Class: Junior Secondary School 3 (JSS3, JSS 3)
Term: 1st Term
Week: 4
Age: 14 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Mathematics
Previous Lesson: Direct and Inverse Proportion
Topic: Rational and Non-rational Numbers
Subject Matter: Identifying rational and non-rational numbers, Determining the approximate value of some non-rational numbers, Determining the approximate value of pi, Finding reciprocals.

Specific Objectives

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

Cognitive Domain:
(a) Distinguish between rational and non-rational numbers.
(b) Determine the approximate value of some non-rational numbers and pi.
Affective Domain:
(a) Appreciate the importance of rational and non-rational numbers in real-life applications.
Psychomotor Domain:
(a) Calculate and represent rational and non-rational numbers on the number line.
(b) Find the reciprocals of given rational numbers.
Social Domain:
(a) Work cooperatively in groups to solve examples on rational and non-rational numbers.

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 – “Rational and Irrational Numbers” (https://www.mathsisfun.com/rational-numbers.html)
Relevant Textbooks

Instructional Materials

The teacher will teach this lesson with the aid of:

Charts showing examples of rational and non-rational numbers
Number line chart
Flash cards with square roots and fractions
Calculators
Whiteboard and markers

Rationale for the Lesson

This lesson helps students understand the distinction between rational and non-rational numbers, their approximate values, and how to find reciprocals for effective mathematical problem-solving.

Prerequisite/Previous Knowledge

Pupils already know about fractions, whole numbers, square roots, and decimals from previous classes and can perform basic arithmetic operations.

Lesson Content/Board Summary

Rational and Non-rational Numbers

Rational and non-rational numbers are types of real numbers. They help us represent quantities accurately in mathematics and daily life.

Rational Numbers

A rational number is any number that can be expressed as a fraction a/b, where a and b are integers and b ≠ 0.
The following are examples of rational numbers:

Whole numbers such as 3, 10, and 25.
Fractions like ½, ¾, and 7/8.
Decimal numbers that terminate or repeat such as 0.5, 2.75, or 0.333….

Example 1:
Show that 0.75 is a rational number.
[
0.75 = frac{75}{100} = frac{3}{4}
]
Hence, 0.75 is rational because it can be expressed as a fraction.

Non-rational Numbers

A non-rational (irrational) number cannot be written as a fraction a/b where a and b are integers. Its decimal form is non-terminating and non-repeating.

These include:

Square roots of numbers that are not perfect squares (e.g. √2, √3, √5).
The mathematical constant π (pi) = 3.1415926…
Non-repeating decimals like 0.1010010001…

Example 2:
Show that √2 is non-rational.
[
sqrt{2} = 1.41421356…
]
This value continues endlessly without repetition, so √2 is non-rational.

Approximate Value of Some Non-rational Numbers

Since non-rational numbers cannot be expressed exactly, we use approximations.

The following are examples:

√2 ≈ 1.41
√3 ≈ 1.73
√5 ≈ 2.24
π ≈ 3.14

Determining the Approximate Value of π

The value of π represents the ratio of the circumference of a circle to its diameter.

Example:
If the circumference of a circle is 31.4 cm and the diameter is 10 cm,
[
π = frac{C}{d} = frac{31.4}{10} = 3.14
]

Finding Reciprocals

The reciprocal of a number is 1 divided by the number. For a fraction a/b, the reciprocal is b/a.

Examples include:

The reciprocal of 5 is 1/5.
The reciprocal of ¾ is 4/3.
The reciprocal of 2/3 is 3/2.

Example 3:
Find the reciprocal of 0.25.
[
0.25 = frac{1}{4}, text{ reciprocal } = frac{4}{1} = 4
]

Teaching Methods/Instructional Techniques:

Lecture, Discussion, Explanation, Demonstration, Question and Answer, Group Work, Guided 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: Teacher reviews previous lesson on real numbers and asks pupils if all numbers can be written as fractions.
Pupils’ Activity: Pupils respond and share examples of numbers they know.
Learning Point: Pupils recall previous knowledge about fractions and decimals.

Step 2: Identification of Rational and Non-rational Numbers

Time: 10 minutes
Teaching Skill: Explanation
Teacher’s Activity: Teacher defines and explains rational and non-rational numbers using charts and examples.
Pupils’ Activity: Pupils observe and write down examples.
Learning Point: Pupils can distinguish between rational and non-rational numbers.

Step 3: Approximation of Non-rational Numbers and π

Time: 10 minutes
Teaching Skill: Demonstration
Teacher’s Activity: Teacher shows how to determine approximate values of √2, √3, and π using calculators and examples.
Pupils’ Activity: Pupils calculate and compare their results.
Learning Point: Pupils learn how to approximate non-rational numbers.

Step 4: Finding Reciprocals

Time: 10 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: Teacher explains how to find reciprocals of numbers and gives examples.
Pupils’ Activity: Pupils work in pairs to find reciprocals of given numbers.
Learning Point: Pupils can calculate reciprocals of rational numbers.

Step 5: Note-Taking

Time: 5 minutes
Teaching Skill: Explanation
Teacher’s Activity: Teacher dictates or writes the board summary for pupils to copy.
Pupils’ Activity: Pupils copy the note into their exercise books.
Learning Point: Pupils record the key points 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 a rational number?
Give two examples of non-rational numbers.
What is the approximate value of π?
Find the reciprocal of ⅔.
Pupils’ Activity: Pupils respond orally or in writing.
Learning Point: Pupils’ understanding of the lesson is assessed.

Step 7: Conclusion

Time: 2 minutes
Teaching Skill: Reinforcement
Teacher’s Activity: Teacher summarizes the lesson and emphasizes real-life uses of rational and non-rational numbers.
Pupils’ Activity: Pupils listen attentively and ask questions.
Learning Point: Pupils consolidate understanding of the topic.

Lesson Keywords

Rational number – a number that can be written as a fraction a/b
Non-rational number – a number that cannot be written as a fraction
Approximation – a close estimate of a value
π (pi) – ratio of a circle’s circumference to its diameter
Reciprocal – one divided by a number

Differentiation

Teacher provides extra support with visual aids and step-by-step examples for slower learners, while faster learners solve additional exercises independently.

Note for teachers using this lesson plan

Emphasize the relationship between rational and non-rational numbers and ensure pupils practice using calculators correctly. Encourage peer collaboration to promote active learning.