Lesson plan of Divisors and Multiples

Objectives (5-10 mins)

1. Understanding basic concepts:

   • To define divisors and multiples of a number.
   • To understand the differences between divisors and multiples.
   • To recognise the importance of these concepts in solving mathematical problems.

2. Identifying divisors and multiples:

   • To develop the skill of identifying divisors and multiples of a number given.
   • To apply the knowledge to finding the divisors and multiples of various numbers.

3. Problem-solving:

   • To apply concepts of divisors and multiples in solving practical problems. -To practice the skill of logical thinking and application of mathematical concepts to real life situations.

Additional Objectives:

-To promote active student participation through practical hands-on, and interactive activities.

• To develop teamwork skills, and the ability to clearly and effectively communicate mathematical ideas. -To foster the love and interest for Mathematics by demonstrating its applications and relevance to real-world situations.

Introduction (10-15 mins)

1. Reviewing Previous Concepts: -The lesson starts with the teacher recalling the concept of prime numbers and composites which have already been taught in the prior class. He may ask questions to the students to check their retention of the concept like " What is a prime number " or "Give an example of composite number" ( 5 minutes )

2. Problem Situation:
   -After the revision the teacher introduces two problem situations that will be the stepping stone of the development theory . These situation could be :" What are the divisors of 12 ?" " What are multiples of 5?" The students are asked by the teacher to do a bit of thinking and attempt the answers even in their intuitive manner. (5 minutes )

3.Contextualisation:

• The teacher now contextualises the importance of the divisors and multiples and explain to them that these concepts are crucial in simplification of fractions and in solving of the problem related to multiples and divisors like arrangements in rows and distributing objects into boxes . Further , he can also mention how the concept has got its wide applications areas such as in Engineering , Physics ,Computer Science. ( 3minutes)

4.** Introduction of Topic**: -The lesson topic is introduced where the students learn that divisors of the numbers is any whole number which divides wholly without any remainders while multiples of the number are those which are the result of multiplication of whole numbers . He may write the definitions on board for the students to copy it down . (2 minutes )

5. Fun Facts and stories:
   To interest the students the teacher may like to share some of the fun facts and stories related to the subject. He can tell them how ancient Greeks considered numbers perfect if sum of the factors (other than itself ) is the number itself and even today mathematicians do not have an answer whether there are infinite such perfect numbers or not. Another fascinating fact he may quote is the multiples of 9 have an amusing characteristic : Sum of digits in multiples 9 always result into multiples of 9 itself (5 minutes)

Development (20-25 minutes)

1.Activity " Divisors and Multiples" ( 10 - 15 minutes ) :

• Divide students in smaller groups and provide them cards having various number written in it ( For Example 12 ,15,20 , 25,30,etc). Each of the group should pick out one number and write its all corresponding divisors as well as multiples. -The teacher moves across the class helping groups , clarifying the doubts and also observes how the group members interact with each other and manages the activities as also how the exchange of ideas are being done. After a few minutes of group activity , each of the groups is asked to share the factors as multiples of the numbers they had picked up .The teacher uses these presentation to reinforce the differences in divisors and multiples and also for correcting any misconceptions.

2. ** Activity " Which Number is IT" ** ( 10-15 minutes) :
   Still in the groups students receive sheet with list numbers that either divisible by particular number (for Example 2,3,4 ,5 ,6 , etc ) or are the multiples of the specific numbers ( for example 10 , 15,20, 25 , 30, etc ) . The challenge here is to identify which number it is specifically . To do this students will be required to use the concepts in divisors and multiples thereby eliminating numbers that do not fit into that category. -The teacher move around helping out the groups that are finding it difficult , asking probing question that encourage logical thinking and understanding of concept. By end of the activities each of the groups should be identifying all the numbers with reason and justification. This part is used by teacher for recapitulation of the concept as also for correction if any wrong learning has happened .

3. ** Discussion and Closure ** ( 5 -10 minutes ) : -The teacher assemble all students in the group and leads the discussion about activities done so far. This could include question such as "What is most significant idea you learnt from today's lesson" , "Were there any challenges you faced and what strategies did helped solve those" . The teacher summarise discussion reinforcing main concepts covered and the significance of the divisors in multiples in Mathematics as well as in different field knowledge .He further gives a short recap of the tasks and the outcome of it ,highlighting the strengths and possible improvements for future classes. The lesson concludes with teacher asking the class to think independently on the concepts learnt in the class with some real life applications of concepts of the divisors and the multiples .He asks the students to write down their reflections and questions to be brought to next class.

Retrieval ( 5-10 mins)

1.Group Discussion (2 -3 minutes ) : -The Teacher gathers the entire class and initiates the discussion on the solution/conclusion derived by every teams during the activity. He seeks the strategy adopted for finding out divisors and the multiples of given number by teams and how these were implemented in the context of given problem solving.

• The students are motivated by the teachers to share their understanding in the comfort zone created.

2. **Linking to the Theory ( 2 - 3 minutes) : The lesson now bridges the practical activity done by students to the theory introduced in the beginning. He reiterates the definition of the divisors and the multiple and how these are seen to be executed to derive solutions in the activities .
   -The teacher here may emphasize that divisors are the number that divide the other number without leaving a remainders and multiples are those which are the outcome of multiplication of wholly number. He may further reinforce that the concept has practical application such as arranging objects sequentially in rows, distribution in boxes , reducing fractions.

3.**Concluding Reflection ** ( 1- 2 minutes ) : To wind up the class students are requested to spend some time in silent contemplation on what was learned. He ask question such as :" What is one important idea that you grasped from the lesson today" or " What are few things that still need to be clarified or practiced" . -A moments is provided to the class to mull over these question before they are asked to voice out there thoughts. He listens intently to the students' responses ,appreciate the class in whole for enthusiastic involvement , and encourage them to continue developing these thoughts till next class encounter .

Feedback & Assessment ( 1 -2 minutes):

-The teacher concludes the class with taking a short feedback on the lesson , asking what students enjoyed most in it and areas which could be improved further in future.He also can do a quick check their level of understanding , by asking if they are feeling comfortable and ready in applying the divisors' concepts and multiple to different real - life situation . -Thank the class for active involvement in the class , reiterating that continuous efforts , studying , practice and revisits of the concept is the essence for learning of Mathematics. He concludes by bidding farewell to the class for the week and reminding them to complete a small assignment to be brought in next class.

Closure( 5 -10 minutes )

1. ** Summary Recap** (2 - 3minutes ) :
   -The class concludes with the teacher wrapping up the main emphasis covered in the class .He recapitulates the definitions of the divisor and multiples, their distinctive characteristics and the identification of them . He then revisits the class activity , emphasizing the application and strategy used for completing it.

2. **Connecting Theory ,Practice and Application **( 2-3 minutes) : The teacher highlights the way in which the class was designed to connect the theory, practice , application of the divisors and multiples.He reinforces that theory introduced beginning of the class were implemented in practical activity and that the activity provided them with better comprehension of the concept and it use cases.
   -The teacher further elaborates some real world examples where this knowledge is applied like in simplifying fraction , organizing things in lines or in rows, distributing things equally into containers.

3.**Additional Resources (1- 2 minutes ) : -For the students who wish extend learning beyond the class teacher may suggest few additional resources. They could be books, educational website , video links or interactive game . For instance the teacher can recommend website " Khan Academy " which has dedicated sections for the topic divisors , multiples with video and interactive exercise. He can further encourage them to practice more exercise in home for mastering the concept and address their doubts or difficulties in next class.

4.** Importance of the Topic (1 -2 minutes): Finally the teacher stresses on the relevance of the study of the concept of divisors and multiples in mathematics and other fields knowledge and studies.He elaborates how this concept is not only essential in Mathematics for problem-solving but it also has many real - life application and relevance to other subject and professions. The teacher finally conclude the lesson ,thank the students and reminding them to review the concept learnt and complete the assigned homework He bids farewell to the students for that day wishing them well and reminding to keep pondering on the concepts to be discussed the following day.