the book keeps the students engaged, active, and leads to
discovery in their learning. Thoughtful answers may be worth candy to reward
participation!
PART III- Teaching
Step 1:
Play the Brainingcamp clip on circumference. This website has three components:
lesson, interactive, and questions. As the lesson is playing, I will ask questions and
have the students elaborate. For example, the clip states that the ratio of the
circumference to the diameter of a circle is a number called Pi. I will ask students to
explain or prove this. How do they know this is true? What have they learned about Pi?
Secondly, the interactive component allows students to change the measure of the
radius which increases the circumference of the circle. This gives students an instant
visual to link the relationship between radius and circumference. I will allow a couple of
students to manipulate this interactive piece. This site will also be linked to my website
so students can play it at a later date or from home. Lastly, the students will use the dry
erase markers and dry erase boards to answer the five questions at the end of the
Brainingcamp lesson. Students will hold up their answers for each question we walk
through together. This provides me with a quick check of who has mastered the basics
and who is struggling. Students will be expected to answer independently and keep
their answers covered. They will not share their answer until I say “go.” If someone
misses a question, they will be asked to explain their thinking, and as a class, we will
help the student understand where he or she went wrong. Students will be encouraged
by positive feedback such as, “good try; etc.” throughout this skill check.
Step 2:
The class will transition from the Brainingcamp website to the Circumference Graphic
Organizer and Bubble Experiment Data Sheet. I will tell the class that the
Circumference Graphic Organizer can be used during the experiment if needed. I will
also have this projected to provide a reference. Students will next look at their Bubble
Experiment Data Sheet. They will be expected to fill this sheet out completely and
neatly. Students will be given a participation grade and grade for completing the data
sheet. Once the students understand the expectations, I will ask them to sit on their
hands and listen up for instructions. I need their hands free and eyes on me so I know I
have everyone’s attention. This will also keep students from trying to get started before
they fully understand what to do. I will inform the students they have a huge experiment
a head of them. They must test blowing bubbles and figure out how to get the
circumference of the bubbles they blow.
The students will be asked to take out the black construction paper, bubbles, yarn, and
ruler. I will give the students about 30 seconds to practice blowing bubbles into the air
only. Next, I will lead them through the first part of the experiment. Students are
working with a partner. Each student will have their own black construction paper, yarn,
and ruler. They will share the bubbles. Below is what I will say as we begin the
experiment.
Now… let’s start experimenting!
1. Blow a bubble and let it burst on the black construction paper. (Each
partner will have a turn.)
2. Using your ruler, measure the diameter of your bubble and record it on
your data sheet. I will have the sheet projected and lead them through
where they will record. This will go out from “Bubble 1.”
3. Wrap your string around the bubble and then measure the string. Record
the circumference. This is still Bubble 1.
4. Find your radius and record it for Bubble 1. How did you find the radius?
5. Share your measurements with your group. Discuss any relationships you
find between the diameter and circumference. I will ask a student to come
up to the board and record their measures for Bubble 1 as an example.
6. Once students have completed their table, bring the class back for
discussion. Ask the following:
-
How do you find the circumference of a circle and what did you notice
about your data sheet?
You should get an answer like: The circumference of a circle is
approximately 3 times larger than the diameter. This approximated
number is called pi (symbol π). Its value is approximately 3.14. or 22/7.
Remind students that instead of multiplying the diameter (d) by 3,
we multiply it by 3.14 π. Circumference = πd. If you are given the radius:
C = 2πr
Part IV- Summarizer (Sum up the lesson)
Step 1:
The students will be given three practice problems using the formulas they discovered!
This will be done as a pair/share; meaning, each student will solve and then share with
one another the answers they got. If someone got a different answer then both will
need to double check to see who is right. Both students are to stand when finished.
Once everyone is finished, I will post the answers on the board. Below are some
example problems:
Find the circumference.
1) diameter = 7 inches
2) radius = 4.5 ft
3) diameter = 11.8 m
I will walk around to each group and check for understanding. Rewards may be given
for a job well done as groups begin to stand! This might include bonus points, stickers,
or candy.
Step 2:
To gain a better understanding of individual mastery, I will have the students complete a
“Ticket Out the Door.” On an index card (ticket) they will answer the following
independently before being dismissed from class. I will project the following on the
board.
Index Card:
1. You be the teacher! Describe the relationship between the
circumference of a circle and its diameter. How do they
relate? How do you know? Think back to the Bubble
Experiment.
2. How would you solve the following problems? Show your
work. What formula will you use?
a.) Find the circumference if the diameter is 8. What is
the area?
b.) Find the circumference if the radius is 2. What is the
area?
3. Stretch your thinking! BONUS!!! Worth 5 points!
You have a circumference that equals 37.68. What is the
radius of the circle? Prove it for full credit!
Assessment:
I will be assessing throughout the lesson by asking questions and having the students
answer both orally and in writing. The BrainPOP quiz will be one assessing method that
will be finished at the end of class if time permits, or it will be finished as homework. It
will be collected and checked for a grade. The questions asked throughout the book,
Sir Cumference and the Dragon of Pi, will give an insight as to who is grasping the
standards being developed in the form of a story while the Brainingcamp website will
allow a quick check of individual student’s understanding. The Bubble Experiment Data
Sheet and the circumference practice problems will measure students’ understanding.
The Ticket Out the Door will be the true indicator of who has reached mastery of first
part of GLE 0606.4.3 Develop and use formulas to determine the circumference and
area of circles. A Pi and Circumference Extended Practice Page will be given to further
check for retention and understanding. I will use Pearson questions periodically to
maintain an ongoing assessment.
Accommodations:
Students with diverse needs will be accommodated with extended time, peer grouping,
and calculators. With my inclusion group period, I will have an additional teacher in my
room to help me with the lesson. Because of this team approach, we can be of
assistance for those who may be struggling along the way. The Circumference Graphic
Organizer is printed in two different versions to allow for special needs.
Name ________________
Date _________________
Pi & Circumference Extended Practice
1. Find the circumference of a circle with a radius of 10m.
a.
b.
c.
d.
6.28m
62.8m
628m
6280m
2. Line AB is what part of a circle?
a.
b.
c.
d.
circumference
radius
diameter
area
3. What is the approximate circumference of the circle if the radius is 6?
a.
b.
c.
d.
38
16
94
57
4. If the radius is 5.2, what is the diameter, circumference and area?
Developed by ITMS Math Teachers
Circle:
Parts of a Circle
Formulas
Circumference:
Center:
Diameter:
Area:
Radius:
Circumference:
Diameter:
Chord:
Radius:
Arc:
Pi:
Developed by ITMS Math Teachers
Circumference Graphic Organizer
Version 1
What is circumference?
Formula using diameter:
The distance around the
circle. Perimeter of a
circle.
Formula using radius:
Circumference
Formula using fraction 22/7:
Developed by ITMS Math Teachers
Circumference Graphic Organizer
Version 2
What is circumference?
The distance around the
circle. Perimeter of a
circle.
Formula using diameter:
C = πd
Formula using radius:
C = 2πr
Circumference
Formula using fraction 22/7:
C = 22/7(d)
Created by Jennifer Moore
Bubble Experiment Data Sheet
Bubbles
1
2
3
4
5
6
Diameter
Radius
Circumference
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
References
This lesson plan was developed using materials taken from the Indian Trail Middle
School Math Notebook and from the websites:
http://www.lessonplanspage.com/MathBubbleCircumferenceDiameterRadiusMania34.htm.
http://www.testdesigner.com/search/index.htm?pageNum=2&keyword=circumference&entityFilterId=1