## AROUND AND AROUND WE GO Grades 4 - 5

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:
• 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
• 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.

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.

Language Arts: 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