Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: 1st Term
Week: 11
Age: 15 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: General Mathematics
Previous Lesson: Set Operations: Union Intersection and Venn Diagrams.
Topic: SIMPLE EQUATIONS
Subject Matter: Change of subject of formulae, Formula involving brackets, roots and powers, Subject of formula and substitution, Revision of simultaneous linear equation in two unknowns.

Specific Objectives

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

Cognitive Domain:

Define the subject of a formula.
State the steps involved in changing the subject of a formula.
Solve equations involving brackets, roots, and powers when changing the subject.
Explain methods for solving simultaneous linear equations in two unknowns.

Affective Domain:

Appreciate the importance of algebraic manipulation in problem-solving.
Show patience and accuracy when solving mathematical problems involving formulae.

Psychomotor Domain:

Accurately change the subject of a given formula.
Correctly substitute values into a formula after changing its subject.
Precisely solve simultaneous linear equations in two unknowns using appropriate methods.

Participate actively in class discussions and problem-solving sessions.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum (Senior Secondary Mathematics)
State Unified Scheme of Work (General Mathematics SSS 1)
New General Mathematics for Senior Secondary Schools 1 by J.B. Channon, A. McLeish Smith, T.J. Akindele

Instructional Materials

The teacher will teach this lesson with the aid of:

Charts displaying processes involved in change of subject in a formula.
Charts displaying various types of formulae.
Whiteboard/Chalkboard and markers/chalk.

Rationale for the Lesson

This lesson helps pupils understand how to rearrange mathematical formulae, which is important for solving problems in various fields like science and engineering. It also reinforces their ability to solve systems of equations, a skill useful for real-world situations involving multiple unknown quantities.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of basic algebra, solving simple linear equations, and understanding variables.

Lesson Content/Board Summary

SIMPLE EQUATIONS

Change of Subject of Formulae

The subject of a formula is the single variable (usually on the left side of the equation) that the formula is expressed in terms of. Changing the subject means rearranging the formula to make a different variable the subject.

The following are the general steps to change the subject of a formula:

Isolate the term containing the new subject.
Move all other terms to the opposite side of the equation.
Perform inverse operations (e.g., addition for subtraction, multiplication for division, square root for squaring) to isolate the new subject.

Formulae Involving Brackets, Roots, and Powers

When changing the subject of a formula that includes brackets, roots, or powers, follow the order of operations in reverse. Expand brackets, deal with roots by squaring (or cubing, etc.), and deal with powers by taking roots.

Example: To make ‘r’ the subject of A = πr², divide both sides by π, then take the square root of both sides.

Subject of Formula and Substitution

After changing the subject of a formula, values can be substituted into the rearranged formula to find the value of the new subject. This is useful when repeatedly calculating a specific variable from different given values.

Revision of Simultaneous Linear Equations in Two Unknowns

Simultaneous linear equations are a set of two or more linear equations that share the same variables. The solution to a set of simultaneous equations is the set of values for the variables that satisfy all equations in the set.

The common methods for solving simultaneous linear equations in two unknowns are:

Substitution Method: Express one variable in terms of the other from one equation, then substitute this expression into the second equation.
Elimination Method: Multiply one or both equations by a constant so that the coefficients of one variable are equal or additive inverses, then add or subtract the equations to eliminate that variable.

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 reviews the previous lesson on simple linear equations. The teacher then introduces the topic by explaining that sometimes we need to rearrange equations to find different unknown values, which is called changing the subject of a formula.
Pupils’ Activity: Pupils respond to greetings, recall previous knowledge, and listen attentively to the introduction.
Learning Point: Pupils connect previous knowledge to the new topic and understand the relevance of changing the subject of a formula.

Step 2: Change of Subject of Formulae

Time: 10 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher defines the subject of a formula and explains the general steps involved in changing the subject. The teacher demonstrates with simple examples like making ‘h’ the subject of A = bh or ‘r’ the subject of C = 2πr.
Pupils’ Activity: Pupils listen, ask questions, and copy notes from the board.
Learning Point: Pupils learn the definition and basic steps for changing the subject of a formula.

Step 3: Formulae Involving Brackets, Roots, and Powers

Time: 10 minutes
Teaching Skill: Explanation/Illustration
Teacher’s Activity: The teacher explains how to handle formulae with brackets, roots, and powers when changing the subject. The teacher uses examples such as making ‘a’ the subject of v² = u² + 2as or ‘r’ the subject of V = (4/3)πr³.
Pupils’ Activity: Pupils observe the examples, take notes, and attempt to solve similar problems presented by the teacher.
Learning Point: Pupils understand how to apply inverse operations for brackets, roots, and powers when rearranging formulae.

Step 4: Subject of Formula and Substitution

Time: 5 minutes
Teaching Skill: Practical Application
Teacher’s Activity: The teacher demonstrates how to substitute given values into a formula after its subject has been changed. For example, if ‘a’ is the subject of v² = u² + 2as, the teacher provides values for v, u, and s, and guides pupils to find ‘a’.
Pupils’ Activity: Pupils follow the demonstration and practice substitution in class.
Learning Point: Pupils learn to apply the changed formula to calculate unknown values.

Step 5: Revision of Simultaneous Linear Equations

Time: 5 minutes
Teaching Skill: Review/Recap
Teacher’s Activity: The teacher briefly revises the methods for solving simultaneous linear equations in two unknowns (substitution and elimination methods) by working through a simple example. For instance, x + y = 5 and x – y = 1.
Pupils’ Activity: Pupils recall and participate in solving the revision example.
Learning Point: Pupils refresh their knowledge of solving simultaneous linear equations.

Step 6: Class Activity/Practice

Time: 5 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher writes a few practice questions on the board for pupils to solve individually or in pairs. Examples: 1. Make ‘x’ the subject of P = (x+y)/2. 2. Solve 2x + y = 7 and x – y = 2.
Pupils’ Activity: Pupils work on the practice questions and seek clarification where needed.
Learning Point: Pupils reinforce their understanding through practical application.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

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

What is the subject of a formula?
List two steps involved in changing the subject of a formula.
Make ‘r’ the subject of the formula A = πr².
State two methods for solving simultaneous linear equations.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 5 minutes
Teaching Skill: Summarization/Assignment
Teacher’s Activity: The teacher summarizes the key points of the lesson, emphasizing the importance of careful algebraic manipulation. The teacher then gives homework assignments related to changing the subject of formulae and solving simultaneous equations.
Pupils’ Activity: Pupils listen to the summary and copy down the homework.
Learning Point: Pupils consolidate their learning and apply it to further practice.

Lesson Keywords

Formula – A mathematical relationship or rule expressed in symbols.
Subject of a formula – The variable that has been isolated on one side of an equation.
Substitution – Replacing a variable with a numerical value or another expression.
Simultaneous equations – A set of equations containing multiple variables that have a common solution.
Variable – A symbol, usually a letter, representing a quantity that can change.

Differentiation

For pupils who grasp concepts quickly, provide more complex formulae involving fractions or multiple terms to rearrange. For struggling pupils, offer additional simpler examples and provide step-by-step guidance, focusing on one type of operation at a time. Encourage peer tutoring during practice sessions.

Note for teachers using this lesson plan

Ensure to clearly explain each step when demonstrating algebraic manipulation. Encourage pupils to show all their working to identify errors easily. Provide ample practice exercises and give constructive feedback. Emphasize the practical applications of these skills in other subjects like Physics and Chemistry.