Mastering Angles: Constructing and Measuring in Technical Drawing SS 1 First Term Lesson Notes Week 9

Technical Drawing, SS 1, First Term, Week 9 on Angles (Construction and Measurement of Angles).

Lesson Plan: Angles (Construction and Measurement of Angles)

Subject: Technical Drawing
Class: SS 1
Term: First Term
Week: 9
Age: 14-16 years
Topic: Angles
Sub-Topic: Construction and Measurement of Angles
Duration: 40 minutes

Behavioral Objectives

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

1. Understand angular relationships in terms of rotation and alignment with surfaces.
2. Classify and describe various types of angles.
3. Relate angles to basic geometric shapes.
4. Identify whether angles are more or less than a right angle and order them in size.

Keywords

• Angle
• Right angle
• Acute angle
• Obtuse angle
• Construction
• Protractor

Set Induction

The teacher will start by showing examples of common objects that form angles, such as a book partially open, a door, and a clock. Students will observe and describe the angles formed by these objects.

Entry Behavior

Students are familiar with basic geometric shapes and have learned about lines in previous lessons.

Learning Resources and Materials

• Protractors
• Set squares
• Rulers
• Compass
• Drawing sheets

Building Background/Connection to Prior Knowledge

Students have studied lines and basic geometric shapes, which are essential for understanding angle construction.

Embedded Core Skills

• Observation and identification
• Practical application of geometry
• Measurement and classification
• Spatial reasoning

Learning Materials

• Lagos State Scheme of Work for Technical Drawing
• Illustrated diagrams of angles

Reference

• Lagos State Scheme of Work
• “Technical Drawing and Engineering Graphics” by A. Bankole

Instructional Materials

• Visual charts showing types of angles (acute, obtuse, right, etc.)
• Drawing instruments for angle construction
• Sample objects that create visible angles (e.g., open door, clock)

Content Outline

1. Types of Angles:
   • Definition and classification: acute, right, obtuse, and straight angles.
2. Angular Relationships:
   • Explanation of angles as they relate to rotation and geometric alignment.
3. Construction of Angles:
   • Step-by-step guide to constructing different types of angles using a protractor and compass.
4. Measurement of Angles:
   • Techniques for measuring angles and determining their size relative to a right angle.
5. Angle Applications in Shapes:
   • Identification of angles within geometric shapes (e.g., triangles, quadrilaterals).

Fill-in-the-Blank Questions

1. An angle of 90 degrees is known as a ______ angle (a. right, b. obtuse, c. acute, d. straight).
2. An angle smaller than 90 degrees is called an ______ angle (a. obtuse, b. acute, c. straight, d. right).
3. A ______ angle is greater than 90 degrees but less than 180 degrees (a. acute, b. obtuse, c. right, d. straight).
4. The tool used to measure angles is called a ______ (a. ruler, b. compass, c. protractor, d. set square).
5. A complete rotation forms a ______ angle (a. acute, b. obtuse, c. straight, d. full).
6. A right angle is formed when two lines are ______ to each other (a. parallel, b. perpendicular, c. aligned, d. diagonal).
7. An angle of 180 degrees is called a ______ angle (a. acute, b. obtuse, c. straight, d. right).
8. When two angles add up to 90 degrees, they are called ______ angles (a. complementary, b. supplementary, c. obtuse, d. right).
9. The corner of a square forms a ______ angle (a. acute, b. obtuse, c. right, d. straight).
10. Angles larger than a right angle but smaller than 180 degrees are called ______ (a. straight, b. obtuse, c. acute, d. full).

FAQ

1. What is an acute angle?
   • An angle smaller than 90 degrees.
2. What is a right angle?
   • A 90-degree angle, typically shown with perpendicular lines.
3. How is an obtuse angle different from an acute angle?
   • An obtuse angle is larger than 90 degrees but smaller than 180 degrees, while an acute angle is smaller than 90 degrees.
4. What is the purpose of a protractor?
   • A protractor is used to measure angles.
5. What are complementary angles?
   • Two angles that add up to 90 degrees.

Angles (Construction and Measurement of Angles)

1. Understand Angular Relationships:
   • Explanation: Angular relationships describe how angles interact or relate to each other within shapes and figures. Recognizing these relationships is crucial in technical drawing, especially in geometry and design, where angle alignment and orientation are essential.
   • Types of Angular Relationships:
     • Adjacent Angles: Angles that share a common side and vertex.
       • Example: The angles formed by two intersecting lines.
     • Complementary Angles: Two angles that add up to 90 degrees.
       • Example: Angles in a right-angled triangle (other than the right angle itself).
     • Supplementary Angles: Two angles that add up to 180 degrees.
       • Example: Angles along a straight line or in a semi-circle.
   • Why it’s Important: Understanding these relationships allows students to build complex shapes accurately, ensuring that all angles fit together seamlessly.
2. Classify and Describe Angles:
   • Explanation: Angles are classified based on their sizes. Each angle type has unique properties and applications in technical drawing, construction, and architecture.
   • Types of Angles:
     • Acute Angle: An angle less than 90 degrees.
       • Example: The angle in the tip of a triangle.
     • Right Angle: An angle of exactly 90 degrees.
       • Example: The corner of a square or rectangle.
     • Obtuse Angle: An angle greater than 90 degrees but less than 180 degrees.
       • Example: The angle of a reclined chair back.
     • Straight Angle: An angle of exactly 180 degrees.
       • Example: The angle formed by a straight line.
     • Reflex Angle: An angle greater than 180 degrees but less than 360 degrees.
       • Example: The angle created by an opened door that swings past a straight line.
   • Why it’s Important: Classifying angles is foundational for constructing accurate geometric shapes and structures. Each angle type serves specific purposes in design and technical drawings.
3. Relate Angles to Shapes:
   • Explanation: Angles are key elements in defining the shape and structure of polygons and other geometric figures. Understanding how angles form and influence shapes helps in creating precise technical drawings.
   • Examples:
     • Triangles: Comprised of three angles that sum up to 180 degrees.
       • Types: Equilateral (all angles are 60°), isosceles (two equal angles), and scalene (all angles are different).
     • Quadrilaterals: Comprised of four angles that sum up to 360 degrees.
       • Types: Rectangle (four right angles), square (four right angles and equal sides), parallelogram (opposite angles are equal).
     • Polygons: General shapes with multiple sides where the sum of the interior angles depends on the number of sides.
   • Why it’s Important: Relating angles to shapes helps in accurately constructing polygons and complex designs. This understanding is essential for drawing items such as floor plans, blueprints, and architectural designs.
4. Identify Angles as More or Less Than a Right Angle:
   • Explanation: Identifying whether angles are greater or less than 90 degrees helps in categorizing angles quickly and understanding their relationships within shapes.
   • Steps to Identify:
     • Use a protractor to measure the angle or visually compare it to a right angle (90 degrees).
     • Classify the angle as either acute (less than 90°) or obtuse (more than 90°).
   • Why it’s Important: This skill is useful in geometry and technical drawing for identifying angle sizes efficiently, enabling faster and more accurate shape constructions.

By mastering these concepts, students will be able to construct, measure, and apply angles accurately in various technical drawing tasks, enhancing their geometric skills and understanding of shapes.

Presentation Steps

Step 1: Revision of Previous Topic
The teacher will briefly review types of lines to prepare students for the concept of angles, as lines form angles when they intersect.

Step 2: Introduction of New Topic
The teacher will introduce the concept of angles, demonstrating various angles with a protractor and visual aids.

Step 3: Student Contributions and Corrections
Students will attempt to measure and construct angles using their protractors and compass under teacher supervision, with corrections and guidance as needed.

Teacher’s Activities

• Demonstrate the use of a protractor to measure angles.
• Explain the steps for constructing various angles (acute, right, obtuse).
• Guide students in classifying and measuring angles they construct on paper.

Learner’s Activities

• Practice using a protractor to measure given angles.
• Construct specified angles on their drawing sheets.
• Identify and classify different types of angles around them in objects.

Assessment

• The teacher will evaluate students’ ability to measure, classify, and construct angles accurately.
• Observation of students’ understanding of the angular relationships and applications.

Evaluation Questions

1. What type of angle is 90 degrees?
2. How would you classify an angle of 45 degrees?
3. Which tool is used to measure angles?
4. What is an obtuse angle?
5. How do you differentiate between acute and obtuse angles?

Conclusion

The teacher will conclude by highlighting the significance of angles in technical drawing and real-life applications, encouraging students to observe and recognize angles in their environment.