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 10 Ch-1 | Real Numbers

lesson Plan Maths Class 10 Real Numbers

Lesson Plan in mathematics class 10 chapter 1 Number System. New Technology Integrated Lesson Planning in Mathematics for mathematics teacher.

Technology Integration Lesson Plan (CBSE Guidelines)

(with Constructivism Elements)

Teacher                    :   XYZ

School                         :     XYZ

Subject Area(s)        :  Mathematics

Grade Level / Class    :  10 th Grade

Lesson Title/Topic   : Number System

Estimated Duration: 

This lesson is divided into eight modules and it is completed in eight class meetings. Each class meeting should be of 40 minutes.


Lesson Goals/ 



What will students experience and be able to do as a result of this lesson or project? 



·         All definitions related to the number system ( definition of natural number, whole numbers, Integers, rational numbers, irrational numbers, Real numbers, odd numbers, even numbers, prime numbers, co-prime numbers, composite numbers).

·         Different types of decimals (Terminating, Non-terminating but repeating, non-terminating non-repeating decimals)

·         Rational and irrational decimals.

·         To find HCF by using Euclid’s Division Algorithm (E.D.A.)

·         To find HCF and LCM of numbers by using Fundamental Theorem of Arithmetics (F.T.A.)

·         Method of proving the given number as  irrational number.

·         Explanation of terminating and non terminating decimals.

·         Method of converting rational 

Curriculum Addressed: 


What specific curriculum learning outcomes will be addressed in this lesson or project? 


Learning Outcomes

After studying this lesson, students will be able to explain and solve the problems related to  the 


i) Euclid's Division Algorithm (EDA) and HCF by EDA,


ii) Fundamental Theorem of Arithmetic  and find LCM and HCF by using FTA


iii)  Students should know the method of proving the given number is an irrational number. 


iv) Students will be able to explain that given number is an irrational number, terminating decimal and non terminating but repeating decimals.

Technology Addressed: 


What technology skills and/or goals will be addressed in this lesson or project? 



Technology used during Lesson Planning

  • Google Site for complete explanation of the topic.
  • Google forms for  online assessment.
  • Google slides for making Video on the Number System.
  • Google Docs to explain the topic.
  • Google meet for audio visual interaction with the students.

Technology Required: 


What software programs and hardware are needed for this lesson or project? 


Technology Required to deliver the lesson

  • Smart Board for the explanation.
  • Laptop or computer, Smart Phone with internet connection.
  • Google Meet app for audio visual interaction with the student.

Other Materials/ 



What other materials will be needed to carry out the lesson objectives? What resources will be needed including books, web page links and/or outside speakers, etc.? 


Basic points and formulas of Number System (Natural Number, Whole Numbers, Integers, Rational numbers, irrational numbers, Real numbers)

Knowledge of divisibility test to factorise

All exercises of NCERT Text Book Class 10 with examples.


Assignment given by the teacher.


Complete Family of Number System

Students can get step by step knowledge about the number system from this figure.



What the student does that is consistent with this model:
Shows interest in the topic by asking questions, such as:

  • "Why did this happen?"
  • "What do I already know about this?"
  • "What can I find out about this?"

Number system is used everywhere in our day to day life. e.g

To engage the students in the teaching learning process, teacher can ask the questions related to the following points :

1. Calling a member of a family or a friend using mobile phone.

2. Calculating your daily budget for your food, transportation, and other expenses.

3. Cooking, or anything that involves the idea of proportion and percentage.

4. Weighing fruits, vegetables, meat, chicken, and others in market.

5. Using elevators to go places or floors in the building.

6. Looking at the price of discounted items in a shopping mall.

7.  Looking for the number of people who liked your post on Facebook.

8.  Switching the channels of your favorite TV shows.

9. Telling time you spent on work or school.

10. Computing the interest you gained on your business.


Teacher can engage the student by showing VIDIO on the NUMBER SYSTEM. 

Google Meet App : Teacher can use Google Meet App for Audio-Visual interaction with the students.


What the student does that is consistent with this model:

  • Uses inquiry to explore and investigate; to satisfy his/her curiosity about the chosen concept/topic.
  • Thinks freely, but within the limits of the activity.
  • Tests predictions and hypotheses.
  • Forms new predictions and hypotheses.
  • Experiments with alternatives and discusses then with others.
  • Records observations and ideas.
  • Suspends judgments’.

With this model students become able to explain :

  • Odd numbers, even numbers, prime numbers, co - prime numbers, composite numbers all are natural numbers.
  • All natural numbers are whole numbers.
  • All whole numbers are Integers.
  • All integers are rational numbers.
  • All rational and irrational numbers are Real numbers.
  • HCF and LCM can be calculated by using different methods.
  • Importance and applications of rational and irrational numbers.


What the student does that is consistent with this model:

  • Uses various informational resources, group discussions, and teacher interaction to derive definitions and explanations of the chosen concept.
  • Explains possible solutions or answers to others' explanations.
  • Listens critically to others' explanations.
  • Questions others' explanations.
  • Listens to and tries to comprehend explanations the teacher offers.
  • Refers to previous activities.
  • Uses recorded observations in explanations.


Teacher will draw a number line and mark rational numbers on it. Teacher will ask the class why there are gaps between two rational numbers. After getting different answers from class, irrational numbers will be introduced.

As all the numbers can ‘not be represented in p/q form, where q 0

Difficulties in expressing length of the diagonals of certain squares  ( eg. Square of side 1 unit) in the form of rational numbers led to the discovery of irrational numbers. Irrational numbers seems to fill gap between rational numbers. 

Smart board content based on representation of irrational numbers on number line will be shown.

Real no. model will be used to show hierarchy of number system.



Teacher should start the topic with Introduction of number system, Definitions of all types of numbers with explanations. Different types of decimals, terminating decimals, non-terminating but repeating decimals, non-terminating non-repeating decimals, rational decimals and irrational decimals. Definitions of Lemma, Algorithm, Euclid’s Division Lemma, and application of E. D. A in some word problems.


Euclid's Division Lemma: For given two positive integers a and b there exist unique integers q and r such that a = bq + r ,    where  0 ≤ r < b Explain the Method of finding the HCF by using Euclid’s Division Lemma with two numbers and with three numbers. Definitions of Fundamental Theorem of Arithmetic’s, L.C.M and H.C.F. Method of finding the HCF and L.C.M. by using F.T.A. and verification of the relation H.C.F. X L.C.M. = Product of two numbers.


Fundamental Theorem of Arithmetic: Every composite number can be expressed as the product of primes and this factorization is unique irrespective of their order.

L.C.M: Product of all factors with greatest power.

H.C.F: Product of common factors with smallest power. Explain the Method of contradiction to prove that given number is an irrational number. Method of finding rational and irrational decimals   without actual division and method of converting the given rational number into decimal form.

Condition of denominator of a Rational Decimal: Denominator can be expressed in the form 2m x 5n



What the student does that is consistent with this model:

  • Makes connections and sees relationships of the concept/topic in other content areas.
  • Forms expanded understanding of original concepts/topics.
  • Makes connections of concept/topic to real world situations.


  • With this model students are able to identify different types of numbers, complete family of Number System, different types of decimals, which are further helpful in understanding and solving the problems.
  • This model is helpful in finding the LCM and HCF by using different techniques like Euclid’s Division Lemma and Fundamental Theorem of Arithmetic.
  • This model also helps the students in understanding the difference between the rational and irrational numbers.



What the student does that is consistent with this model

  • Answers open-ended questions by using observations, evidence, and previously accepted explanations.
  • Demonstrates an understanding or knowledge of the concept or skill.
  • Evaluates his or her own progress and knowledge.
  • Uses alternative assessments to demonstrate their understanding of the concept/topic.


Evaluation Techniques

  • Some worksheets including logical reasoning, application and understanding of the concept based and higher order thinking skills will be prepared separately. It will improve their logical thinking and reasoning power.

  • Teacher can prepare assignments for the students which cover whole topic completely. These assignments can be given for practice and these can be evaluated by conducting class test.

Teacher Self-Assessment: 


How well did the lesson work overall? What were the strengths of the lesson? What were the weaknesses of the lesson? How can I improve the lesson for next time? 




Self Assessment Techniques :

Assignment having three different levels which will include questions from direct application of concept to logical thinking and higher order thinking skills.

  • An assignment comprises of questions covering all the topics discussed in the class with three different levels, from easy to HOTS and previous year board questions will be given for practicing
  • Class test(s) will be conducted. At the end of chapter a class test will be taken. 

  • Re-test(s) will be conducted on the basis of the performance of the students in the test.




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