Circles in Action. Jennifer Moore. Johnson City Schools

Transcription

1 Circles in Action Jennifer Moore Johnson City Schools 6 th Grade

2 Lesson Title: Circles in Action Grade: 6 Alignment with State Standards: GLE 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 for an introductory lesson on circles and 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 Media- 1. Pi BrainPOP Video describing both Pi and circumference (running time is about 2 ½ minutes) 2. Pi BrainPOP Quiz, great assessment to check students understanding. Can be used formally or informally 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 Teacher Tube Video, excellent song to help students remember the formulas for finding area and circumference. Note: If you are not a subscriber of BrainPOP or Brainingcamp, you can sign up for a free trial.

3 Other Materials- 1. Parts of a Circle Handout (use prior to lesson) 2. Circumference Graphic Organizer (Versions 1 & 2) 3. Bubble Experiment Data Sheet 4. Pi & Circumference Extended Practice Page 5. Pi BrainPOP Quiz 6. Ticket Out the Door bottles of bubbles with wands 8. Black construction paper 9. Yarn 10. Rulers 11. 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:

4 - 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

5 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 Wrap your string around the bubble and then measure the string. Record the circumference. This is still Bubble 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:

6 - 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 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.

7 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 What is the radius of the circle? Prove it for full credit!

8 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 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.

9 Name Date Pi & Circumference Extended Practice 1. Find the circumference of a circle with a radius of 10m. a. 6.28m b. 62.8m c. 628m d. 6280m 2. Line AB is what part of a circle? a. circumference b. radius c. diameter d. area

10 3. What is the approximate circumference of the circle if the radius is 6? a. 38 b. 16 c. 94 d If the radius is 5.2, what is the diameter, circumference and area?

11 Developed by ITMS Math Teachers Circle: Center: Parts of a Circle Formulas Circumference: Diameter: Radius: Area: Circumference: Diameter: Chord: Arc: Pi: Radius:

12 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

13 Circumference Graphic Organizer Version 2 What is circumference? The distance around the circle. Perimeter of a circle. Formula using diameter: C = πd Circumference Formula using radius: C = 2πr Formula using fraction 22/7: C = 22/7(d)

14 Created by Jennifer Moore Bubble Experiment Data Sheet Bubbles Diameter Radius Circumference 1 in. in. in. 2 in. in. in. 3 in. in. in. 4 in. in. in. 5 in. in. in. 6 in. in. in.

15 References This lesson plan was developed using materials taken from the Indian Trail Middle School Math Notebook and from the websites: