Student Learning Map

  • Topic:Circles
  • Subject(s):Math
  • Days:12
  • Grade(s):9, 10, 11, 12
Key Learning: Many relationships exist between a circle and lines, segments, and angles.
Unit Essential Question(s):
 
 
What relationships exist between circles and the lines and segments that intersect the circle?
   
Concept: Tangent Lines
LA.1112.1.6.1   LA.1112.1.6.2   LA.1112.1.6.5   MA.912.G.6.1    MA.912.G.6.2  
Concept: Chords and Arcs
MA.912.G.6.2   MA.912.G.6.3  
Concept: Inscribed Angles
MA.912.G.6.3   MA.912.G.6.4  
Lesson Essential Question(s):

What is a tangent line to a circle? (A)

How is the tangent to a circle related to the radius of the circle at the point of tangency? (A)

What relationship exists when two segments are drawn tangent to a circle from one point? (A)

Lesson Essential Question(s):

How are chords and arcs related to each other? (A)

What relationships exist within a circle when a chord bisects a diameter and how are these relationships used to solve measures within a circle? (A)

How is the tangent to a circle related to the radius of the circle at the point of tangency? (ET)

What relationships exist within a circle when a chord bisects a diameter and how are these relationships used to solve measures within a circle? (ET)

Lesson Essential Question(s):

What is an inscribed angle? (A)

What relationship exists between an inscribed angle and the arc it intercepts? (A)

What relationship exists between an inscribed angle and the arc it intercepts? (ET)

How is the relationship between an inscribed angle and its intercepted arc used to find measures within a circle? (ET)

How are chords and arcs related to each other? (ET)

What similarities/differences exist between central angles and inscribed angles? (ET)

Vocabulary:

tangent to a circle, point of tangency, inscribed in, circumscribed about

Vocabulary:

chord

Vocabulary:

inscribed angle, intercepted arc

Concept: Angle Measures & Segment Lengths
MA.912.G.6.2   MA.912.G.6.3   MA.912.G.6.4  
Concept: Circles in the Coordinate Plane
MA.912.G.6.6   MA.912.G.6.7  
Concept: HONORS DISTINCTION - Construction
MA.912.G.6.1   
Lesson Essential Question(s):

What is an inscribed angle? (A)

What relationship exist between segments formed by chords, secants, and tangents of circles? (A)

What relationship exists between an inscribed angle and the arc it intercepts? (A)

What is the relationship between angles formed by chords, secants, and tangents of circles? (A)

Lesson Essential Question(s):

How is the distance formula used to determine the equation of a circle in the coordinate plane? (A)

How is the distance formula used to determine the equation of a circle in the coordinate plane? (ET)

How is the relationship between an inscribed angle and its intercepted arc used to find measures within a circle? (A)

How do you write the standard equation of circle? (A)

Lesson Essential Question(s):

How can a circle passing through three noncolinear points be constructed, and why is this useful?

 (ET)

How are circles inscribed and circumscribed about triangles and regular polygons?

 (A)

How are tangents to a circle constructed, and why is this useful?

(ET)

Vocabulary:

secant

Vocabulary:

standard form of an equation of a circle

Vocabulary:

Additional Info:

Ask an experienced coworker for additional reference texts and/or other materials. Classes using the McDougal-Littell book may use www.classzone.com as a resource. Prentice Hall Geometry Ch.11(11.1-11.5) Text Ancillary Materials Scientific Calculator, Protractor, Graph Paper FCAT Explorer Mission FCAT Polk County FCAT Item Test Bank www.PHSchool.com Kaplan Lesson Plans

Resources:

View As PDF
Student Learning Map of Unit
Vocabulary Report

Vocabulary Report

  • tangent to a circle -
  • chord -
  • inscribed angle -
  • secant -
  • standard form of an equation of a circle -
  • point of tangency -
  • intercepted arc -
  • inscribed in -
  • circumscribed about -