PERMUTATIONS & COMBINATIONS Rank of the word or Dictionary order of the English words like COMPUTER, COLLEGE, SUCCESS, SOCCER, RAIN, FATHER, etc. Dictionary Rank of a Word Method of finding the Rank (Dictionary Order) of the word “R A I N” Given word: R A I N Total letters = 4 Letters in alphabetical order: A, I, N, R No. of words formed starting with A = 3! = 6 No. of words formed starting with I = 3! = 6 No. of words formed starting with N = 3! = 6 After N there is R which is required R ----- Required A ---- Required I ---- Required N ---- Required RAIN ----- 1 word RANK OF THE WORD “R A I N” A….. = 3! = 6 I……. = 3! = 6 N….. = 3! = 6 R…A…I…N = 1 word 6 6 6 1 TOTAL 19 Rank of “R A I N” is 19 Method of finding the Rank (Dictionary Order) of the word “F A T H E R” Given word is : "F A T H E R" In alphabetical order: A, E, F, H, R, T Words beginni
Lesson Plan Math Class 12 Ch-11 | Three Dimensional Geometry
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DAPS
E- LESSON PLAN
SUBJECT MATHEMATICS CLASS 10+2
Lesson Plan, Class XII Subject Mathematics, chapter 11, Three Dimensional Geometry , for Mathematics Teacher. Effective way of Teaching Mathematics. Top planning by the teacher for effective teaching in the class. E lesson planning for mathematics.
Board – CBSE |
CLASS –XII |
SUBJECT- MATHEMATICS |
CHAPTER 11 :- Three Dimensional
Geometry |
TOPIC:- CHAPTER 11
: Three Dimensional Geometry
DURATION:-
This
chapter is divided into 18 modules and is completed in 20 class meetings.
PRE-
REQUISITE KNOWLEDGE:-
Knowledge
of simple concepts of trigonometry , geometry and algebra.
Knowledge
of coordinate geometry class X.
TEACHING
AIDS:-
Green
Board, Chalk, Duster, Charts, smart
board, projector, laptop etc.
METHODOLOGY:- Lecture
method
OBJECTIVES:-
- Direction ratios and direction cosines of a line joining two points.
- Cartesian and vector equation of a line.
- Coplanar and skew lines.
- Angle between two lines. Conditions at which two lines are parallel and perpendicular.
- Shortest distance between two lines. Shortest distance between two parallel lines.
- Cartesian and vector equation of a plane.
- Angle between two planes. Conditions at which two planes are parallel and perpendicular.
- Angle between a line and a plane.
- Distance of a point from a plane.
PROCEDURE
:-
Start
the session by asking the questions related to the scalar and vector
quantities, their scalar product, vector product and their scalar triple product.
Now introduce the topic Three dimensional geometry step by step as follows.
EXPECTED
OUTCOMES:-
After
studying this lesson students should know the
- direction cosines and direction ratios of a line joining two points.
- equation of line passing through one point and two points.
- equation of plane passing through one point and three points
- Students should knows the angle between two lines between two planes between a line and a plane.
- shortest distance between two lines
- shortest distance between two parallel lines.
- perpendicular distance of the point from the plane.
STUDENTS
DELIVERABLES:-
Review questions given by the teacher.
Students should prepare the presentation on different equations of line and
plane in vector and Cartesian form. Solve NCERT problems with examples.
EXTENDED LEARNING:-
Students can extend their learning in Mathematics through the RESOURCE CENTRE
Students can also find many interesting topics on mathematics at cbsemathematics.com
Students can also find many interesting topics on mathematics at cbsemathematics.com
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.
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