Lesson Note on Auxiliary View of Geometrical Solids: Meaning, Uses and Types for SS 2

Class: Senior Secondary School 2 (SS2 / SSS 2)
Term: 2nd Term
Week: 2
Age: 16 years
Duration: 45 minutes
Subject: Technical Drawing
Curriculum Theme: Orthographic Projections and Auxiliary Views
Previous Lesson: Orthographic Projections.
Topic: AUXILIARY VIEW OF GEOMETRICAL SOLIDS
Subject Matter: Meaning of auxiliary view (additional view for showing true shape), uses of auxiliary views (revealing inclined surfaces), types of auxiliary views (first auxiliary view, second auxiliary view).

Specific Objectives

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

Cognitive Domain:

• Define an auxiliary view.
• State at least two uses of auxiliary views.
• Identify the two main types of auxiliary views.

Affective Domain:

• Appreciate the importance of auxiliary views in technical drawing.
• Show interest in drawing auxiliary views accurately.

Psychomotor Domain:

• Sketch a simple auxiliary view of an inclined surface.
• Draw an auxiliary plane correctly.

Social Domain:

• Collaborate with peers in discussing concepts related to auxiliary views.
• Participate actively in class discussions about auxiliary projections.

Reference Materials

The following resources were used in planning this lesson:

• Senior Secondary Schools Education Curriculum
• State Unified Scheme of Work
• N.D. Bhatt, Engineering Drawing
• https://www.youtube.com/watch?v=R913v_X6L64
• https://www.youtube.com/watch?v=078gYvYnL2Q

Instructional Materials

The teacher will teach this lesson with the aid of:

• Video clips showing auxiliary views
• Posters and charts illustrating auxiliary projections
• Whiteboard/Blackboard
• Markers/Chalk
• Drawing instruments (set squares, protractor, ruler)

Rationale for the Lesson

This lesson helps pupils understand how to obtain the true shape and size of inclined surfaces in technical drawings. It is important for accurately representing objects in various engineering and design fields, ensuring clarity and precision in technical communication.

Prerequisite/Previous Knowledge

Pupils should have basic knowledge of orthographic projections, including front view, plan, and end views of simple geometrical solids.

Lesson Content/Board Summary

AUXILIARY VIEW OF GEOMETRICAL SOLIDS

Meaning of Auxiliary View

An auxiliary view is an additional view projected onto a plane that is not parallel to any of the principal planes of projection (horizontal, frontal, or profile). Its main purpose is to show the true shape and size of an inclined surface which would otherwise appear foreshortened or distorted in standard orthographic views.

Uses of Auxiliary Views

The following are the uses of auxiliary views:

• To determine the true shape and size of an inclined surface.
• To find the true length of a line that is inclined to the principal planes.
• To find the true angle between two planes.
• To locate points and lines on inclined surfaces accurately.
• To show the true shape of a hole or feature on an inclined face.

Types of Auxiliary Views

The two main types of auxiliary views are:

• First Auxiliary View: This view is projected directly from one of the primary orthographic views (e.g., front, top, or side view) onto a plane that is perpendicular to one of the principal planes and parallel to the inclined surface whose true shape is required.
• Second Auxiliary View: This view is projected from a first auxiliary view. It is used when the true shape of a surface or the true length of a line is not fully revealed by the first auxiliary view, especially for doubly inclined surfaces. The projection plane for a second auxiliary view is perpendicular to the first auxiliary plane.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and asks them to recall what they learned about orthographic projections. The teacher then introduces the topic of auxiliary views by explaining that sometimes standard views do not show the true shape of inclined surfaces.
Pupils’ Activity: Pupils respond to the teacher’s questions about orthographic projections and listen attentively to the introduction of the new topic.
Learning Point: Pupils connect previous knowledge to the new topic and understand the need for auxiliary views.

Step 2: Explanation of Meaning of Auxiliary View

Time: 10 minutes
Teaching Skill: Explanation/Illustration
Teacher’s Activity: The teacher explains the meaning of an auxiliary view using charts and diagrams to illustrate how it provides the true shape of inclined surfaces.
Pupils’ Activity: Pupils listen, observe the diagrams, and ask questions for clarification.
Learning Point: Pupils understand that an auxiliary view is an additional view to show true shape.

Step 3: Discussion on Uses of Auxiliary Views

Time: 10 minutes
Teaching Skill: Guided Discussion
Teacher’s Activity: The teacher discusses the various uses of auxiliary views, such as finding true shape, true length, and true angles, providing examples where necessary.
Pupils’ Activity: Pupils participate in the discussion, contributing ideas and noting the practical applications.
Learning Point: Pupils comprehend why and when auxiliary views are applied in technical drawing.

Step 4: Explanation of Types of Auxiliary Views

Time: 10 minutes
Teaching Skill: Classification/Elucidation
Teacher’s Activity: The teacher explains the difference between first and second auxiliary views, demonstrating how each is derived with simple sketches on the board.
Pupils’ Activity: Pupils pay attention to the distinctions between the types and observe the sketching process.
Learning Point: Pupils can differentiate between first and second auxiliary views.

Step 5: Practical Demonstration

Time: 5 minutes
Teaching Skill: Demonstration
Teacher’s Activity: The teacher demonstrates how to project a simple first auxiliary view from a given orthographic projection of a solid with an inclined surface on the board.
Pupils’ Activity: Pupils observe the demonstration carefully and ask relevant questions about the projection steps.
Learning Point: Pupils gain a visual understanding of the process of drawing an auxiliary view.

Step 6: Evaluation/Review

Time: 5 minutes
Teaching Skill: Questioning/Assessment
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. Define an auxiliary view.
2. State two uses of an auxiliary view.
3. List the two main types of auxiliary views.
4. Explain why auxiliary views are important in technical drawing.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 7: Conclusion

Time: 2 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the definition, uses, and types of auxiliary views. The teacher then assigns homework, asking pupils to research more complex examples of auxiliary views.
Pupils’ Activity: Pupils listen to the summary and copy down the homework assignment.
Learning Point: Pupils consolidate their understanding and prepare for further study.

Lesson Keywords

• Auxiliary view – An additional view that shows the true shape and size of an inclined surface.
• True shape – The actual, undistorted shape of a surface or object.
• Inclined surface – A surface that is not parallel to any of the principal projection planes.
• First auxiliary view – A view projected from a primary orthographic view.
• Second auxiliary view – A view projected from a first auxiliary view.

Differentiation

For pupils who grasp concepts quickly, the teacher can provide more complex objects with multiple inclined surfaces for sketching. For those needing more support, the teacher will offer one-on-one guidance and simpler shapes, using more visual aids and step-by-step instructions.

Note for teachers using this lesson plan

Emphasize the practical application of auxiliary views in engineering and design. Encourage pupils to use proper drawing instruments and techniques for accuracy. Provide ample practice with various geometrical solids to reinforce understanding and skill development.