Lesson Plan Math Class XI Ch-11 | Three Dimensional Geometry

LESSON PLAN 
MATHEMATICS  CLASS 10+1

Lesson plan for math. class XI  Three Dimensional Geometry, cbse lesson plans for mathematics teachers,  , lesson plan for maths class XI, lesson plan for maths teacher in B.Ed.

RMB DAV CENTENARY PUBLIC SCHOOL NAWANSHAHR
NAME OF THE TEACHER				DINESH KUMAR
CLASS	XI	CHAPTER	11	SUBJECT	MATHEMATICS
TOPIC	THREE DIMENSIONAL GEOMETRY			DURATION : 10 Class Meetings

PRE- REQUISITE KNOWLEDGE:

• Knowledge of coordinate geometry class X

TEACHING AIDS:

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

METHODOLOGY:-   

Lecture method,  Demonstration and scaffolding method of learning.

LEARNING OBJECTIVES:

• Introduction to three Dimensional Geometry.

• Coordinate axis and coordinate planes in three dimensional geometry.

• Distance between two points by using distance formula.

• Section formula and problems based on it.

• Median and centroid of triangle

LEARNING OUTCOMES:

• After studying this lesson student should know
• Quadrants and Octants and their sign convention.
• How to write the coordinates on the axis, in the plane and in the octants.
• Distance formula, section formula, mid-point formula, centroid of the triangle and application of these formulas 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

Three-Dimensional Geometry (3D Geometry) , Cartesian Coordinate System , Coordinate Axes , X-axis , Y-axis , Z-axis , Origin , Coordinate Planes , XY-plane , YZ-plane , ZX-plane , Octants , Ordered Triplet , Coordinates of a Point , Abscissa , Ordinate , Space , Distance formula , Section Formula , Internal Division, External Division , Midpoint Formula , Collinear Points.

CONTENT OF THE TOPIC

• Interoduction

• Coordinate axis and coordinate planes in three dimensional planes

• Quadrants and octants

• Distance formula, section formula, mid-point formula, median, centroid.

LEARNING ACTIVITIES:

INTRODUCTORY ACTIVITY
Mathematics Activity No 19 Class XI

EXPERIENTIAL ACTIVITY
Mathematics Activity No 3 Class XI

ART INTEGRATED ACTIVITY
Art Integrated Project

PROCEDURE  & EXPLANATION

Complete Explanation

Start the session by asking questions on the coordinate geometry based on class X. Now introduce the topic Three Dimensional Geometry  step by step as follows.

Introduction :

To locate the position of a point in a plane we need two intersecting mutually perpendicular lines in the plane. These lines are called coordinate axis and the two points in this case are called the coordinates of the point with respect to the axis.

To locate the position of an object in a space we need three mutually perpendicular planes. These planes are called three coordinate planes.  The three numbers representing the three distances of an object from three coordinate planes are called the coordinates of the point on the object. So any point in space has three coordinates.

Coordinate axis and coordinate planes in three dimensional planes

Coordinate axis in two dimensions divide the plane into four quadrants. 

In three dimensions coordinate planes divide the space(three dimension) into eight octant, as shown in the figure.

Quadrants

With the help of quadrants we can make the sign convention for octant as follows.

For x-axis  and y-axis Sign convention in different quadrant is given as above.

In three dimension we have one more axis that is z-axis. 

For first four octant we take the sign as it is in I to IV  quadrant and the sign of z-axis is taken positive. 

For last four octant we again  take the sign of x axis and y-axis as given in I to IV quadrant and sign of z-axis is taken negative.

Octant

So sign convention for eight octant is written as

Octant	I	II	III	IV	V	VI	VII	VIII
Sign	(+,+,+)	(-,+,+)	(-,-,+)	(+,-,+)	(+,+,-)	(-,+,-)	(-,-,-)	(+,-,-)

Coordinates of the point on x-axis is (x, 0, 0),

Coordinates of the point on y-axis is (0, y, 0), 

Coordinates of the point on x-axis is (0, 0, z),

Coordinate of the point in xy-plane is of the form (x, y, 0), 

Coordinate of the point in yz-plane is of the form (0, y, z), 

Coordinate of the point in zx-plane is of the form (x, 0, z),

Coordinates of a point in space is of the form (x, y, z)

Distance Formula

Distance between two points P(x₁,y₁, z₁) and Q(x₂,y₂,z₂) is given by

Section Formula:

Here two cases are arises

1. If Point P(x,y,z) divide the  line through the points A(x₁,y₁,z₁) and B(x₂,y₂,z₂) in ratio m₁ : m₂  internally, then coordinates of point P are given by section formula:

2. If Point P(x, y, z) divide the  line through the points A(x₁, y₁, z₁) and B(x₂, y₂, z₂) in ratio m₁ : m₂  Externally, then coordinates of point P are given by section formula:

Mid-Point formula:

If Point P(x, y, z) is the mid-points of the line joining the points A(x₁, y₁, z₁) and B(x₂, y₂, z₂) then

Median:

Median is the line segment which join the vertex of the triangle with the mid-point of the opposite side.

Centroid:

Point of concurrence of all the median of the triangle is called its centroid

Centroid of the triangle whose vertices are A(x₁, y₁, z₁),  B(x₂, y₂, z₂)  and C(x₃, y₃, z₃) is given by

Centroid of the triangle divide the median in 2 : 1

Centroid of the given triangle and the triangle obtained by joining the mid-points of the sides of the triangle are same.

STUDENTS DELIVERABLES:

• Review questions given by the teacher.

• Students should prepare the presentation individually or in groups on the basic concepts and formulas based on the topic Three Dimensional Geometry. 

• Solve NCERT problems with examples.

EXTENDED LEARNING:

Students can extend their learning in   through the Resource Centre Mathematics . Students can also find many interesting topics on mathematics at the site:  cbsemathematics.com

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.

ASSESSMENT TECHNIQUES:

• Assignment sheet (Home Assignment) 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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