Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: 3rd Term
Week: 2
Age: 15 years
Duration: 45 minutes
Subject: Technical Drawing
Curriculum Theme: Technical Drawing
Previous Lesson: Special Curves: Locus, Ellipse, Cycloid and Trochoid.
Topic: True Length and Surface Development
Subject Matter: Meaning of development, applications of surface development, determination of true lengths of full solids, determination of true lengths of truncated solids, procedures for accurate true length construction.

Specific Objectives

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

Cognitive Domain:

Define surface development.
State at least three applications of surface development.
Explain the concept of true length in technical drawing.
Describe the procedures for determining true lengths of lines on solids.

Affective Domain:

Appreciate the importance of true length and surface development in various fields.
Show interest in solving problems related to true length and surface development.

Psychomotor Domain:

Construct the true length of a given line on a solid.
Sketch the development of simple solid objects.

Participate actively in class discussions.
Collaborate with peers to solve drawing tasks.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for Senior Secondary Schools.
State Unified Scheme of Work for Technical Drawing (SSS 1).
A. A. Awokoya (2018). Technical Drawing for Senior Secondary Schools 1-3. Learn Africa Plc.
https://www.engineeringdrawingonline.com/true-length-of-a-line/
https://www.youtube.com/watch?v=example_development

Instructional Materials

The teacher will teach this lesson with the aid of:

Models of various geometric solids (e.g., prism, pyramid, cylinder, cone).
Charts showing examples of surface development.
Posters illustrating true length determination.
Drawing instruments (set squares, compass, ruler, pencils).
Cardboard, scissors or knife for practical demonstrations.

Rationale for the Lesson

This lesson helps pupils understand how three-dimensional objects can be represented in two dimensions, which is important for manufacturing and packaging. It also enables pupils to find the actual lengths of lines on objects, a fundamental skill in design and construction.

Prerequisite/Previous Knowledge

Pupils should have basic knowledge of orthographic projections, geometric shapes, and solid objects from their previous lessons.

Lesson Content/Board Summary

TRUE LENGTH AND SURFACE DEVELOPMENT

Meaning of Development

Development, in technical drawing, refers to the unfolding or unwrapping of the entire surface of a three-dimensional object onto a single plane. This process shows the actual shape and size of each surface that forms the solid.

Applications of Surface Development

The following are applications of surface development:

Sheet metal work (e.g., ducting, tanks, pipes).
Packaging design (e.g., cartons, boxes).
Pattern making (e.g., for clothing, shoes).
Design of architectural structures (e.g., roofs, domes).
Manufacturing of containers and enclosures.

Determination of True Lengths of Full Solids

A true length of a line is its actual, unforeshortened length. In orthographic projections, a line will only show its true length if it is parallel to the plane of projection. If a line is inclined to the projection planes, its projected length will be shorter than its true length.

Methods for determining true length include:

Revolution Method: Rotating the line about a point or axis until it is parallel to a projection plane.
Auxiliary View Method: Projecting the line onto a new view plane that is parallel to the line.

Determination of True Lengths of Truncated Solids

Truncated solids are solids that have been cut by a plane. The edges or lines on the cut surfaces may not show their true lengths in standard orthographic views. The same methods (revolution or auxiliary view) are used to find the true lengths of these lines on truncated solids to accurately develop their surfaces.

Procedures for Accurate True Length Construction

The following are general procedures for constructing true lengths:

Identify the line whose true length is required.
Draw the orthographic projections (front and plan views) of the object containing the line.
For the revolution method, select one end of the line as a pivot and rotate the other end in one view until the line becomes parallel to the reference line or projection plane in the other view.
Project the rotated point back to the original view to find the true length.
For the auxiliary view method, draw a reference line parallel to the line in one view.
Project the endpoints of the line perpendicularly from the original view onto the new auxiliary reference line.
Transfer the perpendicular distances from the original view to the auxiliary view to find the true length.

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 observe objects around them, such as a carton or a tin can. The teacher then asks how these objects might have been made from flat sheets of material. This leads to the concept of unfolding or development.
Pupils’ Activity: Pupils respond to the questions and observe the objects.
Learning Point: Pupils are introduced to the topic and relate it to real-life objects.

Step 2: Meaning of Development

Time: 7 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher explains the meaning of surface development, using a cardboard model of a prism or cylinder that can be unfolded to demonstrate the concept. The teacher writes the definition on the board.
Pupils’ Activity: Pupils listen attentively, observe the demonstration, and copy notes from the board.
Learning Point: Pupils understand the definition of surface development.

Step 3: Applications of Surface Development

Time: 5 minutes
Teaching Skill: Listing/Examples
Teacher’s Activity: The teacher discusses various applications of surface development, relating them to industries like sheet metal work and packaging, and writes key examples on the board.
Pupils’ Activity: Pupils contribute examples and copy the applications from the board.
Learning Point: Pupils identify practical uses of surface development.

Step 4: Determination of True Lengths of Full Solids

Time: 8 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains what true length means and why it is important. Using a drawing board and instruments, the teacher demonstrates how to find the true length of an inclined line on a simple solid (e.g., a pyramid edge) using the revolution method.
Pupils’ Activity: Pupils observe the demonstration, ask questions, and try to follow the steps in their sketch pads.
Learning Point: Pupils grasp the concept of true length and one method of finding it on full solids.

Step 5: Determination of True Lengths of Truncated Solids

Time: 8 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher extends the concept to truncated solids, explaining that the same principles apply. The teacher demonstrates finding the true length of a line on a truncated cone or pyramid, emphasizing the need to project accurately.
Pupils’ Activity: Pupils pay attention to the teacher’s demonstration and make notes.
Learning Point: Pupils learn how to determine true lengths on truncated solids.

Step 6: Procedures for Accurate True Length Construction

Time: 7 minutes
Teaching Skill: Step-by-step instruction
Teacher’s Activity: The teacher outlines the general procedures for both the revolution and auxiliary view methods for accurate true length construction, writing the key steps on the board. The teacher clarifies any confusing steps.
Pupils’ Activity: Pupils copy the procedures from the board and ask for clarifications.
Learning Point: Pupils understand the systematic steps involved in true length determination.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

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

Define surface development.
Mention three applications of surface development.
Explain what is meant by the true length of a line.
State two methods used to determine true lengths in technical drawing.

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
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the importance of true length and surface development in various technical fields. The teacher assigns homework involving drawing simple developments or finding true lengths.
Pupils’ Activity: Pupils listen to the summary and copy the homework.
Learning Point: Pupils consolidate their understanding and are given tasks to practice.

Lesson Keywords

Development – The process of unfolding the surfaces of a 3D object onto a 2D plane.
True Length – The actual, unforeshortened length of a line.
Full Solid – A complete three-dimensional object without any cuts.
Truncated Solid – A solid that has been cut by a plane, resulting in a new surface.
Revolution Method – A technique to find true length by rotating a line until it is parallel to a projection plane.
Auxiliary View – An additional view used to show the true shape or length of inclined features.

Differentiation

For pupils who grasp concepts quickly, the teacher can provide more complex solids for true length determination and development. For pupils who need more support, the teacher will provide simplified examples and offer one-on-one guidance during practical exercises, focusing on basic definitions and simple true length problems.

Note for teachers using this lesson plan

Teachers should ensure they have adequate models and drawing instruments for demonstration. Practical exercises are essential for this topic, so allocating enough time for pupils to practice drawing true lengths and simple developments is important. Encourage pupils to use proper drawing techniques and instruments for accuracy.