The Geometry of a Circle - By: Dennis Kapatos

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$By: Melissa Hanel Math B/Grade 11 5 Day Unit Plan Technologies ...$

Reviewing Major Ideas: “Problem with Watering Crops” Because this is a reflection it is for the students’ use only. Also responses will vary _ 1) Describe how the distance formula and the equation of a circle centered at the origin are related? Why does this intuitively make sense? 2) Will farmer Bob ever get this entire field watered without any overlapping areas? Why or why not? 3) Write the general equations that you found below for future reference. THM 12.1 General Equation of Circle with Radius r Centered at the Origin:__________________ THM 12.2 General Equation of Circle with Radius r and Center (h,k): ______________________ 4) How did you determine the first equation? What did you do? 5 How did you determine the second equation? What did you do? 6) It’s easy to make mistakes when first encountering applying these formulas. What mistakes did you make in questions 6-8 and 17-20 (such as squaring r, making h negative, etc)? What things can you think of that will help you remember not to make them again?
Lesson 2: Tangents Discovering and Applying Tangents to Real Life Situations Materials and Handouts: Teacher’s Computer with GSP Projector Student’s Computers with GSP Textbooks Calculators String Measuring Tape Rulers Protractor Pre-measured Cardboard Circles Name: Dennis Kapatos Grade: 11 Subject: Geometry Lesson Objectives: ● Students will be able to write/describe and prove Theorems 12.2 through 12.4. ● Students will be able to model problem situations using circles, tangents, radii, and other lines drawn to a circle. ● Given a geometric figure with missing measurements, students will be able to apply properties of circles, radii, and tangents to find them. ● Students will be able to work cooperatively to find an estimate to a given geometric problem. Reviewing Homework: 1. Answers to the homework questions will be shown with the projector. Students will correct their own homework. 2. Teacher will go over any problems the majority of the students had difficulty with. Developmental Activity: 3. Teacher will present today’s problem situation involving satellites on white board. 4. Teacher will discuss with the class how they might solve this problem. They will decide to first do a rough scale model using a cardboard circles and string and take a more sophisticated approach later. 5. Teacher will split class into groups of 5. There will be a 2 people to hold the ends of the tangent strings (though they won’t call it that, yet), 1 satellite person to hold the two strings together at the proper distance, 1 person to measure the central angle, and 1 person to record the data. 6. Each group will find their own measurement and the class will share their findings afterwards. 7. In order to find a more exact answer, Teacher will ask the class to break up their groups and go to their computers to draw the situation on GSP. 8. Teacher will talk the students through how to create the drawing using the teacher’s instructions below. Teacher will ask questions when indicated.
Page 1 and 2: The Geometry of a Circle Geometry (
Page 3 and 4: G.CN.7 Recognize and apply mathemat
Page 5 and 6: Lesson 1: Introduction to Circles D
Page 7 and 8: Notice that some areas of Bob’s f
Page 9: 15) Fill in the blank: The equation
Page 13 and 14: Satellites There are thousands of s
Page 15 and 16: Lesson 3: Properties of Chords and
Page 17 and 18: Locating the Center of the Satellit
Page 19 and 20: 8. Class will discus why they think
Page 21 and 22: 8. For rest of period, students wil
Page 23 and 24: 80 70 60 50 m CE on AB = 60.00 ° m
Page 25: Corollary 3 The opposite angels of

The Geometry of a Circle - By: Dennis Kapatos

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