3. Student Learning Map

  • Topic:11. Circles (Chapter 11)
  • Subject(s):Math
  • Days:17
  • Grade(s):9, 10
Key Learning:

The study of circles involves many aspects of geometry including lines, segments, arcs, and angles.
Unit Essential Question(s):
 
 

What are the properties of circles and the lines, segments, arcs, and angles involved with them?
   
Concept:

Circles and Arcs

PH: 7.6

MCD: 9.1, 9.3, 11.6

MA.912.G.6.4   MA.912.G.6.2   MA.912.G.6.5   MA.B.2.4.1  
Concept:

Tangent Lines

PH: 11.1

MCD: 9.2

MA.912.G.6.3   MA.912.G.6.2   MA.C.2.4.1   MA.C.1.4.1   MA.B.2.4.1  
Concept:

Chords and Arcs

PH: 11.2

MCD: 9.4

MA.912.G.6.3   MA.912.G.6.2   MA.C.1.4.1   MA.B.2.4.1  
Lesson Essential Question(s):

What is the relationship between central angles, arc length, and circumference? (A)
Lesson Essential Question(s):

What causes a line to be tangent to a circle? (A)
Lesson Essential Question(s):

How are a circle's chords and arcs related to each other? (A)
Vocabulary:

circle, center, radius, congruent circles, diameter, central angle, semicircle, minor arc, major arc, adjacent arcs, circumference, pi, concentric circles, arc length, congruent arcs

Vocabulary:

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

Vocabulary:

chord

Concept:

Inscribed Angles

PH: 11.3

MCD: 9.5

MA.912.G.6.3   MA.912.G.6.4   MA.C.1.4.1   MA.B.2.4.1   MA.B.1.4.2  
Concept:

Angle Measures and Segment Lengths

PH: 11.4

MCD: 9.6, 9.7

MA.912.G.6.4   MA.C.1.4.1   MA.B.2.4.1   MA.B.1.4.2  
Concept:

Circles in the Coordinate Plane

PH: 11.5

MA.912.G.6.7   MA.912.G.6.6   MA.C.3.4.2  
Lesson Essential Question(s):

What is the relationship between an inscribed angle and its intercepted arc? (A)

(ET)
Lesson Essential Question(s):

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

(ET)
Lesson Essential Question(s):

How is the distance formula applied in the formula for the equation of a circle in the coordinate plane?

(A)
Vocabulary:

inscribed angle, intercepted arc

Vocabulary:

secant

Vocabulary:

standard form of an equation of a circle

Additional Information:

Prentice Hall Geometry Textbook Chapter 7 (7.6), Chapter 11 (11.1-11.5)

Geometry (McDougal/Littell-Jergensen/Brown/Jergensen) Textbook Chapter 9 (9.1-9.7), Chapter 11 (11.6)

Calculator, graph paper, compass, straightedge

Pasco Mathematics Performance Tasks: Roll, Poly, Roll

Also include Language Arts Benchmarks: LA.910.1.6.1 (use of vocabulary), LA.910.1.6.2 (read and discuss text), LA.910.1.6.5 (relate new vocabulary), and LA.910.3.1.3 (use organizational strategies and tools (e.g., technology, spreadsheet, outline, chart, table, graph, Venn Diagram)).

Resources:

View As PDF
Know - Understand - Do Organizer
Student Learning Map
Vocabulary Report

Acquisition Lesson:

Extending Thinking Lesson:

Vocabulary Report

  • circle -
  • secant -
  • inscribed angle -
  • chord -
  • tangent to a circle -
  • standard form of an equation of a circle -
  • center -
  • intercepted arc -
  • point of tangency -
  • radius -
  • inscribed in -
  • congruent circles -
  • circumscribed about -
  • diameter -
  • central angle -
  • semicircle -
  • minor arc -
  • major arc -
  • adjacent arcs -
  • circumference -
  • pi -
  • concentric circles -
  • arc length -
  • congruent arcs -