Lesson Note on Development of Truncated Solids for SS 2

Class: Senior Secondary School 2 (SS2 / SSS2)
Term: 1st Term
Week: 7
Age: 16 years
Duration: 45 minutes
Subject: Technical Drawing
Curriculum Theme: Technical Drawing
Previous Lesson: True Shapes of Truncated Solids.
Topic: TRUE SHAPES
Subject Matter: Development of models using true shapes (cardboard development of cut solids)

Specific Objectives

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

Cognitive Domain:

• Define what a true shape is in technical drawing.
• Explain the concept of development of surfaces of solids.
• State the principles used in developing surfaces.

Affective Domain:

• Appreciate the importance of true shapes in engineering and design.
• Show interest in accurately drawing and developing solid models.

Psychomotor Domain:

• Develop the true shape of simple cut solids on paper.
• Construct a cardboard model of a developed cut solid.

Social Domain:

• Collaborate effectively with peers when working on practical development tasks.

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=sKqFq01b96o
• https://www.youtube.com/watch?v=F3zWvGv-vXQ

Instructional Materials

The teacher will teach this lesson with the aid of:

• Models of various solids (e.g., prism, cylinder, pyramid, cone)
• Posters showing developed surfaces of solids
• Drawing instruments (rulers, pencils, set squares, compasses)
• Cardboard sheets
• Scissors
• Glue or adhesive tape

Rationale for the Lesson

Understanding true shapes and the development of solids helps pupils visualize three-dimensional objects in two dimensions. This skill is important for designing and manufacturing objects like packaging, sheet metal products, and various engineering components.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of basic geometric shapes, orthographic projection, and the identification of different solid figures.

Lesson Content/Board Summary

TRUE SHAPES AND DEVELOPMENT OF SOLIDS

Definition of True Shape

A true shape is the actual shape and size of a surface when viewed perpendicularly to it. It represents the undistorted form of a plane or surface, free from any foreshortening caused by projection.

Development of Surfaces

Development is the process of unrolling or unfolding the entire surface of a solid onto a flat plane, showing its true size and shape. The developed surface, when cut out and folded along specific lines, will perfectly form the original solid.

The following are purposes of development:

• To create patterns for manufacturing products from sheet materials (e.g., metal, cardboard).
• To determine the exact surface area of a solid.
• To aid in the visualization and understanding of complex three-dimensional forms.

Principles of Development

The main principles used for developing surfaces are:

• Parallel Line Development: Used for solids with parallel edges or generators, such as prisms and cylinders.
• Radial Line Development: Used for solids with an apex and radiating elements, such as pyramids and cones.
• Triangulation: Used for irregular surfaces and transition pieces that cannot be developed by parallel or radial line methods, by dividing the surface into a series of triangles.

Steps for Developing a Cut Solid

General steps include:

• Draw the orthographic views (front and plan views) of the solid, including the cutting plane.
• Determine the true lengths of all edges or elements that form the surface.
• Unfold the surfaces onto a flat plane, transferring the true lengths and shapes accurately.
• Mark out all cut edges and fold lines clearly on the development.
• Add allowances for laps or joints if a physical model is to be constructed.

Worked Example 1: Development of a Cut Square Prism

Consider a square prism that has been cut by an inclined plane.

1. Step 1: Draw the front view and plan view of the square prism, clearly showing the inclined cutting plane.
2. Step 2: Project the points where the cutting plane intersects the vertical edges of the prism from the front view to the plan view, if necessary, to confirm their positions.
3. Step 3: Draw a horizontal stretch-out line (base line) for the development. The total length of this line should be equal to the perimeter of the prism’s base.
4. Step 4: Along the stretch-out line, mark off the width of each face of the prism (e.g., four equal widths for a square prism). Draw vertical lines upwards from these points.
5. Step 5: From the front view, transfer the true heights of the cut edges (the vertical distances from the base to the cutting plane) to their corresponding vertical lines in the development.
6. Step 6: Connect the transferred points with straight lines to form the outline of the developed surface. This outline represents the true shape of the cut prism’s lateral surface.

Worked Example 2: Development of a Cut Cylinder

Consider a cylinder that has been cut by an inclined plane.

1. Step 1: Draw the front view and plan view of the cylinder, clearly indicating the inclined cutting plane.
2. Step 2: Divide the circumference of the plan view (circle) into a number of equal parts (e.g., 12). Project these divisions up to the front view to create equally spaced element lines along the cylinder’s surface.
3. Step 3: Where the cutting plane intersects these element lines in the front view, mark these intersection points. Project these points horizontally to a vertical reference line to easily transfer their heights.
4. Step 4: Draw a rectangle for the development. Its length will be the circumference of the cylinder (πD) and its height will be the full height of the cylinder.
5. Step 5: Divide the length of the development rectangle into the same number of equal parts as the plan view (e.g., 12). Draw vertical lines (representing the elements) through these points across the development rectangle.
6. Step 6: From the horizontal reference line (from Step 3), transfer the true heights of the cut points onto their corresponding vertical element lines in the development.
7. Step 7: Connect these transferred points with a smooth curve to complete the developed surface. This curve represents the true shape of the cut edge.

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, checks attendance, and introduces the topic by asking pupils if they have ever seen a carton or a tin can opened up flat. The teacher then explains that this flattening is related to “development” in technical drawing.
Pupils’ Activity: Pupils respond to greetings and questions, sharing their observations about flattened containers.
Learning Point: Pupils are introduced to the concept of unfolding solids and connect it to real-world examples.

Step 2: Explanation of True Shape

Time: 7 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher defines “true shape” using a model of a solid with an inclined surface, explaining that the true shape is what you see when looking directly at that surface without distortion. The teacher draws a simple example on the board.
Pupils’ Activity: Pupils listen attentively, observe the model and board drawing, and ask questions for clarification.
Learning Point: Pupils understand the definition and visual representation of a true shape.

Step 3: Explanation of Development of Surfaces

Time: 8 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher defines “development of surfaces” and explains its purpose. The teacher uses a pre-made cardboard model of a simple solid (e.g., a cube or a cylinder) that can be unfolded to demonstrate the concept of development.
Pupils’ Activity: Pupils pay attention to the definition and observe the teacher’s demonstration of unfolding the solid.
Learning Point: Pupils grasp the concept of developing a solid’s surface and its practical applications.

Step 4: Principles of Development

Time: 5 minutes
Teaching Skill: Lecture/Discussion
Teacher’s Activity: The teacher discusses the three main principles of development: parallel line, radial line, and triangulation, briefly explaining when each is used with examples of solids.
Pupils’ Activity: Pupils listen and take notes on the different principles of development.
Learning Point: Pupils identify and understand the basic principles governing the development of various solid surfaces.

Step 5: Demonstration of Development of a Cut Solid

Time: 10 minutes
Teaching Skill: Demonstration/Modeling
Teacher’s Activity: The teacher demonstrates the step-by-step process of developing a simple cut solid (e.g., a cut square prism or cylinder) on the chalkboard or a large drawing sheet, following the steps outlined in the board summary. The teacher emphasizes accuracy and true lengths.
Pupils’ Activity: Pupils observe the teacher’s demonstration carefully, noting each step and asking questions about the procedure.
Learning Point: Pupils learn the practical steps involved in developing the surface of a cut solid.

Step 6: Guided Practice for Pupils

Time: 10 minutes
Teaching Skill: Coaching/Supervision
Teacher’s Activity: The teacher provides pupils with drawing paper and instructs them to begin drawing the orthographic views for a different simple cut solid (e.g., a cut cylinder if a prism was demonstrated) and start its development under supervision. The teacher moves around to offer guidance.
Pupils’ Activity: Pupils attempt to draw and develop the assigned cut solid on their drawing sheets, applying the steps demonstrated by the teacher.
Learning Point: Pupils practice the development process, reinforcing their understanding and skill.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. What is a true shape in technical drawing?
2. Define the term “development” as it relates to solid surfaces.
3. Mention two principles of development.
4. State one practical application of developing solid surfaces.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 5 minutes
Teaching Skill: Summarization/Assignment
Teacher’s Activity: The teacher summarizes the key points of the lesson on true shapes and development. The teacher assigns homework: pupils are to develop a simple cut pyramid on paper and attempt to construct it from cardboard.
Pupils’ Activity: Pupils listen to the summary, ask any final questions, and copy down the homework assignment.
Learning Point: Pupils consolidate their learning and are given an opportunity for further practice.

Lesson Keywords

• True Shape – The actual, undistorted shape and size of a surface.
• Development – The process of unfolding a solid’s surface onto a flat plane.
• Cut Solid – A solid that has been intersected by a cutting plane.
• Parallel Line Development – A method used for prisms and cylinders.
• Radial Line Development – A method used for pyramids and cones.
• Triangulation – A method used for irregular surfaces by dividing them into triangles.

Differentiation

For pupils who grasp the concepts quickly, the teacher can provide more complex cut solids for development or challenge them to consider how to add tabs for gluing. For pupils who need more support, the teacher will provide pre-drawn orthographic views to start their development process and give more one-on-one guidance.

Note for teachers using this lesson plan

Emphasize the importance of accuracy in measurements and drawing. Encourage pupils to use appropriate drawing instruments. When demonstrating, use clear, large drawings on the board. For the practical activity, ensure pupils handle scissors safely and provide enough cardboard and adhesive. Connect the lesson to everyday objects like food packaging or ventilation ducts to make it more relatable.