### Dictionary Rank of a Word | Permutations & Combinations

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 X (Ch- 12) | Area Related to Circle

E- LESSON PLAN   SUBJECT MATHEMATICS    CLASS 10
lesson plan for math class X chapter 12 coordinate geometry, lesson plans for mathematics teachers,  Method to write lesson plan for math class 10, lesson plan for math class X, lesson plan for mathematics grade X, lesson plan for math teacher in B.Ed.

 TEACHER  : SCHOOL : SUBJECT   :   MATHEMATICS CLASS                  :   X  STANDARDBOARD                 :  CBSE LESSON TOPIC / TITLE   : CHAPTER 12:  AREA RELATED TO CIRCLE ESTIMATED DURATION: This topic is divided into seven modules and are completed in seven class meetings.

PRE- REQUISITE KNOWLEDGE:-

Basic knowledge of plane figures like circle triangle and quadrilateral class VIII and IX .

TEACHING AIDS:-  Green Board, Chalk,  Duster, Charts  etc.

METHODOLOGY:-  Demonstration and Lecture method

LEARNING  OBJECTIVES:-
• Introduction and definitions related to the circle, radius, diameter, chord, segment, sector, circumference etc.
• Circumference and perimeter of the circle, semi-circle, quadrant and length of arc.
• Area of circle, minor-sector, major-sector, minor- segment, major-segment etc.
• In calculating area of segment of a circle, problems should be restricted to central angle of  60o, 90o, 120o.
• Area related to the other plane figures like triangles and quadrilaterals should be taken.
• Problems based on the combinations of plane figures: circle, triangle and quadrilateral should taken and discussed thoroughly.

PROCEDURE :-

Start the session by checking the  previous knowledge of the students, by asking the questions about radius, diameter, chord, segment, sector etc. After this introduce the topic area related to the circle(plane figures) step by step as follows.

 S.NO. TOPIC [For Complete Explanation] 1 IntroductionCircle, triangle quadrilateral and other polygons are two dimensional figures. So these figures are called plane figures. In this chapter we will discuss the area related the plane figures and combinations of plane figures. First of all teacher will define all the terms which are related with the circle, like definitions of  Circle, centre of the circle, radius, diameter, chord, segment, sector, minor segment, major segment, minor sector, major sector, semicircle, quadrant and circumference of the circle. 2 Circumference and perimeterNow teacher will explain different properties of circle to the students and explain the difference between the circumference and perimeter of the circle.Length of curved surface is called circumference and length of the boundary is called perimeter.In case of circle circumference and perimeter both are same. But in semi-circle both are different. 3 Now teacher will explain the formula and method of finding the circumference and perimeter of the circle, semi-circle and quadrant. Circumference of semi-circle = 𝞹rPerimeter of semi-circle = 𝞹r + 2r Perimeter of quadrant of circle = (1/2)𝞹r + 2r 4 Area of Segment and SectorNow teacher will explain the formula and method of finding the area of the circle, semi-circle, quadrant, minor segment, major segment, minor sector, major sector all with central angle 60o, 90o, 120o Also help the students in the implementations of all these formulas. Area of circle  $\pi r^{2}$Area of minor sector  $\frac{\theta }{360}\pi r^{2}$Area of major sector = $\left (\frac{360-\theta }{360} \right )\pi r^{2}$Area of minor segment =  $\left (\frac{\theta }{360} \right )\pi r^{2}-\frac{1}{2}r^{2}sin\theta$Area of major segment =  $\pi r^{2}-Area\; of\; minor\; segment$Area of Quadrant =  $\frac{1}{4}\pi r^{2}$ 5 Now explain the area related to different types of triangles and their implementations in different problems. Area of triangle,  right angled triangle,  equilateral triangle and scalene triangle. Area of triangle = $\frac{1}{2}\times \: base\times height$Area of equilateral triangle = $\frac{\sqrt{3}}{4}\times \left ( side \right )^{2}$ 6 Area of QuadrilateralsNow teacher will explain the area related to different types of quadrilaterals  and their implementations in different problems. Area of trapezium, parallelogram, rectangle, rhombus and square.Area of quadrilateral = $Base\times Height$Area of parallelogram = $Base\times Height$Area of rectangle = $Length\times Breadth$Area of rhombus = $\frac{1}{2}\times d_{1}\times d_{2}$Area of square = $side\times side$ 7 Now teacher will introduce the topic combination of different plane figures and explain the topic by taking different examples. 8 Angle made by minute and hour hand of the watch.Here teacher will explain the  angle made by minute hand in one minute = 6o  and angle made by hour hand in one minute = ( ½)oTeacher will also explain the topic by taking some examples 9 Regular HexagonTeacher will explain the concept of regular hexagon and method of finding its area. A regular hexagon can be divided into six equilateral triangles. So Area of regular hexagon = 6 X Area of equilateral triangle.

LEARNING  OUTCOMES:-

After studying this lesson students should know
• The circle and its components.
• The area and perimeter related to all the plane figures like circle, semi-circle, quadrant, segment, sector, different types of triangles and different types of quadrilaterals.
• Method of solving the problems of plane figures in combination form.
STUDENTS DELIVERABLES:-

• Review questions given by the teacher.
• Students can prepare a presentation on the formulas related to the plane figures.
• Solve N.C.E.R.T. problems with examples.
• Solve assignment given by the teacher.

EXTENDED LEARNING:-

Students can extend their learning through the RESOURCE CENTRE and can find more valuable and interesting concepts 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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