Class: Junior Secondary School 2 (JSS2, JSS 2)
Term: 1st Term
Week: 4
Age: 13 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Mathematics
Previous Lesson: Factors, Prime Factors, Rules of Divisibility and H.C.F
Topic: Factors and Multiples (Part 2)
Subject Matter: Multiples of numbers, Common multiples and LCM, Squares and square roots, Finding square roots of numbers by factors.

Specific Objectives

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

Cognitive Domain:
(a) Identify multiples and common multiples of numbers.
(b) Calculate the Lowest Common Multiple (LCM) of given numbers.
(c) Explain the meaning of squares and square roots of numbers.
(d) Find the square roots of given numbers by factorization.
Affective Domain:
(a) Develop accuracy and patience in solving mathematical problems.
(b) Appreciate the importance of finding common multiples and square roots in real-life situations.
Psychomotor Domain:
(a) Perform calculations involving multiples, LCM, squares, and square roots correctly.
Social Domain:
(a) Collaborate effectively in group problem-solving activities involving LCM and square roots.

Reference Materials

The following resources was used in planning this lesson:

9 Years Basic Education Curriculum
Lagos State Unified Scheme of Work for Junior Secondary Schools
Math is Fun – “Multiples and Factors” (https://www.mathsisfun.com/numbers/factors-multiples.html)
BBC Bitesize – “Square and Square Roots” (https://www.bbc.co.uk/bitesize/topics/zyhs7p3/articles/z2ndsrd)
Relevant Textbooks

Instructional Materials

The teacher will teach this lesson with the aid of:

Number charts and multiplication tables
Flash cards showing squares of numbers (1–20)
Factorization charts
Whiteboard and marker
Calculators (optional for verification)

Rationale for the Lesson

This lesson helps students understand multiples and square roots, which are foundational to advanced mathematical concepts like algebra, geometry, and measurement.

Prerequisite/Previous Knowledge

Pupils have previously learned the concept of factors, multiples, and divisibility tests and can recall how to list factors and multiples of smaller numbers.

Lesson Content/Board Summary

Factors and Multiples

Multiples of Numbers

A multiple of a number is the product of that number and any whole number. Multiples help us identify common patterns and relationships between numbers.

Examples include:

The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, etc.
The multiples of 5 are 5, 10, 15, 20, 25, etc.

Common Multiples and Lowest Common Multiple (LCM)

Common multiples are numbers that are multiples of two or more given numbers. The Lowest Common Multiple (LCM) is the smallest of these common multiples.

The following are steps for finding LCM:

List the multiples of the given numbers and find the smallest number common to both.
Or, express each number as a product of prime factors.
Multiply the highest powers of all the prime factors to obtain the LCM.

Example:
Find the LCM of 12 and 18.
12 = 2 × 2 × 3
18 = 2 × 3 × 3
LCM = 2 × 2 × 3 × 3 = 36

Squares and Square Roots

The square of a number is the result of multiplying the number by itself. The square root of a number is the number that, when multiplied by itself, gives the original number.

Examples include:

3² = 3 × 3 = 9
√9 = 3
6² = 36 and √36 = 6

The following are perfect squares:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, etc.

Finding Square Roots by Factors

To find the square root of a perfect square by factors, we break the number down into prime factors and group them in pairs. One number from each pair is multiplied to give the square root.

Example: Find √144
144 = 2 × 2 × 2 × 2 × 3 × 3
Grouping in pairs: (2 × 2), (2 × 2), (3 × 3)
Take one from each pair: 2 × 2 × 3 = 12
Therefore, √144 = 12

Teaching Methods/Instructional Techniques:

Discussion, Lecture, Explanation, Demonstration, Group Work, Drill and Practice

Instructional Procedures

To deliver this lesson, the teacher will adopt the following steps:

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher asks pupils questions to recall what multiples and factors are from the previous lesson and writes a few examples on the board.
Pupils’ Activity: Pupils respond by listing examples of multiples and factors.
Learning Point: Pupils recall their understanding of factors and multiples.

Step 2: Multiples and Common Multiples

Time: 10 minutes
Teaching Skill: Explanation
Teacher’s Activity: The teacher explains multiples and common multiples, using simple examples and number charts.
Pupils’ Activity: Pupils identify and list common multiples of given numbers.
Learning Point: Pupils understand the meaning of multiples and how to find them.

Step 3: Finding the LCM of Numbers

Time: 10 minutes
Teaching Skill: Demonstration
Teacher’s Activity: The teacher demonstrates how to find LCM using both listing and prime factorization methods.
Pupils’ Activity: Pupils practice examples under guidance.
Learning Point: Pupils learn to find LCM correctly.

Step 4: Squares and Square Roots

Time: 10 minutes
Teaching Skill: Explanation and Drill
Teacher’s Activity: The teacher defines squares and square roots, showing examples on the board, and demonstrates how to find square roots using factorization.
Pupils’ Activity: Pupils solve similar problems and compare results.
Learning Point: Pupils can find the square and square root of numbers by factorization.

Step 5: Note-Taking

Time: 5 minutes
Teaching Skill: Reinforcement
Teacher’s Activity: The teacher dictates or writes the board summary for pupils to copy.
Pupils’ Activity: Pupils write the notes in their exercise books.
Learning Point: Pupils have a clear and complete record of the lesson.

Step 6: Evaluation/Review

Time: 3 minutes
Teaching Skill: Questioning
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

What is the LCM of 8 and 12?
Write down three multiples of 7.
What is the square of 9?
Find the square root of 64 by factorization.
Pupils’ Activity: Pupils answer the questions orally or on the board.
Learning Point: Pupils demonstrate understanding of multiples, LCM, squares, and square roots.

Step 7: Conclusion

Time: 2 minutes
Teaching Skill: Reinforcement
Teacher’s Activity: The teacher summarizes the main points of the lesson and encourages pupils to practice more examples at home.
Pupils’ Activity: Pupils listen attentively and ask questions.
Learning Point: Pupils consolidate their understanding of the lesson.

Lesson Keywords

Multiple – product of a number and a whole number
LCM – smallest common multiple of two or more numbers
Square – number multiplied by itself
Square Root – number that produces a given number when multiplied by itself
Prime Factorization – breaking a number into prime factors

Differentiation

Teacher supports slower learners with simpler examples and visual aids, while advanced learners solve higher numbers and explain methods to others.

Note for teachers using this lesson plan

Ensure pupils master prime factorization before moving to square roots. Encourage mental calculations for small numbers and use group activities to promote peer learning.