Lesson Note on Intersection of Two Prisms for SS 2

Class: Senior Secondary School 2 (SS2 / SSS 2)
Term: First Term
Week: 9
Age: 16 years
Duration: 45 minutes
Subject: Technical Drawing
Curriculum Theme: Solid Geometry
Previous Lesson: Intersection of Two Cylinders.
Topic: INTERSECTION OF SOLID
Subject Matter: Two intersecting prisms (square prism, hexagonal prism)

Specific Objectives

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

Cognitive Domain:

• Define intersection of solids.
• State the methods used to determine the intersection of solids.
• Explain the steps involved in drawing the intersection of two prisms.

Affective Domain:

• Appreciate the importance of accuracy in technical drawing.
• Show interest in solving problems involving the intersection of solids.

Psychomotor Domain:

• Draw the intersection lines/curves of two intersecting prisms accurately.
• Use drawing instruments correctly to achieve precise drawings.

Social Domain:

• Collaborate with peers to solve drawing challenges.

Reference Materials

The following resources were used in planning this lesson:

• Senior Secondary Schools Education Curriculum
• State Unified Scheme of Work
• Akinola, O. (2018). Technical Drawing for Senior Secondary Schools. Evans Brothers (Nigeria Publishers) Limited.

Instructional Materials

The teacher will teach this lesson with the aid of:

• Models of intersecting prisms (square and hexagonal).
• Posters and charts illustrating the intersection of solids.
• Drawing instruments (set squares, compass, ruler, pencil, eraser).

Rationale for the Lesson

This lesson helps pupils understand how different solid shapes interact when they penetrate each other. It enables them to develop practical skills in accurately representing these interactions, which is important for various engineering and design applications.

Prerequisite/Previous Knowledge

Pupils should have prior knowledge of orthographic projection, drawing of basic solids like prisms, and the use of drawing instruments.

Lesson Content/Board Summary

INTERSECTION OF SOLID

Definition of Intersection of Solids

Intersection of solids occurs when two or more solid objects penetrate each other, resulting in common lines or curves on their surfaces. These common lines or curves represent the boundary where the solids meet.

Methods of Determining Intersection

The common methods used to determine the intersection of solids include:

• Line Method: This method involves drawing auxiliary lines on the surface of one solid and finding where these lines intersect the surface of the other solid.
• Cutting Plane Method: This method involves passing imaginary cutting planes through both solids to find common points of intersection. This method is often preferred for prisms and cylinders.

Intersection of Two Prisms (e.g., Square and Hexagonal Prisms)

The process of determining the intersection of two prisms involves finding the points where the faces of one prism cut into the faces of the other. The cutting plane method is effective for this, especially for prisms with flat faces.

General Steps for Drawing Intersection of Prisms using the Cutting Plane Method:

1. Step 1: Draw Orthographic Views. Draw the plan, front elevation, and if necessary, the end elevation of both prisms in their given relative positions. Ensure correct alignment and projections.
2. Step 2: Identify Penetration Area. Observe the drawn views to clearly identify the area where one prism penetrates the other.
3. Step 3: Apply Cutting Planes. Pass imaginary cutting planes through one of the prisms (typically the penetrating prism, or the one with simpler faces in the area of intersection). These planes should be parallel to the axis of the penetrating prism or perpendicular to the axis of the main prism, and pass through critical points like vertices or edges.
4. Step 4: Locate Intersection Points. For each cutting plane, determine the points where it cuts the faces of both prisms in all relevant views. Project these points accurately to the other views (front elevation, plan, end elevation).
5. Step 5: Connect Points. Connect the located intersection points in each view to form the lines or curves of intersection. Carefully determine which lines are visible and which are hidden based on the perspective.
6. Step 6: Darken Final Lines. Darken the visible outlines of the prisms and the lines of intersection to complete the drawing. Use dashed lines for hidden lines.

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 reviews their previous knowledge on orthographic projection and drawing of basic solids. The teacher then introduces the topic by showing models of two intersecting prisms.
Pupils’ Activity: Pupils respond to greetings, answer questions on previous knowledge, and observe the models.
Learning Point: Pupils recall previous knowledge and are introduced to the concept of intersecting solids.

Step 2: Presentation of Topic

Time: 5 minutes
Teaching Skill: Explanation
Teacher’s Activity: The teacher writes the topic “INTERSECTION OF SOLID” and the subject matter “Two intersecting prisms (square prism, hexagonal prism)” on the board and states the lesson objectives.
Pupils’ Activity: Pupils copy the topic and subject matter into their notebooks and pay attention to the objectives.
Learning Point: Pupils know the focus of the lesson and its expected outcomes.

Step 3: Explanation of Intersection of Solids

Time: 7 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher defines intersection of solids and explains the two main methods: the line method and the cutting plane method, using charts as visual aids.
Pupils’ Activity: Pupils listen attentively, ask questions for clarification, and take notes.
Learning Point: Pupils understand the definition and methods of determining intersection of solids.

Step 4: Demonstration of Drawing Intersection

Time: 10 minutes
Teaching Skill: Demonstration
Teacher’s Activity: The teacher demonstrates on the board or a large chart how to determine and draw the intersection of a square prism and a hexagonal prism using the cutting plane method, explaining each step carefully.
Pupils’ Activity: Pupils observe the demonstration, paying close attention to the steps and techniques.
Learning Point: Pupils learn the practical steps for drawing the intersection of prisms.

Step 5: Guided Practice

Time: 8 minutes
Teaching Skill: Supervision/Guidance
Teacher’s Activity: The teacher provides a drawing problem involving two intersecting prisms and guides pupils through the initial steps of drawing the orthographic views and setting up the cutting planes.
Pupils’ Activity: Pupils attempt to draw the initial views and apply the cutting planes under the teacher’s guidance.
Learning Point: Pupils begin to apply the learned steps with support.

Step 6: Individual Practice

Time: 5 minutes
Teaching Skill: Monitoring
Teacher’s Activity: The teacher moves around the classroom, observing pupils’ work and offering individual assistance and corrections as needed.
Pupils’ Activity: Pupils continue working independently on the drawing problem, aiming for accuracy.
Learning Point: Pupils practice drawing independently and receive personalized feedback.

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. Define intersection of solids.
2. State two methods used to determine the intersection of solids.
3. List the first three steps in drawing the intersection of two prisms.
4. Why is accuracy important when drawing the intersection of solids?

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 2 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key learning points of the lesson and assigns a related drawing problem as homework.
Pupils’ Activity: Pupils listen to the summary and copy the homework assignment.
Learning Point: Pupils consolidate their understanding and are given tasks for further practice.

Lesson Keywords

• Intersection – The point or line where two or more objects meet or cross.
• Solid – A three-dimensional object having length, width, and height.
• Prism – A solid object with two identical ends (bases) and flat sides.
• Orthographic Projection – A method of representing three-dimensional objects in two dimensions by projecting views onto perpendicular planes.
• Cutting Plane Method – A technique used in technical drawing to determine the lines of intersection between solids by passing imaginary planes through them.

Differentiation

For pupils who grasp the concept quickly, the teacher will provide more complex intersection problems (e.g., prisms intersecting at an angle). For those who need more support, the teacher will provide simplified step-by-step guides and additional one-on-one assistance during practice sessions.

Note for teachers using this lesson plan

Ensure that pupils have a strong foundation in orthographic projection before beginning this lesson. Emphasize the importance of accurate measurement and projection lines. Use physical models to help pupils visualize the intersection before attempting to draw it. Encourage pupils to work neatly and systematically.