Overview
The unit is set up to implement the features of a "Flipped Classroom." That is, students are assigned to watch videos, use tools, and other tasks for homework, leaving them responsible for developing and furthering their own understanding of the given concepts. This allots time in the classroom for teachers to implement high-cognitive demand tasks, answer questions, and work with the students instead of spending class time lecturing and teaching the basics of the topics. Additionally, we have emphasized the use of technology in this unit to increase efficiency, discovery, exploration, and resources available to enhance student learning.
General learning goals for this unit:
- Understand and apply theorems about circles
- Understand the concept of radians
- Find arc lengths of circles and calculate areas of sectors of circles
- Explain and develop an understanding for formulas related to circles and the volume of solid figures and use those formulas to solve problems
Georgia Standards of Excellence addressed in this unit:
MGSE9-12.G.C.1 Understand that all circles are similar.
MGSE9-12.G.C.2 Identify and describe relationships among inscribed angles, radii, chords, tangents, and secants. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
MGSE9-12.G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties inscribed in a circles of angles for a quadrilateral
MGSE9-12.G.C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
MGSE9-12.G.GMD.2 Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
MGSE9-12.G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
MGSE9-12.G.C.1 Understand that all circles are similar.
MGSE9-12.G.C.2 Identify and describe relationships among inscribed angles, radii, chords, tangents, and secants. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
MGSE9-12.G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties inscribed in a circles of angles for a quadrilateral
MGSE9-12.G.C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
MGSE9-12.G.GMD.2 Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
MGSE9-12.G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Lessons included in this unit:
Lesson 1: Understanding and Applying Theorems about Circles
Lesson 2: Finding Arc Lengths and Areas of Sectors of Circles
Lesson 3: Explaining Volume Formulas and Using them to Solve Problems
Lesson 1: Understanding and Applying Theorems about Circles
Lesson 2: Finding Arc Lengths and Areas of Sectors of Circles
Lesson 3: Explaining Volume Formulas and Using them to Solve Problems
Created by Claire Cashin and Bradley Brown for EMAT 4700 at UGA in May 2016