Lesson Plan, Class XI (Ch-10) | Conic Sections

E- LESSON PLAN   SUBJECT MATHEMATICS    CLASS 10+1

Lesson plan for maths class XI (Chapter 11) conic section, cbse lesson plans for mathematics teachers,    lesson plan for mathematics grade XI, lesson plan for maths teacher in B.Ed.

TEACHER'S NAME :    DINESH KUMAR	SCHOOL :   RMB DAV CENTENARY PUBLIC SCHOOL NAWANSHAHR
SUBJECT   :   MATHEMATICS	CLASS                  :   XI  STANDARD BOARD                 :  CBSE
LESSON TOPIC / TITLE   :  CHAPTER 10:   CONIC SECTIONS	ESTIMATED DURATION:  This chapter is divided into 10 modules and is completed in 20 class meetings.

PRE- REQUISITE KNOWLEDGE:-

Simple concept of algebra, addition , subtraction  and ability to solve the equations.

TEACHING AIDS:- 

Green Board, Chalk,  Duster, Charts, smart board, projector, laptop etc.

METHODOLOGY:-   Lecture method  and Demonstration

OBJECTIVES:-

• Different sections of cone : Circle, Parabola, Ellipse, Hyperbola.

• A point, a straight line and a pair of intersecting lines as a degenerate case of a conic section.

• Standard equation of a Circle and their simple properties.

• Standard equation of a Parabola and their simple properties.

• Standard equation of a Ellipse and their simple properties.

• Standard equation of a Hyperbola and their simple properties.

LEARNING OUTCOMES
After studying this lesson student should know  

• The different types of sections of cone i.e. circle parabola, ellipse and hyperbola, 

• Their shapes, their general equations, vertices, focuses, axis, eccentricity, major and minor axis, transverse and conjugate axis and the length of Latus rectum etc.

• Students should also know the applications of conic sections in different problems.

RESOURCES

NCERT Text Book, 

NCERT Exemplar Book of mathematics, 

Resource Material : Worksheets , E-content, Basics and formulas from cbsemathematics.com)

KEY WORDS

Conic Sections, Circle, Parabola, Ellipse, Hyperbola, Degenerate Conic, Focus, Directrix, Eccentricity (e), Axis of the Conic, Latus Rectum, Vertex, Centre (of a Conic), Major Axis (Ellipse), Minor Axis (Ellipse), Transverse Axis (Hyperbola), Conjugate Axis (Hyperbola), Section of a Cone, Double Napped Cone, Intersection of a Plane with a Cone, Focal Property, Reflective Property, Asymptotes (for Hyperbola)

CONTENT OF THE TOPIC

• Interoduction

• Double napped cone

• Different types of conic sections

• Graphical representation of conic sections

• Degenerated cases of Conic Section

• Circle, their definitions

• General equation of the circle

• Parabola, their definitions

• Different types of parabola and their equations

• Ellipse, their definitions

• Different types of ellipse and their equations

• Hyperbola, their definitions

• Different types of hyperbola and their equations.

LEARNING ACTIVITIES:

INTRODUCTORY ACTIVITY

Mathematics Activity No 1 Class XI

Mathematics Activity No. 2 Class XI

EXPERIENTIAL ACTIVITY

Mathematics Activity No 3 Class XI

ART INTEGRATED ACTIVITY

Art Integrated Project on Conic Sections

Art Integrated Project on Conic Sections (Smiley by GeoGebra)

PROCEDURE & EXPLANATIONS

[Conic Section Part- 1]

[Conic section Part-2]

Start the session from the plane figures and ask questions about different types of plane figures such as triangles, circles and rectangles. Now tell the students that there  is also  the possibility  of some other plane figures like parabola ellipse and hyperbola. Now introduce the topic step by step as follows.

Introduction 

The sections of the double napped right circular cone with the plane are called conic sections. eg:- circle, ellipse, parabola and hyperbola etc. all are the examples of conic sections.

Teacher will introduce the topic conic section by giving some examples from the surroundings. Teacher may conduct an activity in the classroom of cutting the carrot in the class with different angles. The main sections of conic sections are circle,  parabola, ellipse and hyperbola.

Teacher can demonstrate the concept of conic section by making sections  of double napped cone and then explain all the conic sections one by one.

These curves have wide applications in the field of planetary motion, design of telescope, antennas, reflectors of flash light and automobile headlights.

Different types of conic sections

There are mainly four types of conic sections, Circle, Parabola, Ellipse and Hyperbola.

• When b = 90^o, then section is a Circle.
• When a < b < 90^o, then the section is an Ellipse.
• When a = b, the section is a Parabola.
• When  0 ≤ b < a , the plane cuts through both the nappes , the curves are called Hyperbola

GRAPHICAL REPRESENTATION OF CONIC SECTIONS

Degenerated  cases of Conic Section

When the plane cuts at the vertex of the cone, then following cases arises.

• When  a < b      90^o , then the section is a point.
• When a = b, the plain contains a generator of the cone and the section is a straight line.
• When 0 ≤  b < a , then the section is the pair of intersecting lines.   

CIRCLE

A circle is the collection (or set) of all points in the plane which are at equidistant from the fixed point.

General equation of the circle

Let (x, y) is any point on the circle and (h, k) is the centre of the circle and r is the radius of the circle then equation of the circle is

(x - h)² + (y - k)² = r²

PARABOLA

A Parabola  is a set of all points in a plane  that are equidistant from a fixed line and  a fixed point in a plane.

Fixed Line is called Directrix and fixed point is called Focus

A line through the focus and perpendicular to the Directrix is called Axis of Parabola

Different types of parabolas

There are mainly four types of parabolas, Upward Parabola, Downward Parabola, Right Parabola, Left Parabola.

ELLIPSE

An ellipse is the set of all points in a plane the sum of whose distances from two fixed points in the plane is a constant.

Two fixed Points are called Foci

Mid-point joining the foci is called the Centre

The line segment through the foci is called the Major axis

The line segment through the centre and perpendicular to major axis is called the Minor axis

The end points of major axis are called the vertices

HYPERBOLA

A Hyperbola is the set of all points in a plane, the difference of whose distances from two fixed points in the plane is a constant

Two fixed points are called Foci

The midpoint of line segment joining the foci is called the Centre

The line through foci is called Transverse Axis

The line through the centre and perpendicular to the Transverse axis is called Conjugate Axis

The points to which the Hyperbola intersects the Transverse axis is called the Vertices of the Hyperbola

PROJECTS ON CONIC SECTIONS

Students can prepare an Art Integrated project on parabola as shown below

Art Integrated project on Conic Section

With the help of butterfly a project can be prepared which can explain all types of conic sections like Circle, Parabola, Ellipse and Hyperbola as shown in the figure given below.

Art Integrated project on Conic Sections

In this project students will download an application Geo-Gebra in their mobile or on their PC. Now with the help of equations of different conic sections a picture of SMILY can be prepared. This picture can explain all types of conic sections as shown in the picture below

REFLECTION OF ACTIVITY

Students will be able to know the

• Different types of conic sections.
• Circle, its definitions and components of circle.
• Parabola, its definitions and components of parabola.
• Ellipse, its definitions and components of ellipse.
  
• Hyperbola, its definitions and components of hyperbola.

IMMEDIATE FEEDBACK

After completing the above activities students will be able to 

• Identify different types of conic sections.
• Identify different geometrical representations of conic sections. 
• Identify the different equations of circle, parabola, ellipse and hyperbola.

SUBJECTS INTEGRATED

1. Physics

• Projectile motion (Parabola)

• Lenses and mirrors (Parabola, Hyperbola, Ellipse)

• Orbits of planets and satellites (Ellipse – Kepler’s laws)

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2. Engineering & Architecture

• Designing bridges, arches, domes (Parabolas, Ellipses)

• Satellite dishes and reflector antennas (Parabola)

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3. Geography / Astronomy

• Paths of celestial bodies (Elliptical orbits)

• Use of conic sections in GPS and mapping

• Study of comet paths (Hyperbola or Parabola)

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4. Economics / Commerce

• Cost curves and revenue graphs can resemble parabolas

• Optimization problems using quadratic functions

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5. Biology

• Eye lens and vision correction (parabolic and hyperbolic lenses)

• Shapes of certain biological structures (e.g., seed dispersal paths)

STUDENTS DELIVERABLES:-

• Review questions given by the teacher. 
• Students can prepare a presentation  as individual or in groups on the properties of conic sections.  
• Students can prepared Art Integrated Project as explained above.
• Solve NCERT problems with examples and some extra questions from refreshers.

DIFFERENTIAL LEARNING

For Below Average Students

• Mind/ Concept maps
• Charts , Models and activity
• Simple questions

For Average Students

• Learning situations through watching video, creating collage, completing puzzles, assignment.

For Above Average Students:

• Group Discussion
• Higher Order Thinking  Skill questions

SKILLS ENHANCED

Observation  skill,  analytical skill,  critical thinking, team work, constructive approach, interpersonal skill,  engagement  in learning process etc.

HOME ASSIGNMENT

Students will be given a Home Assignment for solving at home. 

ASSESSMENT TECHNIQUES:

• Assignment sheet will be given as home work at the end of the topic. 
• Separate sheets which will include questions of logical thinking and Higher order thinking skills will be given to the above average students.
• Class Test , Oral Test , worksheet and Assignments. can be made the part of assessment.
• Re-test(s) will be conducted on the basis of the performance of the students in the test.

Competency based assessment can be taken so as to ensure if the learning outcomes have been achieved or not. e.g.

• Puzzle
• Quiz
• Misconception check
• Peer check
• Students discussion
• Competency Based Assessment link: M C Q

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