This lesson will familiarize students with circles and the critical
attributes of circles. Through hands on exploration, students will identify
the attributes of a circle, as well as discover and apply the ratio between
the diameter and the circumference of a circle.
"Math Vantage Going Around In Circles #110"
Students will be able to:
Define circles and describe their similarities and differences with
other shapes.
Label and define the parts of a circle.
Participate in several activities where many discoveries about circles
will be made.
Create string art designs by first creating a circle with a given
diameter and predetermined number of points on the circle.
Teacher:
overhead projector
transparencies
markers
transparent protractors
transparent circular protractors
16 oz. container of 3 different liquid detergents, gallon size container
and
water
blank sheet of butcher paper
butcher paper with a large circle drawn on it
Class (at least one per two students):
variety of sizes of plastic lids
string
ruler
protractor
compass
tape
scissors
worksheets #1, #2,#3, and #4
calculators
two straws
three cup size containers
chord
major arc
point
radius
center point
arc
central angle
diameter
semi circle
pi
Provide each student with a list of vocabulary words and two
identical circles that have the following parts drawn on them: center, chord,
radius and diameter. Ask the students to label the parts of the circle that
they know. Tell them that they are to use the second circle to record any
information that they find during the lesson. At the end of the lesson,
they will compare their two circles for accuracy.
To give students a specific responsibility for viewing, SAY:
"We will be watching a video in which a young lady explains to us what
circles are. As you watch this tape, listen for the three curves that are
named and write the names on your vocabulary sheet."
BEGIN Tape, Going Around In Circles, at the scene where
the roller coaster is going down the first hill. Start where she is standing
in front of the river boat.
PAUSE Tape after the loop de loop just as the people enter the scene
at the end of their ride. Ask for a volunteer to repeat the three types
of curves mentioned.
To give students a chance to check the three types of curves that they have
written, REWIND Tape to the river boat.
Say: "Listen and check your answer with hers."
PAUSE Tape after she repeats the list. Ask a student to repeat the
three types of curves while you write them on the butcher paper.
To give students a specific responsibility for viewing SAY: "Listen
to find out how the first metal roller coasters were designed."
RESUME Tape and PAUSE Tape as soon as the purple arrows disappear
from the screen. Allow time for students to discuss the answer.
To check students' understanding, REWIND Tape to where the riders
are ending their roller coaster ride.
RESUME Tape to replay the reason for not using perfect circles in
the design of roller coasters.
PAUSE Tape after she says that circles were redesigned into the shape
of teardrops.
To give students a specific responsibility for viewing, SAY: "Listen
to find out why all circles are similar and predictable."
REWIND Tape and PAUSE Tape after she says " ...anyway
you look at it". Try to pause with the picture of the Ferris Wheel
on the screen. Illicit the characteristics of all circles from the students
and write them on the butcher paper.
To check for understanding, REWIND Tape until "profound"
appears above the roller coaster.
RESUME Tape and play to the colorful Ferris Wheel and PAUSE
Tape.
To give the students a specific responsibility for viewing, SAY: "Listen
to find out what the definition of radius is."
RESUME Tape and play to the graphic that has the orange circle and
the center point left after the definition for radius has been given.
To check for students understanding, PAUSE Tape. Allow time for students
to participate in a discussion of the definition. Draw a center point on
the circle that is on the butcher paper. Draw and label a radius.
To compare answers, REWIND Tape to the blue background with the Ferris
Wheel and Play to the end of the definition of radius (orange circle and
center point).
To give students a specific responsibility for viewing, SAY: "Listen
for the definition of a chord".
RESUME Tape and play until the words "Central Angle" appear
on the screen. To check for understanding, PAUSE Tape.
To give students a specific responsibility for viewing, Say: "Listen
to find out what we call a chord that passes through the center of the circle."
RESUME Tape and play until "semicircle" appears on the
screen and she says, "...through the center of the circle."
To check for understanding, PAUSE Tape and illicit responses from
students. Write the word "diameter" in the appropriate place on
the butcher paper.
To give students a specific responsibility for viewing, SAY: "Listen
to find out how many degrees are in a 'major arc'".
RESUME Tape.
PAUSE Tape where the young lady is sitting on the rock in front of
the water. Record students' responses on the butcher paper. To allow students
an opportunity to compare their responses, REWIND Tape to "semicircle".
RESUME Tape to the young lady sitting on the rock.
PAUSE Tape. SAY: "Listen to find out what two things Archimedes,
the Greek Mathematician, compared."
RESUME Tape and play to where the young lady says, "...the distance
across circles, called the diameter".
STOP Tape before the ratio is given.
SAY: "We are going to do an investigation to find out what Archimedes
discovered about the comparison between the diameter and the circumference
of a circle. Each of your teams has been given three (or four) lids, string,
scissors, rulers, calculators and worksheet #3.
Take a piece of string and measure the diameter of a lid. Cut the string
and tape it in the proper place on your worksheet. Next, take a piece of
string and measure the circumference of your lid. Cut the string and tape
it in the appropriate place on your worksheet.
Compare your two pieces of string. About how many times longer is the circumference?
Use your ruler to measure each piece of string. Write these measurements
down.
Now, use your calculator to divide the length of the diameter by the length
of the circumference. Round the number that appears in your display to the
tenths place. Repeat this procedure with the remaining lids. Do you see
a pattern in the comparison of the two strings for each lid? If so, what
is it?
To give students a specific purpose for viewing, SAY: "Let's watch
the tape to find out if what we discovered about the comparison between
the diameter and the circumference is the same as what Archimedes discovered."
PLAY Tape.
PAUSE Tape after the screen is filled with the decimal 3.141592.
Give students a chance to check their answers by discussing their discoveries
and what Archimedes discovered.
To give students a specific responsibility for viewing, SAY: "Listen
to find out what special name has been given for this ratio."
PLAY Tape to the beginning of the ride. Allow students to give the
name for the ratio, Pi.
TURN OFF the Video.
SAY: "Now let's look at circles that come from three-dimensional
objects called spheres. We can represent these spheres using bubbles. To
determine the circumference of a sphere, we must first measure the great
circle; the great circle is like the equator of the earth. We will blow
bubbles on tables, which will create hemispheres. They are one half of a
sphere.
Now we'll explore. Use the straws that I've given to each of you, and the
soap solution, to blow a bubble and let it burst on your table. The outline
of this bubble is the circumference of the sphere.
Using your rulers, find the diameter of the bubble. Use what you've learned
from Archimedes to find the circumference of the bubble without measuring
it. Do this for three bubbles from each solution (containers should be marked
A, B, and C). Record your data on worksheet #4.
Using your calculators, find the average diameter for each solution. Record
this data on worksheet #4
Invite someone from Elitches Amusement Park to come to the classroom
and discuss the thought that went into planning the park. Ask the representative
to bring photographs of the rides, specifically the roller coasters and
ferris wheel, so that students can analyze the designs.
Provide students the opportunity to design a classroom model of an amusement
park. Students should work within the following parameters: cost (determine
a budget and price of materials), area (limited area, to scale), should
be able to be enjoyed by all age groups, environmental issues should also
be considered. They can donate this model to the media center to be enjoyed
by all.
Technology: Have students graph the average diameters
of each of their bubble circles on a computer graphing program.
LanguageArts: The students will take the roles of consumer
testers for a local consumer magazine. Ask them to analyze the data from
the post-viewing activity to determine which brand had the largest average
diameter. They should write a letter to the editor of the magazine to recommend
the one detergent that they believe to be the best buy for the money.
Art: Creating a String Art Project Students need a piece of white
paper and a circular protractor. They are to make a circle in the center
of their paper by tracing the circular protractor. Ask the students to determine
the diameter and the circumference of the circle that they have drawn. Using
the circular protractor, the students should decide on an equally points
to place on the circle. There should be at least 18 points. The next step
is for the students to calculate at least three different patterns. For
example, a student with eighteen (18) points on his/her circle and a pattern
of 6, would list the following: (*start from 1) 7, 13, 1 (over to 2), 8,
14, 2, (over to 3) 9, 15, 3, (over to 4) 10, 16, 4, (over to 5), 11, 17,
5. Upon completion of three different sets of patterns, students should
use markers or colored pencils to make their designs.Students can create
their string art projects on a block of wood, using nails as the points
and colored string to connect the points in each pattern.
Math: Create circles by using compasses. Emphasize using the radius
to construct the circle.
Take children on a circle scavenger hunt. Find objects that are made in
the shape of a circle. For example, clocks, bicycle wheels, etc.
Science: Have students discuss the "circle of life". Students
may want to prepare a diagram or diorama that depicts the circle of life.
Social Studies: The great circle on a globe is called the equator.
Ask students to measure the equator to determine the circumference and the
diameter of the globe and extend to the actual dimensions of the earth.
Compare students' results with resources from the library.
Resources:
Lawrence Hall of Science - Great Explorations in Math and Science: Bubble-ology
MECC Graph - Computer program
Lawrence Hall of Science - EQUALS: Family Math, Lid Ratios
