Meaning of a multiple and a common multiple for JSS 1

Class: JSS 1
Term: First Term
Week: 3
Age: 12 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: NUMBER NUMERATION
Focal competence: Calculate the LCM of two or more whole numbers
Key competencies/values: Collaboration; Critical Thinking
Skills:

• Determining of common multiples of two or more whole numbers

Previous Lesson: Writing numbers in millions, billions and trillions
Topic: Lowest Common Multiples (Lcm)
Subject Matter: Meaning of a multiple, Meaning of a common multiple

Specific Objectives

By the end of the lesson, pupils/students should be able to:

Cognitive Domain

• Define a multiple.
• Define a common multiple.
• Identify multiples of two or more whole numbers.
• Identify common multiples of two or more whole numbers.

Psychomotor Domain

• Generate multiples of selected numbers using repeated addition or multiplication.
• Determine common multiples of whole numbers by listing.

Social Domain

• Collaborate with peers to solve problems involving common multiples.

Reference Materials

The following resources were used in planning this lesson:

• 2025 Revised 9 Years Basic Education Curriculum
• Relevant State Unified Scheme of Work
• New General Mathematics for Junior Secondary Schools 1
• The HeadTeacher Scheme of work

Instructional Materials

The teacher will teach this lesson with the aid of:

• Place value Number Charts
• Flash cards showing multiplication facts
• Number cards
• Whiteboard/Blackboard and markers/chalk

Rationale for the Lesson

Understanding multiples and common multiples is foundational for many mathematical concepts, especially for finding the Lowest Common Multiple (LCM) and working with fractions. This lesson provides students with essential skills for number manipulation and problem-solving in everyday contexts.

Prerequisite/Previous Knowledge

Students should have a basic understanding of multiplication tables and repeated addition of whole numbers.

Lesson Content/Board Summary

Lowest Common Multiples (LCM)

Meaning of a Multiple

A multiple of a number is the result of multiplying that number by any whole number (except zero). In other words, multiples are the numbers you get when you count by a specific number.

For example, the multiples of 3 are obtained by multiplying 3 by 1, 2, 3, 4, and so on:

1. (3 times 1 = 3)
2. (3 times 2 = 6)
3. (3 times 3 = 9)
4. (3 times 4 = 12)
5. (3 times 5 = 15)

So, the multiples of 3 are 3, 6, 9, 12, 15, …

Generating Multiples

Multiples can be generated through:

1. Repeated Addition: Add the number to itself repeatedly.

Example: Multiples of 4

• (4)
• (4 + 4 = 8)
• (8 + 4 = 12)
• (12 + 4 = 16)

Example: Multiples of 5

• (5 times 1 = 5)
• (5 times 2 = 10)
• (5 times 3 = 15)
• (5 times 4 = 20)

Listing Multiples of Selected Numbers

To list multiples, simply follow the pattern of multiplication or repeated addition.

1. Multiples of 6: 6, 12, 18, 24, 30, 36, …
2. Multiples of 7: 7, 14, 21, 28, 35, 42, …
3. Multiples of 10: 10, 20, 30, 40, 50, 60, …

Meaning of a Common Multiple

A common multiple of two or more numbers is a number that is a multiple of all those numbers. It appears in the list of multiples for each of the numbers.

For example, to find common multiples of 2 and 3:

1. Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, …
2. Multiples of 3: 3, 6, 9, 12, 15, 18, 21, …

The common multiples of 2 and 3 are 6, 12, 18, …

Identifying Common Multiples

To identify common multiples, list the multiples of each number and then find the numbers that appear in all the lists.

Example: Find the first three common multiples of 4 and 6.

1. Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, …
2. Multiples of 6: 6, 12, 18, 24, 30, 36, 42, …

The common multiples of 4 and 6 are 12, 24, 36.

Teaching Methods/Instructional Techniques

Discussion, Explanation, Question and Answer, Guided Practice, Group Work, Individual Practice

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Activating prior knowledge

Teacher’s Activity: The teacher greets the students and reviews multiplication facts by asking questions like, “What is (3 times 4)?” or “What is (5 times 2)?” The teacher then introduces the topic by explaining that today’s lesson builds on their knowledge of multiplication.

Pupils’ Activity: Students respond to the multiplication questions and listen attentively to the introduction.

Learning Point: Prior knowledge of multiplication

Step 2: Meaning of a Multiple

Time: 8 minutes

Teaching Skill: Explanation/Definition

Teacher’s Activity: The teacher defines a multiple as the result of multiplying a number by a whole number. The teacher provides examples of multiples for small numbers (e.g., multiples of 2: 2, 4, 6, 8…). The teacher demonstrates how to generate multiples using repeated addition and multiplication.

Pupils’ Activity: Students listen, ask questions for clarity, and identify the next few multiples of a given number when prompted.

Learning Point: Definition of a multiple

Step 3: Generating and Listing Multiples

Time: 7 minutes

Teaching Skill: Demonstration/Guided Practice

Teacher’s Activity: The teacher guides students to generate and list the first five multiples of numbers like 3 and 5 on the board. The teacher uses both repeated addition and multiplication methods, linking to number patterns.

Pupils’ Activity: Students participate by suggesting multiples and listing them in their rough notebooks, observing the number patterns.

Learning Point: Generating and listing multiples

Step 4: Meaning of a Common Multiple

Time: 7 minutes

Teaching Skill: Explanation/Comparison

Teacher’s Activity: The teacher introduces the concept of a common multiple by listing multiples of two different numbers (e.g., 2 and 3) and asking students to identify numbers that appear in both lists. The teacher then formally defines a common multiple.

Pupils’ Activity: Students observe the lists, identify common numbers, and listen to the definition.

Learning Point: Definition of common multiple

Step 5: Identifying Common Multiples

Time: 7 minutes

Teaching Skill: Guided Practice/Problem Solving

Teacher’s Activity: The teacher presents an example, such as finding the common multiples of 4 and 6. The teacher guides students through the steps: list multiples of 4, list multiples of 6, and then identify the numbers common to both lists. The teacher uses flash cards or number charts to aid visual understanding.

Pupils’ Activity: Students work in groups to list multiples and identify common multiples, discussing their findings.

Learning Point: Identifying common multiples

Step 6: Group Activity for Determining Common Multiples

Time: 6 minutes

Teaching Skill: Collaboration/Application

Teacher’s Activity: The teacher divides students into groups and provides them with numbers (e.g., 3 and 5, or 6 and 9) to find their first few common multiples using the listing method. The teacher monitors and provides support.

Pupils’ Activity: Students work collaboratively in their groups to determine the common multiples, comparing their answers within the group.

Learning Point: Determining common multiples

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. What is a multiple?
2. List the first five multiples of 7.
3. What is a common multiple?
4. Identify the first two common multiples of 2 and 5.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Understanding of multiples

Step 8: Note-Taking

Time: 4 minutes

Teaching Skill: Guided Writing

Teacher’s Activity: The teacher guides pupils/students to copy the essential Board Summary notes on the meaning of multiples and common multiples into their notebooks.

Pupils’ Activity: Pupils/students copy the notes carefully into their notebooks.

Learning Point: Recording lesson notes

Step 9: Conclusion

Time: 1 minute

Teaching Skill: Summarisation

Teacher’s Activity: The teacher briefly recaps the definitions of multiples and common multiples, emphasising their importance in number theory.

Pupils’ Activity: Students listen and confirm their understanding.

Learning Point: Recap of key concepts

Continuous Assessment/Further Study

Type: Homework

Instruction: Answer the following questions in your notebook:

1. Define a multiple in your own words.
2. Write down the first six multiples of 8.
3. Define a common multiple.
4. Find the first three common multiples of 3 and 4.
5. List the first five common multiples of 5 and 10.

Lesson Keywords

• Multiple – The product of a number and any whole number.
• Common Multiple – A number that is a multiple of two or more given numbers.
• Repeated Addition – Adding the same number multiple times.
• Number Pattern – A sequence of numbers following a specific rule.

Differentiation

For weaker learners: Provide a multiplication chart to help them generate multiples. Focus on finding common multiples of smaller numbers (e.g., 2 and 3). Offer more one-on-one guidance during group activities.

For faster learners: Challenge them to find common multiples of three numbers (e.g., 2, 3, and 4) or larger numbers. Encourage them to explain their methods to their peers.

Suggested Lesson Videos

Search YouTube for: JSS 1 multiples and common multiples

Teacher Guide for Using This Lesson Plan

Before the lesson, ensure you have your number charts, flash cards, and number cards ready. Begin by quickly reviewing multiplication to activate prior knowledge. When introducing multiples, use clear, simple language and demonstrate both repeated addition and multiplication methods. For common multiples, visually show the lists of multiples for two numbers side-by-side on the board to make identification easier. Encourage group work for identifying common multiples to foster collaboration and critical thinking. During the note-taking stage (Step 8), guide students to copy the Board Summary accurately. Pay attention to students who might confuse factors with multiples. Reinforce that multiples are always equal to or greater than the original number. Conclude by reiterating the main concepts and assigning homework to consolidate learning.