HSG-C.B.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.

 
15 Lesson(s)
   

Sector Area Application: The Grazing Goat

Geometry » Unit: Geometric Measurement and Dimension
Geometry » Unit: Geometric Measurement and Dimension
Jessica Uy
Sunnyvale, CA
Environment: Suburban
 
Big Idea:

Students use a variety of tools (graph paper, compasses, string) and strategies to solve the Grazing Goat problem in their groups.

 
Favorites (2)
 
Resources (12)
 
Reflections (1)
grazing goat
   

Strategies for Decomposing 2-D Figures

Geometry » Unit: Geometric Measurement and Dimension
Geometry » Unit: Geometric Measurement and Dimension
Jessica Uy
Sunnyvale, CA
Environment: Suburban
 
Big Idea:

Through small group and whole class discussion, students will be able to make connections between multiple ways of viewing composite areas and shaded areas of circles.

 
Favorites (2)
 
Resources (19)
 
Reflections (1)
area application sample resized
   

Circumference-Diameter Ratio and Arc Length

Geometry » Unit: Discovering and Proving Circles Properties
Geometry » Unit: Discovering and Proving Circles Properties
Jessica Uy
Sunnyvale, CA
Environment: Suburban
 
Big Idea:

Through a hands-on task involving circular objects, string, and measuring tools, students will make sense of pi!

 
Favorites (6)
 
Resources (13)
 
Reflections (1)
pi eye
   

Sectors of Circles

Geometry » Unit: Geometric Measurement and Dimension
Geometry » Unit: Geometric Measurement and Dimension
Jessica Uy
Sunnyvale, CA
Environment: Suburban
 
Big Idea:

In a group-worthy task, students use clues about sector area, arc length, and sector perimeter to solve their "dominos".

 
Favorites (2)
 
Resources (10)
 
Reflections (2)
sector sample resized
   

Extreme Couponing: Pizza Edition

Geometry » Unit: Geometric Measurement and Dimension
Geometry » Unit: Geometric Measurement and Dimension
Jessica Uy
Sunnyvale, CA
Environment: Suburban
 
Big Idea:

In Extreme Couponing, students use a variety of tools to convince each other of which coupon offers the customer a better deal.

 
Favorites (1)
 
Resources (7)
   

Riding a Ferris Wheel - Day 2 of 2

12th Grade Math » Unit: Trigonometric Functions
12th Grade Math » Unit: Trigonometric Functions
Tim  Marley
Troy, MI
Environment: Suburban
 
Big Idea:

Make the transition from the Ferris wheel problem to the unit circle.

 
Favorites (3)
 
Resources (10)
 
Reflections (1)
untitled
   

Arc Length and Sector Area

12th Grade Math » Unit: Trigonometry: Circles
12th Grade Math » Unit: Trigonometry: Circles
James Dunseith
Worcester, MA
Environment: Urban
 
Big Idea:

Students find their friend similarity lurking in a table of repeated calculations. A firm concept of radian measure follows close behind.

 
Favorites (11)
 
Resources (14)
find the similarity
   

Area of Sectors in Circles

Geometry » Unit: Circles
Geometry » Unit: Circles
Stephanie Conklin
Saratoga Springs, NY
Environment: Suburban
 
Big Idea:

After watching a BrainPop! students will derive the formula for area of a sector and apply these to problems.

Standards:
 
Favorites (16)
 
Resources (14)
image area of sectors of circles
   

Is John Guilty

12th Grade Math » Unit: Trigonometry as a Real-Valued Functions
12th Grade Math » Unit: Trigonometry as a Real-Valued Functions
Katharine Sparks
Independence, MO
Environment: Suburban
 
Big Idea:

By analyzing data from an accident students will determine whether a driver was speeding when he wrecked his vehicle.

 
Resources (19)
 
Reflections (2)
wreck
   

Radian Measure

12th Grade Math » Unit: Trigonometry: Circles
12th Grade Math » Unit: Trigonometry: Circles
James Dunseith
Worcester, MA
Environment: Urban
 
Big Idea:

Time invested in understanding similarity and in the π project pays off when students see the common sense behind the idea of radian measure.

 
Resources (13)
similarity and proportionality
   

Area "Quest"

Geometry » Unit: Geometric Measurement and Dimension
Geometry » Unit: Geometric Measurement and Dimension
Jessica Uy
Sunnyvale, CA
Environment: Suburban
 
Big Idea:

On this unit assessment, students will demonstrate their understanding of area on problems of varying difficulty.

 
Favorites (1)
 
Resources (8)
 
Reflections (1)
assessment sample resized
   

Review of Circles Learning Targets

12th Grade Math » Unit: Trigonometry: Circles
12th Grade Math » Unit: Trigonometry: Circles
James Dunseith
Worcester, MA
Environment: Urban
 
Big Idea:

Students work together to review and synthesize their knowledge of circles.

 
Resources (10)
review and delta math
   

Deriving Formulas for Sector Area and Arc Length

Geometry » Unit: Unit Circle Trigonmetry
Geometry » Unit: Unit Circle Trigonmetry
Anthony Carruthers
Pasadena, CA
Environment: Suburban
 
Big Idea:

We're PROs at PORTIONS of circles.

Standards:
 
Favorites (4)
 
Resources (11)
 
Reflections (1)
sector
   

Define Radian Measure

Geometry » Unit: Unit Circle Trigonmetry
Geometry » Unit: Unit Circle Trigonmetry
Anthony Carruthers
Pasadena, CA
Environment: Suburban
 
Big Idea:

Radius, radii, radians....Ready?

 
Resources (15)
 
Reflections (1)
radian
   

Unit 3 Exam

12th Grade Math » Unit: Trigonometry: The Unit Circle
12th Grade Math » Unit: Trigonometry: The Unit Circle
James Dunseith
Worcester, MA
Environment: Urban
 
Big Idea:

This exam consists of both Unit Circle SLTs, as well as two earlier SLTs into which we've delved deeper in this unit.

 
Resources (4)
unit 3 exam 2013
Common Core Math
 
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