Class: Junior Secondary School 3 (JSS3, JSS 3)
Term: 1st Term
Week: 8
Age: 14 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Mathematics
Previous Lesson: Equations Involving Fractions, Word Problems and Simplifying Brackets
Topic: Simultaneous Equations
Subject Matter: Solution of simultaneous equations by substitution method, Solution by elimination method, Applying substitution and elimination method of solving simultaneous equations to real life activities.

Specific Objectives

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

Cognitive Domain:
(a) Solve simultaneous equations using substitution method.
(b) Solve simultaneous equations using elimination method.
(c) Apply both methods to solve real life problems involving simultaneous equations.
Affective Domain:
(a) Appreciate the importance of accuracy in solving mathematical problems.
(b) Show interest and confidence in solving algebraic equations.
Psychomotor Domain:
(a) Demonstrate steps in solving simultaneous equations correctly on the board or in their notebooks.
Social Domain:
(a) Work cooperatively in pairs or small groups to solve mathematical problems.

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
BYJU’S – “Simultaneous Equations: Methods, Examples and Solving Tips” (https://byjus.com/maths/simultaneous-equations)
Relevant Textbooks

Instructional Materials

The teacher will teach this lesson with the aid of:

Whiteboard and markers
Algebra charts showing worked examples
Flash cards with sample equations
Graph sheets
Calculator

Rationale for the Lesson

This lesson enables students to understand and apply algebraic methods to solve simultaneous equations, which are useful in solving real life mathematical and logical problems.

Prerequisite/Previous Knowledge

Pupils already know how to solve simple linear equations with one variable and can perform basic algebraic manipulations such as addition, subtraction, and substitution.

Lesson Content/Board Summary

Simultaneous Equations

Simultaneous equations are two or more equations that have the same variables and are solved together to find values that satisfy all equations at once.

Solution by Substitution Method

In this method, one of the variables is made the subject of the equation and substituted into the other equation to find the unknown values.

The following are the steps:

Make one variable the subject in one of the equations.
Substitute the expression into the second equation.
Simplify and solve for one variable.
Substitute the value obtained into any of the original equations to find the other variable.

Example 1:
Solve:
( 2x + y = 7 )
( x – y = 1 )

From the second equation, ( x = 1 + y ).
Substitute into the first:
( 2(1 + y) + y = 7 )
( 2 + 2y + y = 7 )
( 3y = 5 )
( y = frac{5}{3} )

Substitute ( y = frac{5}{3} ) into ( x = 1 + y ):
( x = 1 + frac{5}{3} = frac{8}{3} )

Therefore, ( x = frac{8}{3}, y = frac{5}{3} ).

Solution by Elimination Method

This method involves adding or subtracting the equations to eliminate one of the variables.

The following are the steps:

Arrange both equations properly.
Multiply one or both equations to make the coefficients of one variable equal.
Add or subtract the equations to eliminate one variable.
Solve for the remaining variable.
Substitute the found value into one equation to find the other variable.

Example 2:
Solve:
( 3x + 2y = 12 )
( 2x + 3y = 13 )

Multiply the first equation by 3 and the second by 2 to make the coefficients of ( y ) equal:
( 9x + 6y = 36 )
( 4x + 6y = 26 )

Subtract:
( (9x – 4x) + (6y – 6y) = 36 – 26 )
( 5x = 10 )
( x = 2 )

Substitute ( x = 2 ) into the first equation:
( 3(2) + 2y = 12 )
( 6 + 2y = 12 )
( 2y = 6 )
( y = 3 )

Hence, ( x = 2, y = 3 ).

Application of Simultaneous Equations to Real Life

Simultaneous equations are used to solve problems involving two conditions or quantities that depend on each other, such as prices, ages, distances, or mixtures.

Example 3:
The sum of two numbers is 10, and their difference is 2. Find the numbers.

Let the numbers be ( x ) and ( y ).
Then,
( x + y = 10 )
( x – y = 2 )

Add both equations:
( 2x = 12 Rightarrow x = 6 )

Substitute ( x = 6 ) into ( x + y = 10 ):
( 6 + y = 10 Rightarrow y = 4 )

Therefore, the two numbers are 6 and 4.

Teaching Methods/Instructional Techniques:

Discussion, Lecture, Explanation, Demonstration, Guided Practice, Group Work, Question and Answer

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 revises the previous lesson on linear equations and asks pupils if they know what happens when two equations have two unknowns.
Pupils’ Activity: Pupils respond and share ideas.
Learning Point: Pupils are introduced to the concept of simultaneous equations.

Step 2: Substitution Method

Time: 10 minutes
Teaching Skill: Explanation
Teacher’s Activity: Teacher explains and demonstrates the substitution method with example 1.
Pupils’ Activity: Pupils follow the example and solve similar problems.
Learning Point: Pupils learn to solve simultaneous equations by substitution.

Step 3: Elimination Method

Time: 10 minutes
Teaching Skill: Demonstration
Teacher’s Activity: Teacher explains elimination method using example 2 and works through each step on the board.
Pupils’ Activity: Pupils copy and practice similar examples.
Learning Point: Pupils learn how to eliminate variables systematically.

Step 4: Application to Real Life

Time: 10 minutes
Teaching Skill: Discussion
Teacher’s Activity: Teacher presents real life problems and guides pupils to form and solve equations as in example 3.
Pupils’ Activity: Pupils solve problems in pairs and discuss results.
Learning Point: Pupils apply simultaneous equations to real situations.

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 write the notes neatly in their books.
Learning Point: Pupils have a written record of key points.

Step 6: Evaluation/Review

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

List two methods of solving simultaneous equations.
State the steps involved in the elimination method.
Solve for ( x ) and ( y ) if ( 2x + 3y = 12 ) and ( x – y = 2 ).
Pupils’ Activity: Pupils respond to questions orally or in writing.
Learning Point: Pupils’ understanding of the lesson objectives is tested.

Step 7: Conclusion

Time: 2 minutes
Teaching Skill: Reinforcement
Teacher’s Activity: Teacher summarizes key points and encourages pupils to practice more exercises at home.
Pupils’ Activity: Pupils listen and ask final questions.
Learning Point: Pupils consolidate understanding of simultaneous equations.

Lesson Keywords

Simultaneous equations – two or more equations solved together
Substitution – replacing one variable with its expression from another equation
Elimination – removing one variable by addition or subtraction
Variable – a symbol representing an unknown quantity
Coefficient – the numerical value multiplying a variable

Differentiation

The teacher will simplify explanations and use visual aids for slower learners while assigning more complex problems to faster learners for enrichment.

Note for teachers using this lesson plan

Ensure pupils practice several examples to build confidence. Encourage accuracy in substitution and arithmetic operations. Always verify answers by substituting values back into the original equations.