LESSON PLANNING OF PROBLEMS INVOLVING HCF AND LCM

Subject Mathematics

Grade 5^{th}

Students` Learning Outcomes

- Solve real life problems involving HCF and LCM.

Information for Teachers

- HCF and LCM are of great importance in our daily life.

- We use HCF, when we have to make smaller parts of anything through division.
- We use LCM, if there are repeated events.
- Similarly we need the least common multiple to find a common denominator, for adding or subtracting fractions, and to write the fractions into simplest form, we need greatest common divisor.

- Practice more and more to the students, of finding HCF and LCM mentally.
- Review some tables to students, especially 12 x 12, 13 x 13, 22 x 22 etc. because if students are good at tables, they can make correct estimates.
- It`s good if these types of special multiplications are reinforced every now and then.

Material / Resources

Writing board, chalk/ marker, duster, paper chits on which questions are written, textbook

Introduction

- Ask the students;

o What do we mean by HCF?

o What are the methods of finding HCF?

o Which method you like and why?

o Does anyone know any other new method of finding HCF?

o Tell me with estimation, what would be the HCF of 60 and 84?

o What would be the HCF of 30, 24, 16, 42, give estimated answer?

o What do we mean by LCM?

o What are the methods of finding LCM?

o Which method you like and why?

o Does anyone know any other new method of finding LCM?

o Tell the students that, today we are going to look at the application or use of HCF and LCM in real life.

o For example we need the least common multiple to find a common denominator, for adding or subtracting fractions, and to write the fractions into simplest form, we need greatest common divisor.

Development

Activity 1

- With the help of following examples, we can see the use of HCF and LCM.
- How long a stick can exactly measure 10, 12, 14 meters lengths?
- As it is clear from the question that the length of the stick should divide exactly these given three lengths
- So we have to find HCF, as it is a division question.

- The HCF of given numbers is 2, so two meter long stick can measure all the lengths exactly.
- Ali takes Milk after every 12 hour and eats bread after every 8 hour. How often does he need to take both foods at once?
- To answer this, you need to find the LCM of 12 and 8 which is 24.
- It means after every 24 hours Ali takes both foods at the same time.
- With these examples, we have seen that HCF and LCM has application in our daily life as well.

Activity 2

- The following are the Method to solve word problems of HCF and LCM.
- o Keep following in mind.

o Use the KWL method for approaching all problems.

o K means: What do you know?

o W means: What do you want to know?

o L means: What did you learn?

- o Repeat KWL two or three times with the help of the student.

If it is a HCF problem:

o What is the question asking us?

o Do we have to split things into smaller sections?

o Are we trying to figure out how many people we can invite?

o Are we trying to arrange something into groups or rows?

Activity 3

- Write following problem on board and ask students to write on their copies.

- Ask students to underline the important points as per KWL.
- Allocate time 5 minutes.
- Let them think and do independently.
- Allow them to share in pairs.
- After collecting their answers, explain on the board as follows.
- K; the pieces of cloth are 72 and 90 meters wide.
- W; how wide should she cut the strips so that they are the largest possible equal length?
- L; this problem can be solved using HCF because we are cutting or ‘dividing’ the strips of cloth into smaller pieces (factors) of 72 and 90.
- Hence we have seen that where there is dividing or making its smaller, we use HCF.
- Find the HCF of 72 and 90. When you are done do the thumbs up, as such; HCF = 2 x 3 x 3 =18
- So Shumaila should cut each piece to be 18 meters wide.

Activity 4

- If it is a LCM problem (being the discussion again)
- What is the question asking us?
- Do we have an event that is or will be repeating over and over?
- Are we trying to figure out when something will happen again at the same time?
- Write the following problem on the board and ask students to write as well.

- Ask students to underline the important points as per KWL.
- Allocate time 5 minutes.
- Let them think and do independently.
- Allow them to share in pairs.
- After collecting their answers, explain on the board as follows.

K: Bilal exercises every 12

^{th}day and Ismail every 8^{th}day and they both exercised today.W: How many days is it until they will both exercise on the same day again.

L: This problem can be solved using LCM. Because we are trying to figure out when will be the next time they are exercising together. Further we have seen that where there are repeated events, we use LCM.

- Ask to find the LCM of 12 and 8.
- LCM = 2 x 2 x 2 x 3 = 24.
- Hence Bilal and Ismail would exercise after every 24 days.

Activity 5

- Divide the students into groups of mix ability.
- Now provide each group one paper chit / slip of HCF question and other chit / slip of LCM question.
- Give students 10 minutes to solve.
- Now one by one call any two students from each group and ask them to solve and explain the given questions on board.
- At the end, appreciate students through clapping.

Sum up / Conclusion

- HCF and LCM are of great importance in our daily life.
- We use HCF, when we have to make smaller parts of anything through division.
- We use LCM, if there are repeated events.
- Similarly we need the least common multiple to find a common denominator, for adding or subtracting fractions, and to write the fractions into simplest form, we need greatest common divisor.

Use the KWL method for approaching all problems.

K means: What do you know?

W means: What do you want to know?

L means: What did you learn?

Assessment

- Write the following questions on board.

- Now read questions one by one and ask students to think and tell this question will solve with the help of HCF or LCM?
- After taking response from students, tell them that which is the HCF question and which is the LCM?
- Now ask students to solve these questions independently.
- Collect copies from students and check.

Follow up

- Ask students to create any two such word problems to be solved using HCF or LCM.