Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: First Term
Week: 10
Age: 15 years
Duration: 45 minutes
Subject: Further Maths
Curriculum Theme: Further Mathematics
Previous Lesson: Logical Reasoning II.
Topic: LOGICAL REASONING
Subject Matter: truth tables, logical disjunction and conjunction, implication and biconditional statements, simple true or false statements

Specific Objectives

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

Cognitive Domain:

Define a simple statement and its truth value.
Identify the symbols for logical conjunction, disjunction, implication, and biconditional.
State the truth conditions for conjunction, disjunction, implication, and biconditional statements.

Affective Domain:

Appreciate the importance of logical reasoning in problem-solving.
Participate actively in class discussions and problem-solving.

Psychomotor Domain:

Construct truth tables for logical conjunction, disjunction, implication, and biconditional statements.
Solve simple problems involving logical statements.

Collaborate with peers to construct truth tables.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum (Senior Secondary)
State Unified Scheme of Work for Further Mathematics
New Further Mathematics Project for Senior Secondary Schools 1

Instructional Materials

The teacher will teach this lesson with the aid of:

Charts showing truth tables and logical symbols.
Whiteboard and markers/chalk.
Worksheet with logical statements for practice.

Rationale for the Lesson

This lesson helps pupils develop clear thinking skills and understand how to evaluate the truth of statements. This understanding is important for solving mathematical problems and making logical decisions in everyday life.

Prerequisite/Previous Knowledge

Pupils have a basic understanding of statements as sentences that can be either true or false from everyday language.

Lesson Content/Board Summary

LOGICAL REASONING

Simple True or False Statements

A simple statement is a declarative sentence that is either true or false, but not both. The truthfulness or falsity of a statement is called its truth value.

Examples:

“Abuja is the capital of Nigeria.” (True)
“2 + 3 = 6.” (False)

Logical Connectives and Symbols

Logical connectives are words or symbols used to combine simple statements into compound statements. The common logical connectives are:

Conjunction (AND) – Symbol: $land$ (read as “and”)
Disjunction (OR) – Symbol: $lor$ (read as “or”)
Implication (IF…THEN) – Symbol: $to$ (read as “implies” or “if…then”)
Biconditional (IF AND ONLY IF) – Symbol: $leftrightarrow$ (read as “if and only if”)

Conjunction ($land$)

Let P and Q be two statements. The conjunction of P and Q (P $land$ Q) is true ONLY when both P and Q are true. Otherwise, it is false.

Disjunction ($lor$)

Let P and Q be two statements. The disjunction of P and Q (P $lor$ Q) is false ONLY when both P and Q are false. Otherwise, it is true.

Implication ($to$)

Let P and Q be two statements. The implication P $to$ Q (If P, then Q) is false ONLY when P is true and Q is false. Otherwise, it is true.

Biconditional ($leftrightarrow$)

Let P and Q be two statements. The biconditional P $leftrightarrow$ Q (P if and only if Q) is true ONLY when P and Q have the same truth value (both true or both false). Otherwise, it is false.

Truth Tables

A truth table is a mathematical table used in logic to compute the functional values of logical expressions. It lists all possible truth values for the simple statements and the resulting truth value for the compound statement.

The following are examples of truth tables:

For Conjunction (P $land$ Q):
If P is True and Q is True, then P $land$ Q is True.
If P is True and Q is False, then P $land$ Q is False.
If P is False and Q is True, then P $land$ Q is False.
If P is False and Q is False, then P $land$ Q is False.
For Disjunction (P $lor$ Q):
If P is True and Q is True, then P $lor$ Q is True.
If P is True and Q is False, then P $lor$ Q is True.
If P is False and Q is True, then P $lor$ Q is True.
If P is False and Q is False, then P $lor$ Q is False.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher introduces the topic by asking pupils to state if certain sentences are true or false (e.g., “The sun rises in the West,” “Lagos is a state in Nigeria”). The teacher explains that in Further Maths, we study how to logically combine and evaluate such statements.
Pupils’ Activity: Pupils respond to the teacher’s questions and share their answers.
Learning Point: Pupils recall the concept of true/false statements and are introduced to the relevance of logical reasoning.

Step 2: Simple Statements and Truth Values

Time: 5 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher defines a simple statement and its truth value, providing various examples for clarity. The teacher ensures pupils understand that a statement must be unambiguously true or false.
Pupils’ Activity: Pupils listen, take notes, and identify the truth values of given simple statements.
Learning Point: Pupils understand what constitutes a simple statement and its truth value.

Step 3: Logical Conjunction (AND)

Time: 7 minutes
Teaching Skill: Demonstration/Explanation
Teacher’s Activity: The teacher introduces the logical connective “AND” (conjunction) and its symbol ($land$). The teacher explains how two simple statements are combined using “AND” and demonstrates how to construct its truth table, emphasizing that P $land$ Q is true only when both P and Q are true.
Pupils’ Activity: Pupils observe, ask questions, and practice constructing a simple truth table for conjunction.
Learning Point: Pupils learn about conjunction and its truth table.

Step 4: Logical Disjunction (OR)

Time: 7 minutes
Teaching Skill: Demonstration/Explanation
Teacher’s Activity: The teacher introduces the logical connective “OR” (disjunction) and its symbol ($lor$). The teacher explains how two simple statements are combined using “OR” and demonstrates how to construct its truth table, emphasizing that P $lor$ Q is false only when both P and Q are false.
Pupils’ Activity: Pupils observe, ask questions, and practice constructing a simple truth table for disjunction.
Learning Point: Pupils learn about disjunction and its truth table.

Step 5: Logical Implication (IF…THEN)

Time: 7 minutes
Teaching Skill: Demonstration/Explanation
Teacher’s Activity: The teacher introduces the logical connective “IF…THEN” (implication) and its symbol ($to$). The teacher explains its meaning and demonstrates the construction of its truth table, highlighting the specific case where P $to$ Q is false (P is true, Q is false).
Pupils’ Activity: Pupils pay attention, ask questions for clarification, and attempt to construct the truth table for implication.
Learning Point: Pupils understand implication and its truth table.

Step 6: Logical Biconditional (IF AND ONLY IF)

Time: 7 minutes
Teaching Skill: Demonstration/Explanation
Teacher’s Activity: The teacher introduces the logical connective “IF AND ONLY IF” (biconditional) and its symbol ($leftrightarrow$). The teacher explains its meaning and demonstrates the construction of its truth table, emphasizing that P $leftrightarrow$ Q is true when P and Q have the same truth value.
Pupils’ Activity: Pupils observe, ask questions, and construct the truth table for biconditional statements.
Learning Point: Pupils learn about biconditional statements and their truth table.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

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

Define a simple statement and give an example.
List the four common logical connectives and their symbols.
State the truth condition for a conjunction (P $land$ Q).
Construct a truth table for P $lor$ Q.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 2 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the importance of understanding logical connectives and truth tables. The teacher assigns homework involving the construction of truth tables for various compound statements.
Pupils’ Activity: Pupils listen to the summary and copy down the homework.
Learning Point: Pupils consolidate their understanding and receive further practice.

Lesson Keywords

Statement – A declarative sentence that is either true or false.
Truth Value – The truthfulness (True) or falsity (False) of a statement.
Logical Connective – A word or symbol used to combine simple statements.
Conjunction – The logical connective “AND” ($land$).
Disjunction – The logical connective “OR” ($lor$).
Implication – The logical connective “IF…THEN” ($to$).
Biconditional – The logical connective “IF AND ONLY IF” ($leftrightarrow$).
Truth Table – A table showing all possible truth values for a logical expression.

Differentiation

For pupils who grasp the concepts quickly, the teacher can provide more complex logical statements for truth table construction. For pupils needing additional support, the teacher can offer simplified examples or provide pre-filled parts of truth tables to complete, and encourage peer tutoring within groups.

Note for teachers using this lesson plan

Encourage pupils to relate logical reasoning to real-life scenarios to enhance understanding. Emphasize step-by-step construction of truth tables to avoid errors. Allow ample time for practice and questions.