Lesson Plan: Factors and Multiples

Lesson Objectives (अधिगम उद्देश्य)

By the end of the lesson, students will be able to:

English:

  1. Understand the meaning of factors and multiples.
  2. Find factors of given numbers.
  3. Find multiples of given numbers.
  4. Identify common factors and common multiples.
  5. Solve real-life problems based on factors and multiples.

हिंदी:

  1. गुणनखंड और गुणज का अर्थ समझ सकेंगे।
  2. किसी संख्या के गुणनखंड ज्ञात कर सकेंगे।
  3. किसी संख्या के गुणज लिख सकेंगे।
  4. समान गुणनखंड और समान गुणज पहचान सकेंगे।
  5. गुणनखंड और गुणज पर आधारित दैनिक जीवन की समस्याएँ हल कर सकेंगे।

Teaching Aids (शिक्षण सामग्री)

  • Number cards (संख्या कार्ड)
  • Multiplication chart (गुणा तालिका)
  • Blackboard/Whiteboard
  • Counters or beads (गिनती की वस्तुएँ)
  • Worksheets
  • Activity sheets

Previous Knowledge (पूर्व ज्ञान)

Students should know:

  • Multiplication facts (गुणा के तथ्य)
  • Division facts (भाग के तथ्य)
  • Basic numbers up to 1000

Day 1: Introduction to Factors (गुणनखंड का परिचय)

Introduction Activity (प्रारंभिक गतिविधि)

Teacher writes:

12 = 1 × 12
12 = 2 × 6
12 = 3 × 4

Ask students:

"Which numbers are used to make 12?"

Students answer:
1, 2, 3, 4, 6, 12

Teacher explains:

Study Material: Factors (गुणनखंड)

Definition of Factor:

English:
A factor is a number that divides another number exactly without leaving any remainder.

Hindi:
गुणनखंड वह संख्या होती है जो किसी संख्या को पूरा-पूरा विभाजित करती है और शेषफल नहीं छोड़ती।

Example:

Find factors of 12.

Pairs:

1 × 12 = 12
2 × 6 = 12
3 × 4 = 12

Therefore,

Factors of 12 are:

1, 2, 3, 4, 6 and 12

12 के गुणनखंड हैं:

1, 2, 3, 4, 6 और 12

Important Points (महत्वपूर्ण बिंदु)

  1. Every number has at least two factors.

    हर संख्या के कम से कम दो गुणनखंड होते हैं।

Example:

Factors of 5:

1 × 5

Factors: 1 and 5

  1. The smallest factor of every number is 1.

हर संख्या का सबसे छोटा गुणनखंड 1 होता है।

  1. The greatest factor of a number is the number itself.

किसी संख्या का सबसे बड़ा गुणनखंड वही संख्या होती है।

Classroom Activity

Find factors using multiplication:

Example:

Factors of 18:

1 × 18
2 × 9
3 × 6

Factors:

1, 2, 3, 6, 9, 18

Practice Questions

Find the factors:

  1. Factors of 8 = _______
  2. Factors of 15 = _______
  3. Factors of 20 = _______
  4. Factors of 25 = _______

Day 2: Introduction to Multiples (गुणज का परिचय)

Warm-up Activity

Teacher asks:

Write the table of 5:

5, 10, 15, 20, 25...

Teacher explains:

These numbers are called multiples of 5.

Study Material: Multiples (गुणज)

Definition:

English:
Multiples are numbers obtained by multiplying a number by whole numbers.

Hindi:
किसी संख्या को 1, 2, 3, 4... से गुणा करने पर प्राप्त संख्याएँ उस संख्या के गुणज कहलाती हैं।

Example:

Multiples of 4:

4 × 1 = 4
4 × 2 = 8
4 × 3 = 12
4 × 4 = 16
4 × 5 = 20

Therefore:

Multiples of 4:

4, 8, 12, 16, 20...

Important Points:

  1. Every number has unlimited multiples.

हर संख्या के अनंत गुणज होते हैं।

Example:

Multiples of 3:

3, 6, 9, 12, 15, 18...

  1. The first multiple of every number is the number itself.

किसी संख्या का पहला गुणज वही संख्या होती है।

Activity

Write first five multiples:

Number

Multiples

2

2, 4, 6, 8, 10

5

5, 10, 15, 20, 25

7

7, 14, 21, 28, 35

Day 3: Difference Between Factors and Multiples

Comparison Chart

Factors (गुणनखंड)

Multiples (गुणज)

Factors divide a number exactly.

Multiples are obtained by multiplication.

गुणनखंड संख्या को विभाजित करते हैं।

गुणज गुणा करने से प्राप्त होते हैं।

They are limited.

They are unlimited.

They are smaller or equal to the number.

They are equal to or greater than the number.

Example:

Number = 6

Factors of 6:

1, 2, 3, 6

Multiples of 6:

6, 12, 18, 24, 30...

Activity: Sort the Numbers

Circle factors of 12:

1, 2, 5, 6, 12, 15

Answer:

1, 2, 6, 12

Day 4: Common Factors and Common Multiples

Common Factors (समान गुणनखंड)

Definition:

English:
Factors common to two or more numbers are called common factors.

Hindi:
दो या दो से अधिक संख्याओं के समान गुणनखंड समान गुणनखंड कहलाते हैं।

Example:

Factors of 12:

1, 2, 3, 4, 6, 12

Factors of 18:

1, 2, 3, 6, 9, 18

Common factors:

1, 2, 3, 6

Common Multiples (समान गुणज)

Example:

Multiples of 3:

3, 6, 9, 12, 15, 18...

Multiples of 4:

4, 8, 12, 16, 20...

Common multiples:

12, 24...

Day 5: Application and Revision

Word Problems (शब्द समस्याएँ)

Question 1:

There are 24 students in a class. They are divided equally into groups. How many different groups can be made?

Solution:

Factors of 24:

1, 2, 3, 4, 6, 8, 12, 24

Possible groups:

1 group of 24 students
2 groups of 12 students
3 groups of 8 students etc.

Question 2:

A bell rings every 5 minutes and another bell rings every 10 minutes. After how many minutes will they ring together?

Multiples of 5:

5, 10, 15, 20...

Multiples of 10:

10, 20, 30...

Common multiples:

10, 20...

Answer:

They will ring together after 10 minutes.

Worksheet (अभ्यास पत्र)

A. Fill in the blanks:

  1. Factors divide a number without leaving ______.
  2. Multiples are obtained by ______ a number.
  3. The smallest factor of every number is ______.
  4. Every number has ______ multiples.
  5. The greatest factor of 20 is ______.

B. Find the factors:

  1. Factors of 16:
  2. Factors of 30:
  3. Factors of 36:

C. Write first five multiples:

  1. Multiples of 3:
  2. Multiples of 8:
  3. Multiples of 12:

D. True or False:

  1. 5 is a factor of 25. (_____)
  2. 20 is a multiple of 5. (_____)
  3. Factors are unlimited. (_____)
  4. Multiples are always greater than the number. (_____)

Assessment Questions (मूल्यांकन)

  1. Define factor.
  2. Define multiple.
  3. Write all factors of 24.
  4. Write first ten multiples of 6.
  5. Find common factors of 15 and 20.

Homework (गृहकार्य)

  1. Write factors of numbers:
    • 14
    • 21
    • 28
    • 40
  2. Write first 10 multiples of:
    • 4
    • 7
    • 9
  3. Find common factors:
    • 12 and 18
    • 20 and 30