GSE Pre-Calculus
Unit Five Information
Curriculum Map: Conics
Concept 1: Review of Parabolas and Circles as Conic Sections
Concept 2: Ellipses
Concept 3: Hyperbolas
Content from Frameworks: Conics
Unit Length: Approximately 20 days
20152016
TCSS – GSE Pre-Calculus – Unit 5
Curriculum Map
Big Idea / Unit
Students will be able to derive the equation of conic sections given information.
Unit Essential Questions:
How do you derive the
equation of conic sections?
Prerequisites: As identified by the GSE Frameworks
Length of Unit
 quantitative reasoning
 seeing the generalizability of relationships in building quadratic relations (and geometric concepts in
general)
 using algebraic methods, such as completing the square, to change forms of equations
 see relationships between algebraic manipulation of equations and characteristics of corresponding
graphs
Concept 1
Circles and Parabolas
GSE Standards
Translate between the geometric
description and the equation for a conic
section.
MGSE9‐12.G.GPE.1 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.
MGSE9‐12.G.GPE.2 Derive the equation
of a parabola given a focus and directrix.
Lesson Essential Question
How do I derive the equation of a circle
given its center and radius using the
Pythagorean Theorem?
How do I complete the square to find the
center of a circle?
How do I derive the equation of a parabola
given the focus and directrix?
How can we solve real-world problems
using what we know about conics?
TCSS
20 Days
Concept 2
Concept 3
Ellipses
Hyperbolas
GSE Standards
Translate between the geometric description
and the equation for a conic section.
MGSE9‐12.G.GPE.3 (+) Derive the equations of
ellipses and hyperbolas given the foci, using the
fact that the sum or difference of distances from
the foci is constant.
Translate between the geometric description
and the equation for a conic section.
MGSE9‐12.G.GPE.3 (+) Derive the
equations of ellipses and hyperbolas given the
foci, using the fact that the sum or difference
of distances from the foci is constant
Lesson Essential Question
How can ellipses be defined in relation to their
foci?
How do I derive the equation of an ellipse given
the foci?
How can we solve real-world problems using
what we know about conics?
7/23/2015
How can hyperbolas be defined in relation to
their foci?
How do I derive the equation of a hyperbola
given the foci?
How can we solve real-world problems using
what we know about conics?
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TCSS – GSE Pre-Calculus – Unit 5
Vocabulary
Vocabulary
Cone
Coplanar
Conic Section
Circle
Center
Radius
Parabola
Directrix
Focus
Locus of Points
Plane
Vertex
Ellipse
Locus of Points
Major axis
Minor axis
Co-vertices
Foci
Resources – Concept 1
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Circles Teacher Notes –prerequisite
skills
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Graphing Conics Graphic Organizer
Blank Conics Graphic Organizer
Conic Sections Formulas
Basic Circle Review
Circle Packet – guided notes and
practice
Circles Review (formative)
Circles Review Practice
Completing the Square Drill
9-1 Homework Practice (circles)
9-1 Guided notes and practice
(parabola)
Lesson on Parabolas (power point)
Vocabulary
Hyperbola
Resources – Concept 2
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Resources – Concept 3
Ellipse’s Guided notes and practice
Lesson on ellipse (power point)
Graphing Ellipses practice
Mixed Practice – Circles and Ellipses
Ellipse complete the square worksheet
Complete ellipse homework
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Hyperbola Guided notes
Hyperbola Worksheet
Ellipse and Hyperbola Sorting Activity
MathO (Bingo game)
Classifying Conics
These tasks were taken from the
GSE Frameworks.
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Ellipses & Hyperbolas
Application
These tasks were taken from the
GSE Frameworks.
 Circles & Parabola Review
Differentiated Activities
Concept 1
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TCSS
Differentiated Activities
Concept 2
 Ellipse Activity
7/23/2015
Differentiated Activities
Concept 3
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Conic Card Activity
Conic Section Project
Rubric
3
TCSS – GSE Pre-Calculus – Unit 5
Unit 5 Checklist – Trigonometric Identities
Good luck to ________________________Date_______ Period___
Keep this list handy and refer to it periodically to see how you are doing. If you know how to each of these you should do well on
an exam.
Unit 5 – Conics
In this unit I :
sort of
really
can identify the general and standard forms of the four types of conic sections.
can use the method of completing the square to convert from general form to
standard form of a conic equation.
understand conic sections pictorially as the intersection of a plane and a doublenapped cone, algebraically as the result of specific quadratic equations, and
geometrically as the relationship of the locus of points to foci.
can use basic conic understanding to apply to realistic phenomena.
TCSS
7/23/2015
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