Conic Clash Teacher Guide
Conic Clash Review
Instructional Facilitation Guide • 12th Grade / Undergrad
Duration
45 MIN
Learning Objective
Students will synthesize knowledge of circles, ellipses, hyperbolas, and parabolas to rapidly identify equations and key features (eccentricity, foci, asymptotes, etc.).
Materials Needed
- Conic Clash Slides
- Formula Sheet Template
- Large Poster Paper
- Markers (Assorted Colors)
Lesson Procedure
5m
Warm-up: Rapid Fire Identify
Use the provided slides to flash equations on the screen. Students must shout out the shape as soon as they recognize it. Teacher Note: Challenge them to explain *why* (e.g., "The signs are different, so it's a hyperbola").
10m
Video Synthesis
Screen the "Conic Sections" video. Students should have their Formula Sheet Templates ready. Pause the video at the summary screens (approx 4:00, 12:45, 20:30, 27:50) to allow students to verify and refine their notes.
25m
Group Project: The Master Cheat Sheet
Students work in groups of 3-4. Using their verified templates, they create a visual "Conic Decision Tree" poster. Requirement: Posters must include a flowchart for telling equations apart based on coefficients and signs.
5m
Peer Review Closure
Gallery walk. Groups leave a sticky note on another poster identifying one "pro-tip" they liked or one correction needed.
Rapid Fire Answer Key (Slides)
1. \(x^2 - y^2 = 1\) HYPERBOLA
4. \(y = (x-2)^2 + 5\) PARABOLA
2. \(x^2 + 2y^2 = 1\) ELLIPSE
5. \(3x^2 + 3y^2 = 27\) CIRCLE
3. \((x+1)^2 + (y-3)^2 = 4\) CIRCLE
6. \(4y^2 - x^2 = 16\) HYPERBOLA
Conic Clash Slides
Conic Clash
Equation Masterclass & Review
Circle • Ellipse • Hyperbola • Parabola
Rapid Fire!
Ready?
- 1 An equation will appear on the next slides.
- 2 Shout out the SHAPE as fast as you can.
- 3 Be ready to explain YOUR REASONING.
Don't think. Just spot the signs!
Challenge 01
\[x^2 - y^2 = 1\]
Challenge 02
\[x^2 + 2y^2 = 1\]
Challenge 03
\[(x+1)^2 + (y-3)^2 = 4\]
Challenge 04
\[y = (x-2)^2 + 5\]
Challenge 05
\[3x^2 + 3y^2 = 27\]
Challenge 06
\[4y^2 - x^2 = 16\]
Synthesis Check
10 MIN VIEWING
Embedded media
Watch For:
- Verification of your formula sheet.
- The Pythagorean relationship differences (\(c^2\) formulas).
- Eccentricity (\(e\)) values for each shape.
Master Cheat Sheet
Phase 3: Collaborative Construction
Timer
25:00
Poster Requirements
- • All 4 standard equations
- • Coordinate formulas for Foci & Vertices
- • Asymptote equations for Hyperbolas
- • Geometric diagrams for each section
The "Decision Tree"
Create a flowchart that answers: "Given a general equation, how do I know which conic it is in 5 seconds?"
Hint: Look at the coefficients of \(x^2\) and \(y^2\).
Conic Clash Formula Sheet
Conic Mastermind Template
Comprehensive Summary Sheet • Synthesis Phase
Name: _________________________________
Date: __________________________________
CIRCLE e = 0
Standard Equation
Center
Radius
Key Tip: Semi-circle equations are derived by solving for ________.
ELLIPSE 0 < e < 1
Horizontal Eq
Vertical Eq
Pythagorean Rel.
Eccentricity (e)
Major Axis Length: ________ Minor Axis Length: ________
HYPERBOLA e > 1
Horiz. Transverse
Vert. Transverse
Asymptote Formulas (y - k = ...)
Key Difference: Unlike an ellipse, \(c^2 = a^2\) ________ \(b^2\).
PARABOLA e = 1
Horizontal Eq
Vertical Eq
Vertex
Focus
Directrix
Value of p: distance from ________ to ________.
The "Conic Decision Tree" Blueprint
How do you tell them apart just by looking at the general equation? Sketch your strategy for identifying the conic section in 5 seconds below. (Consider coefficients \(A\) and \(C\) in \(Ax^2 + Cy^2 + ... = 0\)).
Pro-Tip:
If only ONE variable is squared, it's ALWAYS a parabola. If both are squared and the signs are different, it's ALWAYS a hyperbola.
