Download Bundle 7 Geometry - East Allen County Schools

EAST ALLEN COUNTY SCHOOLS
Bundle 7
Geometry
Circles
Big Idea: Things that go around
Enduring Understandings
Essential Questions
Special lines, angles, and arcs of a circle have many special relationships.
Properties fo right triangles are used to derive equations for circles and
parabolas.
Constructions are used to determine many properties of a circle.
How can the coordinate plane be used to derive the equation of a circle and a
parabola?
What is the relationship between angles and arcs formed by chords, secants,
and tangents?
How can constructions be used to inscribe and circumscribe a circle in a
triangle?
CC/Learning Targets
G.GPE.1
G.GPE.2
G.C.2
G.C.3
G.C.4
G.C.5
Core Vocabulary
Links to Technology
chord
secant
tangent to a circle
Bundle Performance Task(s)
The students will create a new clock design of the Floral Clock in Niagara Falls, Canada, given the circumference.
Students need to find the lengths of the hands of the clock, the area of each of the 12 sectors in which the letters to spell out Niagara Parks will be placed, and the
final design of the clock face using geometry software or hand drawn visual to present to the class. The final product will be displayed throughout the school.
Geometry
Bundle 7
Quarter 4
Mar.-Apr.
Geometry
CC/Learning Targets
G.GPE.1
(G.6.8a,c)
G.GPE.2
G.C.2
(G.6.1a)
(G.6.2a-b)
(G.6.4c)
(G.6.5a-c)
G.C.3
(G.6.1b)
(G.6.4c)
(G.8.9a)
G.C.4
(G.6.4c)
(G.8.9a)
Derive the equation of a circle of given
center and radius using the
Pythagorean Theorem; complete the
square to find the center and radius of a
circle given by an equation.
Derive the equation of a parabola given
a focus and directrix.
Identify and describe relationships
among inscribed angles, radii, and
chords. 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.
Construct the inscribed and
circumscribed circles of a triangle, and
prove properties of angles for a
quadrilateral inscribed in a circle.
Construct a tangent line from a point
outside a given circle to the circle.
Bundle 7
Resource of Ideas
-Completing the square: Circle Equations
-Equation of a circle
-Prentice Hall Mathematics
Lessons 11.5
-iBook Prentice Hall Geometry
Lesson 12.5
-Equation of a Parabola
-iBook Prentice Hall Geometry
Lesson 12.5
-Angles in a circle
-Segments of a circle
-Prentice Hall Mathematics
Lessons 5.3, 7.6, 7.7, 11.1-11.5
-iBook Prentice Hall Geometry
Lessons 10.6, 12.1-12.4
-Construct inscribed circle in a triangle
-Prentice Hall Mathematics
Lessons 5.3
-iBook Prentice Hall Geometry
Lessons 5.3, 12.3
-Construct tangent to a circle from external point
-Prentice Hall Mathematics
Lessons 5.3
-iBook Prentice Hall Geometry
Lesson 12.3
Evidence of Learning
-Class discussion
-Graphing
-White Board
-Worksheet
-Class Discussion
-Graphing
-White Board
-Journal
-Flip Chart
-Flash Cards
-Nearpod
-Homework
-Quiz/test
-Construction
-White Board
-Patty Paper
-Homework
-Construction
-White Board
-Patty Paper
-Homework
Geometry
G.C.5
(G.6.7d)
Bundle 7
Derive using similarity the fact that the
length of the arc intercepted by an
angle measured in radians 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.
Correlating CC/Learning Targets
G.CO.1
G.CO.2
G.CO.4
G.CO.6
G.CO.9
G.CO.13
G.GMD.1
G.GMD.3
G.SRT.4
G.SRT.5
G.SRT.6
G.SRT.7
G.SRT.8
G.GPE.4
G.C.1
-Area of sector
-Radian measure
-Derive formula for area of a sector
-Class Discussion
-Group Work
-Homework
-Quiz/Test
-Prentice Hall Mathematics
Lessons 7.7
-iBook Prentice Hall Geometry
Lessons 10.6, 10.7
Teacher Notes
All embeded apps included in this curriculum are free.