Subject: Pre Calculus
Grade Level: Grade 11
Objective:
a. Define conic section;
b. Enumerate the different types of conic sections; and
c. Understand the different types of conic sections: parabola, ellipse, circle, hyperbola,
and degenerate cases.
Learning across the curriculum:
1. Mathematics - Analyzing the different types of conic sections using mathematical
equations and properties.
2. Science - Understanding the real-life applications of conic sections in physics and
engineering.
3. Art - Creating artistic representations of conic sections using various mediums.
Engage:
1. Show a video clip demonstrating real-life examples of conic sections, such as the trajectory
of a projectile or the shape of a satellite's orbit.
2. Present a set of images featuring different conic sections and ask students to identify and
describe each type.
3. Conduct a class discussion on how conic sections are used in architecture, design, and
technology.
Explore:
Activity 1: Exploring Conic Sections through Shapes
Materials: Paper, pencils, rulers, compasses
Instructions:
1. Divide the class into groups of 3-4 students.
2. Provide each group with paper, pencils, rulers, and compasses.
3. Instruct the groups to create different conic sections (parabola, ellipse, circle, hyperbola)
using the given materials.
4. After creating the shapes, have the groups label and describe each conic section.
Rubric:
Criteria: Accuracy of shape construction, labeling, and description
Points: 10
Assessment Questions:
1. What is the main difference between a parabola and a hyperbola?
2. How can you determine if a given shape is an ellipse or a circle?
Activity 2: Analyzing Conic Section Equations
Materials: Whiteboard, markers
Instructions:
1. Write several conic section equations on the whiteboard, such as y = x^2, x^2 + y^2 = 4,
x^2/9 - y^2/4 = 1, etc.
2. Engage the students in a discussion on how to identify the type of conic section based on
its equation.
3. Provide examples of equations for each type of conic section and ask students to analyze
and classify them.
Rubric:
Criteria: Correct identification and classification of conic section equations
Points: 10
Assessment Questions:
1. What is the equation of a parabola with its vertex at (0, 0)?
2. How can you determine if a given equation represents an ellipse or a hyperbola?
Activity 3: Exploring Degenerate Cases of Conic Sections
Materials: Geometric shapes (circles, rectangles, triangles, etc.)
Instructions:
1. Distribute various geometric shapes to the students.
2. Instruct them to manipulate the shapes to create degenerate cases of conic sections.
3. Have the students explain and present their creations to the class.
Rubric:
Criteria: Creativity in creating degenerate cases, clarity of explanation
Points: 10
Assessment Questions:
1. How can you create a degenerate case of a parabola using a geometric shape?
2. Can a circle be considered a degenerate case of an ellipse? Explain why or why not.
Explain:
1. Lecture: Provide a detailed explanation of each type of conic section, including their
defining characteristics, equations, and real-life applications. Encourage student participation
and ask questions to ensure understanding.
2. Interactive Discussion: Engage students in a discussion where they explain conic sections
to their classmates, using visual aids and examples to support their explanations.
Elaborate:
1. Application Project: Assign students to research a specific real-life application of conic
sections (e.g., satellite communication, architectural design). They should create a
presentation showcasing how conic sections are utilized in their chosen field.
2. Collaborative Problem Solving: Divide the class into groups and give them complex
problems involving conic sections. They should work together to solve the problems and
present their solutions to the class.
Evaluate:
1. Conic Section Quiz: Prepare a quiz that assesses students' understanding of the different
types of conic sections, their equations, and properties.
2. Performance Task: Assign a task where students have to identify and analyze conic
sections in real-life scenarios, such as finding the shape of a satellite's orbit or determining
the trajectory of a projectile.
Assignment:
Research and write a short essay discussing the historical development and significance of
conic sections in mathematics, science, and engineering. Include examples of how conic
sections are used in modern applications.