Mathematics - Junior Secondary 2 - Angles of elevation and depression

Angles of elevation and depression

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TERM: 3RD TERM

WEEK 3

Class: Junior Secondary School 2
Age: 13 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Angles of Elevation and Depression
Focus: Defining and understanding angles of elevation and depression

SPECIFIC OBJECTIVES:

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

  1. Define angle of elevation and explain with a practical illustration.
  2. Measure and identify angles of elevation in various situations.
  3. Define angle of depression and provide real-life examples.
  4. Distinguish between angle of elevation and angle of depression.
  5. Apply knowledge of angles of elevation and depression to solve practical problems.

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Practical illustrations
  • Discussion and problem-solving exercises
  • Real-life applications

INSTRUCTIONAL MATERIALS:

  • Protractors
  • Whiteboard and marker
  • Visual aids (diagrams of angles of elevation and depression)
  • Scale drawing (for practical exercises)
  • Flashcards for key terms

PERIOD 1 & 2: Introduction to Angles of Elevation and Depression

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces the terms "angle of elevation" and "angle of depression" with real-life illustrations (e.g., looking up at a tall building vs. looking down at a valley).

Pupils listen, ask questions, and give examples.

Step 2 - Explanation

Demonstrates with a diagram: angle of elevation (looking upwards), angle of depression (looking downwards).

Pupils observe and take notes.

Step 3 - Demonstration

Uses a practical example: “If you are standing on the ground and looking at the top of a tree, what is the angle between the ground and your line of sight?”

Pupils provide responses and practice.

Step 4 - Note Taking

Teacher writes the definitions on the board.

Pupils copy the notes.

NOTE ON BOARD:

  • Angle of Elevation: The angle formed by the line of sight above the horizontal when you look at an object above your level.
  • Angle of Depression: The angle formed by the line of sight below the horizontal when you look at an object below your level.

EVALUATION (5 exercises):

  1. Define angle of elevation.
  2. Define angle of depression.
  3. Give an example of an angle of elevation.
  4. Give an example of an angle of depression.
  5. What is the difference between the two?

CLASSWORK (5 questions):

  1. Draw and label an angle of elevation and depression.
  2. Identify the angle of depression in a real-life scenario (e.g., a plane descending).
  3. Define the terms “line of sight” and “horizontal line.”
  4. Measure the angle of elevation for a building using a protractor.
  5. Explain how the angle of depression is measured.

ASSIGNMENT (5 tasks):

  1. Define angle of elevation and depression in your own words.
  2. Measure the angle of elevation of a tall object (e.g., a tree).
  3. Measure the angle of depression while sitting at a higher position looking down.
  4. Create a diagram illustrating both angles.
  5. Identify real-life examples of elevation and depression in newspapers or magazines.

 

PERIOD 3 & 4: Measurement of Angles of Elevation

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Revisits the concept of angle of elevation and demonstrates how to measure it using a protractor.

Pupils listen and ask clarifying questions.

Step 2 - Explanation

Demonstrates with a simple example: Using a protractor to measure the angle of elevation to the top of a tree or building.

Pupils practice measuring angles of elevation using protractors.

Step 3 - Demonstration

Guides pupils in measuring the angle of elevation for different objects in the classroom or outdoors.

Pupils measure angles with the teacher’s assistance.

Step 4 - Practice

Pupils independently measure angles in various scenarios (e.g., from the window to the ground below).

Pupils practice measuring angles independently.

NOTE ON BOARD:

  • To measure an angle of elevation:
    • Use a protractor.
    • Align the baseline with the horizontal line (ground level).
    • Measure the angle between the baseline and the line of sight.

EVALUATION (5 exercises):

  1. Measure the angle of elevation to the top of a nearby building.
  2. Measure the angle of elevation to a flag on top of a pole.
  3. Identify and label the components involved in measuring an angle of elevation.
  4. Practice measuring angle of elevation in pairs.
  5. Solve a practical example: What is the angle of elevation from a car parked at the base of a hill to the top?

CLASSWORK (5 questions):

  1. Measure the angle of elevation to a tree from a distance of 10 meters.
  2. Using a protractor, measure the angle of elevation to a classroom window.
  3. Draw a diagram of an object with an angle of elevation measurement.
  4. What tool is best for measuring angles of elevation?
  5. Measure and report the angle of elevation of your classroom’s ceiling.

ASSIGNMENT (5 tasks):

  1. Measure the angle of elevation to the nearest tall building from your school.
  2. Create a scale drawing showing the angle of elevation of a building.
  3. Find a photo in a magazine showing a high object and estimate the angle of elevation.
  4. Solve a word problem involving measuring the angle of elevation.
  5. Write a brief explanation of how measuring angles of elevation is useful in real life.

 

PERIOD 5: Application of Angles of Elevation and Depression in Problem Solving

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces problems that apply both angles of elevation and depression to calculate distances and heights.

Pupils listen and ask questions.

Step 2 - Explanation

Uses scale drawings to demonstrate how to calculate heights and distances based on angles of elevation and depression.

Pupils watch the demonstration and ask questions.

Step 3 - Demonstration

Solves sample problems involving measuring angles and calculating distances (e.g., calculating the height of a building).

Pupils follow along and attempt the problems.

Step 4 - Practice

Pupils work through sample problems with guidance.

Pupils solve problems independently or in groups.

NOTE ON BOARD:

  • Example Problem: If the angle of elevation to the top of a building from a point 100 meters away is 30°, how high is the building?
  • To solve, use trigonometric relationships or scale drawings.

EVALUATION (5 exercises):

  1. Find the height of a building if the angle of elevation from a point 50 meters away is 40°.
  2. Use a scale drawing to calculate the height of an object.
  3. Calculate the distance to an object using angle of depression.
  4. Identify a real-life scenario where angle of elevation or depression is used.
  5. Solve a word problem involving both angles of elevation and depression.

CLASSWORK (5 tasks):

  1. Solve a word problem using angle of depression.
  2. Use a scale drawing to calculate the height of a tree based on angle of elevation.
  3. Create a simple word problem involving angle of depression.
  4. Solve for the distance between two objects using angles.
  5. Calculate the height of a tower using a diagram.

ASSIGNMENT (5 tasks):

  1. Calculate the height of a tree using a scale drawing and angle of elevation.
  2. Create a story problem where angle of depression is used to solve a height calculation.
  3. Use angles of elevation to calculate the height of a building.
  4. Write a word problem involving both angle of elevation and angle of depression.

Practice measuring angles of elevation and depression from different vantage points.