Mathematics - Senior Secondary 1 - Simple equation and variations

Simple equation and variations

Get it on Google Play
Get it on the Apple App Store
  1. Home
  2. Comprehensive Lesson Plan and Notes
  3. Senior Secondary 1
  4. Simple equation and variations

 

TERM: 1ST TERM

WEEK: 12
Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Simple Equation and Variations
Focus: Revision of Simultaneous Linear Equations in Two Unknowns, Types and Applications of Variations

 

SPECIFIC OBJECTIVES:

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

  1. Revise and solve simultaneous linear equations in two unknowns.
  2. Understand the types of variations (direct, inverse, joint, and combined variations).
  3. Apply variations to real-life problems.
  4. Solve word problems involving all types of variations.

 

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
    • Guided demonstration
    • Discussion
    • Practice exercises
    • Real-life application of variations

 

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
    • Charts on types of variations
    • Flashcards with examples of simultaneous equations and variations
    • Worksheets for solving equations and problems on variations

 

PERIOD 1 & 2: Revision of Simultaneous Linear Equations in Two Unknowns

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Revises the concept of simultaneous linear equations in two unknowns using examples (e.g., x + y = 10, x - y = 2).

Students listen and recall methods of solving simultaneous equations.

Step 2 - Solving Methods

Demonstrates solving using substitution and elimination methods.

Students observe, take notes, and ask questions for clarity.

Step 3 - Example 1

Solves a problem: 2x + 3y = 7 and x - y = 1. Demonstrates the steps using substitution: solving for x or y first.

Students follow along, taking notes.

Step 4 - Example 2

Solves another problem: 3x - y = 5 and 2x + y = 6 using the elimination method (add the equations to eliminate y).

Students observe and practice in pairs.

NOTE ON BOARD:
Simultaneous Equations:

  • Substitution Method: Solve one equation for one variable, substitute in the other.
  • Elimination Method: Add or subtract equations to eliminate one variable.

 

EVALUATION (5 exercises):

  1. Solve 2x + 4y = 12 and x - 2y = 1.
  2. Solve 3x - 2y = 4 and 4x + y = 10.
  3. Solve 5x + y = 15 and 2x - 3y = -4.
  4. Solve 6x + 3y = 18 and 2x + y = 7.
  5. Solve 7x - 3y = 11 and 3x + y = 5.

CLASSWORK (5 questions):

  1. Solve 4x + 2y = 10 and x + 3y = 7.
  2. Solve 5x - y = 8 and x + 4y = 9.
  3. Solve 3x + y = 7 and 2x - 2y = 4.
  4. Solve 6x - 3y = 9 and 2x + y = 5.
  5. Solve 3x + 2y = 10 and x - y = 4.

ASSIGNMENT (5 tasks):

  1. Solve 4x - 3y = 5 and 5x + y = 11.
  2. Solve 7x + y = 9 and 2x - y = 3.
  3. Solve 5x + 3y = 15 and 2x + y = 7.
  4. Solve 3x + y = 7 and 2x + y = 5.
  5. Apply simultaneous equations to solve a real-life problem (e.g., cost of two items when given total costs for different quantities).

PERIOD 3 & 4: Types and Application of Variations

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction to Variations

Introduces the concept of variations: direct, inverse, joint, and combined.

Students listen attentively and ask questions.

Step 2 - Direct Variation

Explains direct variation (y = kx) with an example (e.g., y = 3x). Discusses how y increases as x increases.

Students observe, take notes, and discuss real-life examples.

Step 3 - Inverse Variation

Explains inverse variation (y = k/x) with an example (e.g., y = 12/x). Discusses how y decreases as x increases.

Students take notes and relate examples to real-life situations.

Step 4 - Joint and Combined Variation

Introduces joint variation (y = kxz) and combined variation (y = kx/z). Provides examples of combined and joint variations in practical scenarios.

Students observe and practice with examples in pairs.

NOTE ON BOARD:
Types of Variation:

  • Direct Variation (y = kx): y increases as x increases.
  • Inverse Variation (y = k/x): y decreases as x increases.
  • Joint Variation (y = kxz): y varies with the product of x and z.
  • Combined Variation (y = kx/z): y varies with x and inversely with z.

 

EVALUATION (5 exercises):

  1. If y = 6x, find y when x = 4.
  2. If y = 12/x, find y when x = 3.
  3. If y = kxz, find k if x = 2, z = 3, and y = 24.
  4. If y = kx/z, find y when x = 8, z = 4, and k = 5.
  5. Solve a real-life problem involving direct variation (e.g., speed and distance).

CLASSWORK (5 questions):

  1. If y = 5x, find y when x = 6.
  2. If y = 10/x, find y when x = 5.
  3. If y = kxz, find k when x = 1, z = 4, and y = 12.
  4. If y = kx/z, find y when x = 10, z = 2, and k = 3.
  5. Solve a word problem involving inverse variation (e.g., pressure and volume).

ASSIGNMENT (5 tasks):

  1. Solve a real-life problem involving joint variation (e.g., area of a triangle with base and height).
  2. Solve a word problem involving combined variation (e.g., the relationship between speed, time, and distance).
  3. If y = 2x, find y when x = 7.
  4. If y = 15/x, find y when x = 5.
  5. Apply variations to solve a practical problem (e.g., how temperature affects the volume of a gas).

 

PERIOD 5: Solving Problems Involving All Types of Variations

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Problem-Solving Techniques

Guides students in solving word problems involving all types of variations (direct, inverse, joint, and combined).

Students listen and ask questions about solving practical problems.

Step 2 - Example Problem 1

Provides an example of a word problem involving direct and inverse variation: "If the amount of time taken to fill a tank is directly proportional to the size of the tank and inversely proportional to the speed of water, how long will it take to fill a 5-liter tank at a speed of 2 liters per hour?"

Students observe the solution and discuss the method.

Step 3 - Example Problem 2

Provides a combined variation example: "The area of a rectangle is directly proportional to the length and inversely proportional to the width. If the area is 24 cm² when the length is 6 cm and the width is 4 cm, what is the area when the length is 8 cm and the width is 3 cm?"

Students follow the solution process and solve similar problems.

NOTE ON BOARD:

  • Direct and Inverse Variation Problems: Use y = kx and y = k/x.
  • Joint and Combined Variation Problems: Use y = kxz and y = kx/z.

 

EVALUATION (5 exercises):

  1. Solve a word problem involving direct variation.
  2. Solve a word problem involving inverse variation.
  3. Solve a word problem involving joint variation.
  4. Solve a word problem involving combined variation.
  5. Solve a mixed variation problem with all types of variation.

CLASSWORK (5 questions):

  1. Solve a real-life problem involving direct variation (e.g., salary and hours worked).
  2. Solve a real-life problem involving inverse variation (e.g., pressure and volume of gas).
  3. Solve a word problem involving combined variation (e.g., speed, distance, and time).
  4. Solve a problem involving joint variation (e.g., area of a triangle).
  5. Solve a mixed variation problem using all four types of variation.

ASSIGNMENT (5 tasks):

  1. Solve a word problem involving direct variation.
  2. Solve a word problem involving inverse variation.
  3. Solve a word problem involving joint variation.
  4. Solve a combined variation problem.

Apply variations to solve a practical real-life problem.