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Class: Junior Secondary School 3 (JSS3, JSS 3)
Term: 1st Term
Week: 3
Age: 14 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Mathematics
Previous Lesson: Conversion and Application of Binary Numbers
Topic: Direct and Inverse Proportion
Subject Matter: Direct proportion, Indirect proportion, Apply direct and inverse proportions to practical problems

Specific Objectives

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

Cognitive Domain:
(a) Differentiate between direct and inverse proportion.
(b) Solve problems involving direct and inverse proportion.
Affective Domain:
(a) Develop an interest in solving proportion-related mathematical problems.
Psychomotor Domain:
(a) Accurately apply proportion formulas to real-life problems involving time, distance, and work.
Social Domain:
(a) Cooperate with classmates in group activities to solve given proportion exercises.

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 – Directly Proportional and Inversely Proportional
Relevant Textbooks

Instructional Materials

The teacher will teach this lesson with the aid of:

Charts showing examples of direct and inverse proportion
Flashcards showing formulae and worked examples
Mathematical tables
Marker and whiteboard
Real-life examples such as work-time and speed-distance charts

Rationale for the Lesson

Understanding direct and inverse proportion helps students relate quantities in daily life situations like speed and time, work and workers, and cost and quantity.

Prerequisite/Previous Knowledge

Pupils already know how to solve basic ratio and proportion problems and can relate simple quantities using multiplication and division.

Lesson Content/Board Summary

Direct and Inverse Proportion

Direct Proportion

Two quantities are said to be in direct proportion when an increase in one quantity leads to an increase in the other, and a decrease in one causes a decrease in the other, in the same ratio.

In direct proportion,
x1 / y1 = x2 / y2
or
y = kx
where k is the constant of proportionality.

The following are examples of direct proportion:

The more the number of goods bought, the more the total cost.
The longer the time spent working, the higher the wages earned.
The greater the speed, the longer the distance covered in a fixed time.

Example 1:
If 3 pencils cost ₦150, find the cost of 5 pencils.
The formula is: 3 / 150 = 5 / x
Cross multiply:
3x = 750
x = 250
Therefore, 5 pencils cost ₦250.

Example 2:
If a car travels 60 km in 2 hours, how far will it travel in 5 hours at the same speed?
The formula is: 60 / 2 = x / 5
Cross multiply:
2x = 300
x = 150 km
Hence, the car will travel 150 km.

Inverse Proportion

Two quantities are said to be in inverse proportion when an increase in one causes a decrease in the other, and vice versa, in such a way that their product remains constant.

In inverse proportion,
x1 * y1 = x2 * y2
or
y = k / x
where k is the constant of proportionality.

The following are examples of inverse proportion:

The more workers employed to do a job, the less time they will take to complete it.
The faster the speed, the less the time taken to cover a fixed distance.
The more taps opened, the less time required to fill a tank.

Example 3:
If 8 men can build a wall in 12 days, how many days will 6 men take to build the same wall?
The formula is: 8 * 12 = 6 * x
96 = 6x
x = 16 days
Hence, 6 men will take 16 days to complete the wall.

Teaching Methods/Instructional Techniques:

Lecture, Discussion, Explanation, Demonstration, 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: The teacher asks pupils questions about daily life examples like “If you buy more oranges, what happens to the cost?” or “If fewer people do the same work, what happens to the time taken?”
Pupils’ Activity: Pupils respond and share examples.
Learning Point: Pupils recall the relationship between quantities in everyday situations.

Step 2: Explanation of Direct Proportion

Time: 10 minutes
Teaching Skill: Explanation
Teacher’s Activity: The teacher explains direct proportion and writes the formula on the board, using simple examples to demonstrate.
Pupils’ Activity: Pupils listen, observe, and take notes.
Learning Point: Pupils understand the concept of direct proportion and how to solve problems using the formula.

Step 3: Explanation of Inverse Proportion

Time: 10 minutes
Teaching Skill: Discussion
Teacher’s Activity: The teacher discusses inverse proportion using real-life examples and derives the formula for solving problems.
Pupils’ Activity: Pupils contribute and relate examples to daily experiences.
Learning Point: Pupils understand that inverse proportion means one value increases while the other decreases.

Step 4: Application to Practical Problems

Time: 10 minutes
Teaching Skill: Demonstration
Teacher’s Activity: The teacher solves example problems on both direct and inverse proportion on the board and guides pupils through similar classwork.
Pupils’ Activity: Pupils participate actively and solve given exercises.
Learning Point: Pupils apply the formulas of direct and inverse proportion correctly.

Step 5: Note-Taking

Time: 5 minutes
Teaching Skill: Explanation
Teacher’s Activity: Teacher writes the board summary for pupils to copy.
Pupils’ Activity: Pupils copy notes into their books.
Learning Point: Pupils retain key points for study and revision.

Step 6: Evaluation/Review

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

Define direct and inverse proportion.
Solve: If 5 men take 8 days to finish a job, how many days will 10 men take?
State one real-life example each of direct and inverse proportion.
Pupils’ Activity: Pupils answer the questions orally.
Learning Point: Pupils demonstrate comprehension of the key concepts.

Step 7: Conclusion

Time: 2 minutes
Teaching Skill: Reinforcement
Teacher’s Activity: The teacher summarizes the lesson and emphasizes the importance of understanding proportional relationships in solving mathematical and real-life problems.
Pupils’ Activity: Pupils listen attentively and ask questions.
Learning Point: Pupils consolidate their understanding of direct and inverse proportion.

Lesson Keywords

Proportion – a relationship showing how quantities compare to each other
Constant – a fixed number that remains unchanged in proportion
Direct Proportion – when one value increases as the other increases
Inverse Proportion – when one value increases as the other decreases
Variable – a quantity that can change or vary

Differentiation

Provide guided examples for slower learners, while advanced learners handle more complex problem-solving exercises involving multiple variables.

Note for teachers using this lesson plan

Encourage pupils to link proportion problems to real-life examples for better understanding. Use visual aids and practical examples to strengthen comprehension.