Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: 2nd Term
Week: 4
Age: 15 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: General Mathematics
Previous Lesson: Locus of Moving Points: Constructions and Steps.
Topic: LOGICAL REASONING (I)
Subject Matter: Meaning of simple statement – open and close statements, true or false., Negation of simple statements, Compound statements – conjunctions, disjunctions, implication, bi-implication with examples.

Specific Objectives

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

Cognitive Domain:

Define a simple statement and distinguish between open and closed statements.
Identify the truth value (true or false) of simple statements.
Explain the meaning of negation in logical statements.
Define compound statements and list their common types.
Identify the symbols and meanings of conjunction, disjunction, implication, and bi-implication.

Affective Domain:

Appreciate the importance of logical reasoning in everyday problem-solving.
Show interest in constructing and analyzing logical statements.

Psychomotor Domain:

Construct simple statements and determine their truth values.
Negate simple statements correctly using appropriate phrases.
Formulate compound statements using conjunctions, disjunctions, implications, and bi-implications.

Participate actively in class discussions on logical reasoning.
Collaborate with peers to identify and classify different types of statements.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for General Mathematics (Senior Secondary)
State Unified Scheme of Work for General Mathematics SSS 1
New General Mathematics for Senior Secondary Schools 1 by M.F. Macrae, et al.
https://www.mathsisfun.com/logic/statements.html
https://www.dummies.com/education/math/calculus/logic-for-dummies-statements-and-quantifiers/

Instructional Materials

The teacher will teach this lesson with the aid of:

Charts showing examples of simple statements.
Charts illustrating true and false statements.
Charts demonstrating negation statements.
Charts displaying examples of compound statements with their connectors and symbols.

Rationale for the Lesson

This lesson helps pupils understand how to analyze statements logically, which is important for critical thinking. It teaches them to evaluate information and form clear arguments, skills useful in mathematics and daily decision-making.

Prerequisite/Previous Knowledge

Pupils are assumed to have a basic understanding of sentences and their meanings in English Language. They should also be able to identify facts and opinions.

Lesson Content/Board Summary

LOGICAL REASONING (I)

Meaning of Simple Statements

A simple statement is a declarative sentence that is either true or false, but not both. It cannot be broken down into simpler statements.

Simple statements can be classified as either open or closed:

Closed Statement: A statement whose truth value (true or false) can be determined without any additional information.
- Example: “Abuja is the capital of Nigeria.” (True)
- Example: “2 + 3 = 7.” (False)
Open Statement: A statement whose truth value depends on the value of a variable within the statement. Its truth value cannot be determined until the variable is replaced by a specific value.
- Example: “x + 5 = 10.” (Truth value depends on ‘x’)
- Example: “She is a student.” (Truth value depends on ‘she’)

Truth Value: The truth value of a closed statement is either ‘True’ (T) or ‘False’ (F).

Negation of Simple Statements

The negation of a statement is a new statement that has the opposite truth value of the original statement. If the original statement is true, its negation is false, and vice versa. It is denoted by the symbol ‘¬’ (not).

To negate a simple statement, one can use phrases like “not,” “it is not true that,” or “it is false that.”

Examples of negation:

Statement (P): “Lions are mammals.” (True)
Negation (¬P): “Lions are not mammals.” (False)
Statement (Q): “The sun rises in the west.” (False)
Negation (¬Q): “It is not true that the sun rises in the west.” (True)

Compound Statements

A compound statement is formed by combining two or more simple statements using logical connectors (also called connectives or operators).

The main types of compound statements are:

Conjunction: Connects two statements with “and” (symbol: ∧). The compound statement is true only if both simple statements are true.
Disjunction: Connects two statements with “or” (symbol: ∨). The compound statement is true if at least one of the simple statements is true.
Implication (Conditional): Connects two statements with “if… then…” (symbol: →). The compound statement is false only if the first statement is true and the second statement is false.
Bi-implication (Biconditional): Connects two statements with “if and only if” (symbol: ↔). The compound statement is true if both simple statements have the same truth value (both true or both false).

Examples:

Let P: “It is raining.”
Let Q: “The ground is wet.”
Conjunction (P ∧ Q): “It is raining and the ground is wet.”
Disjunction (P ∨ Q): “It is raining or the ground is wet.”
Implication (P → Q): “If it is raining, then the ground is wet.”
Bi-implication (P ↔ Q): “It is raining if and only if the ground is wet.”

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 greets the pupils and introduces the topic by asking pupils to identify if certain sentences are true or false, or if their truth depends on more information. For example, “Lagos is a state in Nigeria.” (True), “x is an even number.” (Depends on x). This leads to the concept of logical statements.
Pupils’ Activity: Pupils respond to the teacher’s questions and share their opinions on the truthfulness of the sentences.
Learning Point: Pupils are introduced to the idea of statements with definite truth values.

Step 2: Meaning of Simple Statements

Time: 10 minutes
Teaching Skill: Explanation/Illustration
Teacher’s Activity: The teacher explains what a simple statement is, differentiating between open and closed statements with clear examples from the charts. The teacher also defines truth value. The teacher then writes several sentences on the board and guides pupils to classify them as simple/not simple and open/closed, stating their truth values where possible.
Pupils’ Activity: Pupils listen attentively, ask questions for clarification, and participate in classifying statements and determining their truth values.
Learning Point: Pupils understand the definition of simple statements, distinguish between open and closed statements, and identify truth values.

Step 3: Negation of Simple Statements

Time: 8 minutes
Teaching Skill: Demonstration/Practice
Teacher’s Activity: The teacher explains the concept of negation and demonstrates how to negate simple statements using “not” or “it is not true that.” The teacher provides examples and asks pupils to negate other given simple statements.
Pupils’ Activity: Pupils observe the examples, understand the process of negation, and practice negating various simple statements.
Learning Point: Pupils learn how to form the negation of a simple statement and understand its effect on the truth value.

Step 4: Compound Statements

Time: 7 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher introduces compound statements as combinations of simple statements. The teacher lists and briefly explains the four main types of compound statements (conjunction, disjunction, implication, bi-implication) and their corresponding logical connectors and symbols using charts.
Pupils’ Activity: Pupils listen and take notes, familiarizing themselves with the types of compound statements and their symbols.
Learning Point: Pupils understand what a compound statement is and are introduced to the main logical connectors.

Step 5: 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 two examples.
Distinguish between an open statement and a closed statement.
What is the negation of the statement: “All birds can fly”?
Mention three types of compound statements.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 6: Conclusion

Time: 5 minutes
Teaching Skill: Summarization/Assignment
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the definitions of simple and compound statements, negation, and the different logical connectors. The teacher then assigns homework.
Pupils’ Activity: Pupils listen to the summary and copy the homework.
Learning Point: Pupils consolidate their understanding of logical reasoning concepts.
Homework:
1. Identify if the following are open or closed statements and state their truth value if closed:
a) “Lagos is the capital of Nigeria.”
b) “x + 2 = 7.”
2. Write the negation of the following statements:
a) “The sun is hot.”
b) “Dogs cannot bark.”
3. Let P: “It is cold.” and Q: “It is snowing.” Write the following compound statements in words:
a) P ∧ Q
b) P ∨ Q
c) P → Q

Lesson Keywords

Statement – A declarative sentence that is either true or false.
Open Statement – A statement whose truth value depends on a variable.
Closed Statement – A statement whose truth value is definite (true or false).
Truth Value – The property of a statement being either true or false.
Negation – The opposite of a statement, changing its truth value.
Compound Statement – A statement formed by combining two or more simple statements.
Conjunction – A compound statement using “and” (∧).
Disjunction – A compound statement using “or” (∨).
Implication – A compound statement using “if… then…” (→).
Bi-implication – A compound statement using “if and only if” (↔).

Differentiation

For pupils who grasp concepts quickly, the teacher can provide more complex statements for negation or ask them to create truth tables for simple compound statements. For pupils who need more support, the teacher can offer additional guided practice with simpler examples and provide sentence starters for forming negations or compound statements.

Note for teachers using this lesson plan

Emphasize the clear distinction between simple and compound statements and the precise meaning of each logical connector. Encourage pupils to use real-life examples to make the concepts more relatable. Pay attention to the correct use of logical symbols.