Mathematics - Junior Secondary 3 - Whole Numbers III – Application of Direct and Inverse Proportions, Compound Interest

Whole Numbers III – Application of Direct and Inverse Proportions, Compound Interest

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TERM: 1ST TERM

WEEK 3

Class: Junior Secondary School 3
Age: 14 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Whole Numbers III – Application of Direct and Inverse Proportions, Compound Interest
Focus: Direct and Inverse Proportions, Compound Interest
SPECIFIC OBJECTIVES:
By the end of the lesson, pupils should be able to:

  1. Understand and apply direct and inverse proportions.
  2. Solve problems involving direct and inverse proportions.
  3. Understand and calculate compound interest using the formula.
  4. Solve compound interest problems in real-life contexts.
    INSTRUCTIONAL TECHNIQUES:
    Question and answer
    • Guided demonstration
    • Problem-solving exercises
    • Real-life application
    INSTRUCTIONAL MATERIALS:
    • Place value charts
    • Flashcards
    • Whiteboard and marker
    • Calculator (optional)
    • Worksheets

PERIOD 1 & 2: Application of Direct Proportions

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Explains the concept of direct proportion using examples (e.g., speed and time).

Pupils listen and ask questions.

Step 2 - Explanation

Demonstrates the relationship between two quantities in direct proportion.

Pupils observe and practice examples.

Step 3 - Demonstration

Solves examples like "If 2 workers can complete a task in 4 hours, how long will 4 workers take?"

Pupils work on similar examples with guidance.

Step 4 - Note Taking

Teacher writes summary on direct proportions.

Pupils copy notes and practice.

NOTE ON BOARD:

  • Direct Proportion: y=kxy = kxy=kx, where k is a constant.
  • Example: If 2 workers take 4 hours to complete a task, 4 workers will take 2 hours.

EVALUATION (5 exercises):

  1. If 3 workers take 6 hours to finish a task, how many hours will 9 workers take?
  2. If 5 liters of paint cover 100 m², how much area will 10 liters cover?
  3. A car travels 60 km in 2 hours. How far will it travel in 5 hours?
  4. If a machine uses 5 liters of fuel for 100 km, how much fuel is needed for 300 km?
  5. A car consumes 5 liters of fuel for 100 km. How much fuel will it need for 250 km?

CLASSWORK (5 questions):

  1. Solve: If 2 workers can complete a task in 6 hours, how long will 8 workers take?
  2. If 4 oranges cost 200 Naira, how much do 10 oranges cost?
  3. Solve: A garden needs 3 hours to be watered by 2 people. How long will it take for 6 people to water it?
  4. Solve: 5 kg of rice costs 250 Naira. How much does 8 kg cost?
  5. Solve: If 10 workers can finish a task in 20 hours, how many hours will 5 workers take?

ASSIGNMENT (5 tasks):

  1. Solve: If 4 workers can finish a task in 10 hours, how long will it take for 12 workers?
  2. If 3 bags of cement cover 12 m² of floor space, how many bags are needed for 36 m²?
  3. A factory produces 500 items in 4 hours. How many items will it produce in 6 hours?
  4. A train travels 180 km in 3 hours. How long will it take to travel 540 km?
  5. A chef uses 3 liters of oil to fry 15 chickens. How much oil will be needed for 25 chickens?

 

PERIOD 3 & 4: Application of Inverse Proportions

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Explains the concept of inverse proportion (e.g., speed and time).

Pupils listen and ask questions.

Step 2 - Explanation

Demonstrates the relationship between quantities in inverse proportion.

Pupils observe and solve problems.

Step 3 - Demonstration

Solves an example: "If 4 workers can finish a task in 12 hours, how long will 2 workers take?"

Pupils solve similar examples.

Step 4 - Note Taking

Teacher writes summary of inverse proportions.

Pupils copy notes and practice.

NOTE ON BOARD:

  • Inverse Proportion: y=kxy = \frac{k}{x}y=xk, where k is a constant.
  • Example: If 4 workers can finish a task in 12 hours, 2 workers will take 24 hours.

EVALUATION (5 exercises):

  1. If 5 workers can finish a task in 10 hours, how long will 10 workers take?
  2. If a car consumes 50 liters of fuel in 100 km, how much will it consume for 400 km?
  3. If a machine uses 6 liters of fuel for 100 km, how much fuel will it use for 600 km?
  4. If 10 workers take 12 hours to finish a task, how many hours will 20 workers take?
  5. If 4 workers complete a task in 8 hours, how long will 2 workers take?

CLASSWORK (5 questions):

  1. If 3 workers can finish a task in 9 hours, how long will it take 6 workers?
  2. If 12 workers take 15 hours to finish a task, how many hours will it take 6 workers?
  3. A machine requires 10 liters of fuel to produce 50 items. How much fuel will it need to produce 100 items?
  4. A project requires 100 hours of work to be completed by 5 workers. How long will it take if 10 workers are working?
  5. If 10 workers can finish a task in 20 hours, how long will 5 workers take?

ASSIGNMENT (5 tasks):

  1. If 6 workers can finish a task in 18 hours, how long will 12 workers take?
  2. If 2 workers can finish a task in 14 hours, how long will 7 workers take?
  3. A machine takes 6 hours to produce 200 units of a product. How long will it take to produce 100 units?
  4. If 4 workers can finish a task in 16 hours, how long will it take for 8 workers?
  5. If 5 liters of fuel are used to produce 100 items, how much fuel is needed for 250 items?

 

PERIOD 5: Compound Interest

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces compound interest and explains how it works using examples.

Pupils listen and ask questions.

Step 2 - Explanation

Shows how to use the compound interest formula: A=P(1+r100)t

where A is the amount, P is the principal, r is the rate, and t is the time in years.

Pupils observe and practice calculations.

Step 3 - Demonstration

Solves an example problem step-by-step.

Pupils practice solving compound interest problems.

Step 4 - Note Taking

Teacher writes down the compound interest formula and example on the board.

Pupils copy the formula and example.

NOTE ON BOARD:

  • Compound Interest Formula: A=P(1+r100)t

A=P(1+100r)t

  • Example: If you invest 5000 Naira at 5% interest for 2 years, how much will you have at the end?
  • Calculation: A=5000(1+5100)2=5000(1.05)2=5000×1.1025=5512.5

= 5000(1.05)^2 = 5512.5

A=5000(1+1005)2=5000(1.05)2

=5000×1.1025=5512.5

EVALUATION (5 questions):

  1. Calculate the compound interest on 2000 Naira at 10% for 2 years.
  2. If 5000 Naira is invested at 8% compound interest for 3 years, what will the amount be?
  3. Calculate the compound interest on 3000 Naira at 12% for 1 year.
  4. If 1000 Naira is invested at 6% interest for 4 years, what is the amount?
  5. A principal of 2000 Naira is invested at 5% interest for 5 years. What is the total amount after interest?

CLASSWORK (5 questions):

  1. Find the compound interest on 1000 Naira at 10% for 3 years.
  2. Calculate the amount for 1500 Naira invested at 6% for 2 years.
  3. What is the compound interest on 2000 Naira at 4% for 2 years?
  4. Find the total amount after 2 years for 10000 Naira invested at 7%.
  5. If 8000 Naira is invested at 3% for 5 years, how much will the total amount be?

ASSIGNMENT (5 tasks):

  1. Calculate the compound interest on 3000 Naira at 8% for 2 years.
  2. A principal of 5000 Naira is invested at 5% for 3 years. What is the total amount?
  3. If 2000 Naira is invested at 10% for 4 years, how much interest will be earned?
  4. Find the total amount for 1200 Naira invested at 7% for 5 years.

Calculate the compound interest on 10000 Naira at 12% for 1 year.