Designed by: Andress Carter-Sims, Virginia Pack Elementary School

1) Core Curriculum Objective(s): Estimate and determine the dimensions (e.g. circumference, radius, diameter) of a circle. 5GS5-3

Grade Level: Five                    Subject(s): Math

2) Overview: Through exploration and discovery style of teaching, students will predict, measure and determine the relationships between the diameter, radius and circumference of a circle. Students will also write an explanation of how ratios. multiplication or division facts can be used to describe the relationship between the radius, diameter and circumference of a circle.

3) Focus/Essential Question(s): What makes a circle round? Where is the radius of a circle? How can ratios be used to determine the radius, diameter and the circumference of a circle?

4) Time Frame: Five One Hour Class Periods.

Resource Materials

Dish Detergent
Water
1 Two liter Soda Bottle for each group
Straws
Hole puncher
Laminated paper
Rolls of paper towels
Teaspoon
String
Paper
Scissors
Index cards
Markers
Brown paper bag
Rulers

6) Culminating Assessment: The first task during the culminating assessment will be for each student to determine the diameter and circumference after being given the radius of a circle. The next task will be to determine the diameter and radius after being given the circumference. Students will also be asked to create a diagram of a circle and label the 3 parts of a circle, which will be discussed in this lesson. During the creation of their circle, they will be allowed to trace a circle and use a ruler so that the radius and diameter lines will be as straight as possible. Finally, they will be asked to write an explanation describing the relationships between the radius and diameter and the diameter and the circumference. Note: The teacher may place in the assessment chart any numbers that he/she feels are appropriate.

"The Real Deal On Circles" Rubric

7) INSTRUCTIONAL ACTIVITIES:

Activity One: Students will be placed into small groups (2-3 students) and given a large white piece of paper. On this piece of paper, each group will be asked to write their own definition of a circle. This same sheet of paper should be used to draw what they think a circle looks like. * NOTE: They should not be allowed to use a dictionary or a circular object to trace during this activity.

Each group will share their definition of a circle with the class and then describe how their circle looks. They will also be encouraged by the teacher to explain how they felt drawing a circle freehand. During this guided instruction from the teacher he/she will explain that every point on the circle must be the same distance from the center of the circle in order for it to be a circle. *NOTE: This is also the true definition of a circle. During on-going assessments, the teacher will monitor to see that students provide the appropriate definition for a circle from this point on.

Each small group will be given a bottle of bubble solution, a roll of paper towels, a laminated dot, and a straw. They will be instructed to use the top on the soda bottle to measure the bubble solution. Each student in the group will pour a cap full of bubble solution into the cap and then pour that cap full onto their desk. *NOTE: The bubble solution is prepared by placing three teaspoons of dish detergent into a two liter soda bottle and filling the rest of the bottle with water. Shake the bottle well to disperse the dish detergent throughout the entire solution.

Next, the students will use the palm of their hand (in a circular motion) to produce a small amount of lather on their desk. The students should then place one end of the straw in their mouth and the other end should touch the table where the bubble solution is located. Very gently they should blow until a bubble begins to form on their desk. *NOTE: Bubble may not occur on the first try so practice is needed.

Students will blow the bubble to an appropriate size. The bubble may burst before they want to stop blowing. This is fine and will not cause the lesson to fail. Once the bubble pops, students will be able to see the size of the bubble from the lather print left around the popped bubble.

Each student should then locate the center of their circle and place a laminated dot in the center of their circle. *NOTE: Laminated dots are created by laminating paper and using a hole puncher to make small circles for each student. The lamination protects the dot from the moisture of the bubble solution.

Next, they will measure from the dot to any point on the circle several different places and record the data. The teacher can decide what form of measurement the students will use. Example: ( cm., mm., in.) The teacher will ask some students to share with her and others to share with their groups their results. The teacher will guide the students to know that what they have measured is called the radius.

The teacher should then construct a diagram on the board of a circle with the radius labeled.

Students should be allowed to blow several more circles and measure several radii so that they can visually see that from the center of the circle to any point on the circle will always have the exact same measurement. Once the students have measured several different radii, the teacher should measure several different radii on their circle to demonstrate how all measurements should be the same. *NOTE: Assessment Question: What does this mean if each radius has the exact same measurement for one particular circle? Students should independently write their answer on a sheet which should be given to the teacher.

Activity Two: Small groups will be given bubble solution and a roll of paper towels. Each student will be given a laminated dot and a new straw. They will be asked to blow a bubble on their desk and measure the radius of the circle again and record their information.

Using the same circle, they will be asked to measure from one point on the circle to the opposite point on the circle and again record their information. * NOTE: a twelve-inch ruler will usually measure from one side of the circle to the opposite side. The ruler also helps the students to measure in a straight line.

Once the students have recorded their data, the teacher should then trace a circle on the board, label the radius, measure the radius, record the measurement, measure from one side of the circle to the other side and record that data. This will provide the students with a model. The teacher will guide the students to know that the measurement from one side of the circle to the other side of the circle is called the diameter.

The teacher will explain that the diameter should always be a straight line through the center of the circle to the other side of the circle.

Next the students will blow several bubbles, adding bubble solution as needed. Paper towels can be used to dry the desk and start again. Once the students have blown several different bubbles and recorded the radius and diameter of each, students will be asked to share with groups what they notice. *NOTE: The teacher may guide students to choose the number that they are closer to or they may record their measurement using decimals, depending on the level of the class.

After sharing within their groups, each group will pick one person to share with the entire class what they noticed about their radius and diameter.

Next, the teacher will go back to the board and explain the relationship between their radius and diameter that was placed on the board. *NOTE: Key Facts To Include. The ratio between the radius and diameter is 1:2. If given the radius you can multiply by two to get the diameter. If given the diameter you can divide by two to get the radius. Assessment Question: If given the measurement of a radius of 6 cm., what multiplication fact can you use to get the diameter and why? 6 x 2 = 12. The ratio of radius to diameter is 1:2 or the diameter is two times larger than the radius. Students should write their answer on a sheet of paper, which should be given to the teacher.

Activity Three: Students will be given bubble solution, a roll of paper towels, a laminated dot and a new straw. They will be asked to blow a bubble on their desk and measure the radius and the diameter of the circle and record both data.

Using the same circle, students will use party string to measure around the circle and record that data. Party string is used because it is difficult to use a ruler while measuring the curves of a circle. The string will then be placed on the ruler to get the measurement around the circle. *NOTE: Do not use yarn because it stretches causing the data to be false. Once the students have had the opportunity to record all three numbers the teacher will explain that the measurement around the entire circle is called the circumference of a circle.

The teacher should then go to the board, trace a circle, label the radius, measure the radius, and record the measurement. Each student will be given an index card and a marker with which to write what he/she thinks the diameter will be. *NOTE: Students need to write the answer large enough for the teacher to see it from the front of the class. On the other side of the index card, the students should write in pencil how they got their answer. The teacher can decide if she would like to take up the index cards.

Next, the teacher should measure the diameter and record the data so that students can check their answer. The teacher, at this point, could have students to hold their index card up so that their answer can be assessed by the teacher.

The teacher will then measure the distance around the circle and explain to the students that this is called the circumference of the circle. After measuring, the teacher will record the data.

Students, at this point in the lesson, will again be allowed to blow several bubbles. They should measure the radius and predict the diameter. After the prediction, they should measure the diameter and record the data.

Next, they should measure the circumference with string and record the data. This process should occur several times.

After the students have measured the radius, diameter, and circumference of several circles, guided questions should be used. Example: What relationship or ratio do we see that exists between the radius and the diameter? How can we explain the ratio or relationship between the diameter and the circumference? How can we use multiplication to find the circumference if the diameter is given? How can we use division to find the diameter if given the circumference? *NOTE: Teachers can create other guided questions as needed to provide students with the skills to successfully complete the culminating assessment.

Activity Four: Individually, students will work to cut out three circles. Students can decide what size they would like their circles to be.

Students will draw a diagram on each circle. The first circle will have the radius labeled on it with the measurement included. The second circle will have the diameter labeled on it with the measurement. The third circle will have the circumference labeled on it, also. Example: If the radius on the first circle is 2cm, then the diameter on the second circle should be 4cm. The third circle should have the circumference labeled as 12 cm. Consider that in fifth grade we want students to understand the concept of a 1:2 ratio and a 1:3 ratio. *NOTE: Students may use any numbers or units of measurement they choose. Those students that are more advanced may use numbers larger than ten. This is a great form of enrichment.

The teacher can assess this activity by walking around the room. Help can be provided as needed.

Now the teacher will place the students into small groups. No more than three or four in each group will be appropriate.

Each small group will place their three labeled circles in the brown bag and mix them up silently.

The students should then place all the circles on the desk and match each set of circles together using the measurements provided by their peers. This is a great time for peer tutoring for someone that may need help.

This activity may be repeated by placing the students into other small groups.

Activity Five: Students will be assessed using the rubric and charts provided.

*NOTE: Alternative resources could be used during the lesson. 1) Houghton Mifflin Grade Five Issue Copyright 1995; 2) Houghton Mifflin MathKeys Software: Unlocking Geometry, Volume II, software 1995.