Mathematics - Junior Secondary 3 - Study of measurement using clinometers

TERM: 2^ND TERM

WEEK 10
Class: Junior Secondary School 3
Age: 14 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Study of Measurement Using Clinometers
Focus: Use clinometers to demonstrate and estimate or calculate distances

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

Define and use a clinometer.
Measure angles of elevation and depression with a clinometer.
Estimate or calculate distances using clinometers.
Apply the clinometer in real-life scenarios such as measuring heights of buildings and trees.
Solve problems using the clinometer for accurate measurements.

INSTRUCTIONAL TECHNIQUES:
• Question and answer
• Guided demonstration
• Practical use of clinometers
• Problem-solving exercises

INSTRUCTIONAL MATERIALS:
• Clinometers
• Measuring tapes
• Worksheets
• Whiteboard and marker

PERIOD 1 & 2: Introduction to Clinometers and Measuring Angles

PRESENTATION:

Step	Teacher’s Activity	Pupil’s Activity
Step 1 - Introduction	Introduces the concept of clinometers and their purpose. Explains how clinometers are used to measure angles of elevation and depression.	Pupils listen and ask questions.
Step 2 - Explanation	Demonstrates how to use a clinometer to measure an angle of elevation (e.g., measuring the angle to the top of a tree).	Pupils observe the demonstration.
Step 3 - Demonstration	Uses a clinometer to measure the angle of elevation and depression of different objects in the classroom or outdoor area.	Pupils practice using the clinometer to measure angles of elevation and depression.
Step 4 - Note Taking	Teacher writes a summary of how to measure angles with a clinometer.	Pupils take notes.

NOTE ON BOARD:

Angle of Elevation: The angle between the horizontal and the line of sight to an object above the observer.
Angle of Depression: The angle between the horizontal and the line of sight to an object below the observer.

EVALUATION (5 exercises):

Define the angle of elevation.
Define the angle of depression.
Measure the angle of elevation to the top of a classroom board using the clinometer.
Measure the angle of depression to the floor from the top of the classroom using the clinometer.
Discuss real-life scenarios where these measurements might be useful.

CLASSWORK (5 questions):

Measure the angle of elevation to a tree outside the classroom.
Measure the angle of depression from the roof of the building to the ground.
Identify three real-life situations where measuring angles of elevation or depression would be useful.
Write a short explanation of how to use a clinometer.
Calculate the angle of elevation to a distant object (e.g., a building or mountain).

ASSIGNMENT (5 tasks):

Measure the angle of elevation to the top of a structure in your home or neighborhood.
Record your findings and explain how you took the measurement.
Use the clinometer to measure angles of elevation and depression in different parts of your school.
Write a short report on how clinometers can be used in real-world applications.
Research and identify an instance where clinometers are used professionally (e.g., in construction, surveying).

PERIOD 3 & 4: Calculating Distances Using Clinometers

PRESENTATION:

Step	Teacher’s Activity	Pupil’s Activity
Step 1 - Introduction	Introduces the concept of calculating distances using clinometers. Explains the relationship between angles and distances.	Pupils listen and ask questions.
Step 2 - Explanation	Demonstrates how to calculate the distance from the observer to an object using the clinometer. Explains the trigonometric ratios (e.g., tan = opposite/adjacent).	Pupils observe and take notes.
Step 3 - Demonstration	Calculates the height of a building using the clinometer, angle of elevation, and a known distance from the building.	Pupils practice calculating distances using different scenarios.
Step 4 - Note Taking	Teacher writes the formula for calculating distances:

Distance = Height / tan(Angle of Elevation)
Distance = Height / tan(Angle of Depression)
| Pupils copy the formula and examples. |

EVALUATION (5 exercises):

Given the angle of elevation and the distance to the object, calculate the height of the object.
Use the angle of depression and distance to calculate the height of a building or tree.
Solve for the height of an object using the clinometer and trigonometric ratios.
Calculate the distance to an object using the clinometer and the angle of elevation.
Solve a word problem involving the use of a clinometer to calculate distances.

CLASSWORK (5 questions):

If the angle of elevation to a tree is 30°, and you are standing 10 meters away from the tree, calculate its height.
Measure the angle of elevation to a building 25 meters away, and calculate its height using a clinometer.
Calculate the height of an object using the angle of depression and the distance from the object.
Solve a problem using the formula for distance calculation in a real-life situation.
Calculate the height of a tall object if you know the distance from the object and the angle of elevation.

ASSIGNMENT (5 tasks):

Use a clinometer to calculate the height of a building or tree near your school.
Report on the method you used and your final measurements.
Use the trigonometric formula to calculate the distance to a high object you can measure from a distance.
Write a problem involving calculating distances using clinometers, and solve it.
Discuss how this technique can be applied in fields like construction, architecture, or environmental science.

PERIOD 5: Real-life Application and Problem Solving

PRESENTATION:

Step	Teacher’s Activity	Pupil’s Activity
Step 1 - Introduction	Introduces real-life scenarios, such as measuring distances and heights in environmental studies, construction, and navigation.	Pupils listen and ask questions.
Step 2 - Examples	Provides examples from newspapers, surveys, or internet where clinometers are used in real-life.	Pupils discuss examples and real-life applications.
Step 3 - Problem Solving	Gives pupils a series of real-life problems to solve using the clinometer, such as measuring the height of a tree or distance to an object.	Pupils solve problems using the clinometer and trigonometric ratios.
Step 4 - Evaluation	Provides a final set of exercises for pupils to apply all they have learned.	Pupils complete the exercises independently.

EVALUATION (5 exercises):

Measure the angle of elevation to the top of a large tree and calculate its height.
Use the clinometer to calculate the height of a school building from a distance.
Solve a problem where the angle of depression is given, and the height needs to be calculated.
Create a word problem involving the use of a clinometer.
Discuss how clinometers are used in different professional fields (e.g., surveying, construction).

CLASSWORK (5 tasks):

Measure and calculate the height of a building or tree near your school.
Write a report explaining how you calculated the height and distance.
Solve a problem involving a clinometer and submit the solution.
Apply the knowledge to a new problem involving distance and angle calculations.
Review real-life applications of clinometers in different fields.

ASSIGNMENT (5 tasks):

Find a real-life example where clinometers are used, research it, and explain how the clinometer was applied.
Measure the angle of elevation to a distant building or structure, and calculate its height.
Use the trigonometric formula to calculate the height of a tall object at a distance from you.
Solve a problem from your textbook or notes that involves angles of elevation and depression.

Write a report on how clinometers can be used in geography and environmental science.