Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: Second Term
Week: 5
Age: 15 years
Duration: 45 minutes
Subject: Technical Drawing
Curriculum Theme: Technical Drawing
Previous Lesson: Enlargement and Reduction: Concept and Applications.
Topic: ENLARGEMENT AND REDUCTION
Subject Matter: enlargement of regular plane figures, reduction of regular plane figures, enlargement of irregular plane figures, reduction of irregular plane figures, applying given ratios to triangles quadrilaterals and polygons

Specific Objectives

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

Cognitive Domain:

Define enlargement and reduction.
State the methods used for enlargement and reduction.
Explain the steps for enlarging and reducing regular and irregular plane figures.
Apply given ratios to enlarge or reduce triangles, quadrilaterals, and polygons.

Affective Domain:

Appreciate the importance of scale in technical drawing.
Show interest in performing accurate geometric constructions.
Follow instructions carefully when enlarging or reducing figures.

Psychomotor Domain:

Accurately use drawing instruments to enlarge given figures to a specified ratio.
Accurately use drawing instruments to reduce given figures to a specified ratio.
Construct enlarged and reduced triangles, quadrilaterals, and polygons.

Work cooperatively with peers during practical exercises.
Share drawing techniques and solutions with classmates.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum
State Unified Scheme of Work
Technical Drawing for Senior Secondary Schools by F.N. Okoro

Instructional Materials

The teacher will teach this lesson with the aid of:

Drawing board
Tee square
Set squares
Compasses
Pencils (HB, 2H)
Ruler
Charts showing examples of enlarged and reduced figures
Posters illustrating steps for enlargement and reduction
Models of objects with different scales

Rationale for the Lesson

This lesson helps pupils understand how to change the size of objects while maintaining their proportions, which is important in various fields like engineering, architecture, and cartography. It enables pupils to accurately represent large or small objects on paper according to specific scales.

Prerequisite/Previous Knowledge

Pupils are expected to have prior knowledge of basic geometric constructions, properties of plane figures (triangles, quadrilaterals, polygons), and the use of drawing instruments.

Lesson Content/Board Summary

ENLARGEMENT AND REDUCTION

1. Definition of Enlargement

Enlargement is the process of drawing a figure larger than its original size while maintaining its original shape and proportions. It involves scaling up the dimensions by a given ratio.

2. Definition of Reduction

Reduction is the process of drawing a figure smaller than its original size while maintaining its original shape and proportions. It involves scaling down the dimensions by a given ratio.

3. Methods of Enlargement and Reduction

The following are common methods for enlargement and reduction:

Radial Line Method (Method of Similar Triangles): This method uses a reference point (pole) and radial lines drawn from the pole through the vertices of the original figure. The enlarged or reduced figure is then constructed along these radial lines at the specified ratio.
Grid Method (Method of Squares): This method involves superimposing a grid of squares over the original figure. An enlarged or reduced grid is then drawn, and the figure is copied square by square into the new grid.

4. Steps for Enlargement of Regular Plane Figures (Radial Line Method)

To enlarge a regular plane figure (e.g., triangle, square, pentagon) using the radial line method:

Choose a convenient pole (P) outside or inside the figure.
Draw radial lines from the pole through each vertex of the original figure (A, B, C…).
Measure the distance from the pole to each vertex (PA, PB, PC…).
Multiply these distances by the enlargement ratio (e.g., if ratio is 2:1, multiply by 2).
Mark the new points (A’, B’, C’…) along the radial lines at the calculated distances from the pole.
Join the new points to form the enlarged figure (A’B’C’…).

5. Steps for Reduction of Regular Plane Figures (Radial Line Method)

To reduce a regular plane figure using the radial line method:

Choose a convenient pole (P) outside or inside the figure.
Draw radial lines from the pole through each vertex of the original figure (A, B, C…).
Measure the distance from the pole to each vertex (PA, PB, PC…).
Divide these distances by the reduction ratio (e.g., if ratio is 1:2, divide by 2).
Mark the new points (A’, B’, C’…) along the radial lines at the calculated distances from the pole.
Join the new points to form the reduced figure (A’B’C’…).

6. Enlargement and Reduction of Irregular Plane Figures

Irregular plane figures can be enlarged or reduced using both the radial line method and the grid method. The principles remain the same:

For the radial line method, all key points (vertices, curve control points) of the irregular figure are treated as vertices.
For the grid method, the figure is accurately copied from square to square of the original grid onto the new scaled grid.

7. Applying Given Ratios to Triangles, Quadrilaterals, and Polygons

A ratio indicates the scale factor for enlargement or reduction.

Enlargement Ratio: If the ratio is given as X:Y where X > Y (e.g., 2:1, 3:2), the figure will be enlarged by a factor of X/Y.
Reduction Ratio: If the ratio is given as X:Y where X < Y (e.g., 1:2, 2:3), the figure will be reduced by a factor of X/Y.
The ratio dictates how much each dimension of the original figure is multiplied or divided by to obtain the new figure.

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 introduces the topic by showing pupils various objects or images, some of which are scaled versions of others (e.g., a map and a real area, a small model car and a real car, a photograph and its original subject). The teacher asks pupils to observe the differences in size and how the shapes remain the same. The teacher then relates this concept to technical drawing.
Pupils’ Activity: Pupils observe the examples, respond to questions about size differences, and identify that shapes remain constant.
Learning Point: Pupils understand the concept of changing object size while maintaining shape and proportion.

Step 2: Presentation of Enlargement

Time: 10 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher defines enlargement and explains its purpose. Using a chart or whiteboard, the teacher demonstrates the radial line method for enlarging a simple regular figure (e.g., a triangle) by a given ratio (e.g., 2:1). The teacher clearly shows how to choose a pole, draw radial lines, measure distances, and mark new points.
Pupils’ Activity: Pupils listen attentively, observe the demonstration, and ask questions for clarification.
Learning Point: Pupils understand the definition of enlargement and the steps involved in the radial line method.

Step 3: Pupils Practice Enlargement

Time: 5 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher gives pupils a simple triangle on a handout and instructs them to enlarge it by a ratio of 1.5:1 using the radial line method. The teacher moves around the class, providing guidance and correcting errors.
Pupils’ Activity: Pupils attempt to enlarge the given triangle on their drawing sheets, applying the steps demonstrated by the teacher.
Learning Point: Pupils practice and reinforce their understanding of the enlargement process.

Step 4: Presentation of Reduction

Time: 10 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher defines reduction and explains its purpose. The teacher then demonstrates the radial line method for reducing a simple regular figure (e.g., a square) by a given ratio (e.g., 1:2), emphasizing the division of distances. The teacher also briefly introduces the grid method for reduction, especially useful for irregular figures.
Pupils’ Activity: Pupils listen and observe the demonstration of reduction methods, noting the differences from enlargement.
Learning Point: Pupils understand the definition of reduction and the steps for its execution using the radial line and grid methods.

Step 5: Pupils Practice Reduction

Time: 5 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher provides pupils with a simple quadrilateral and instructs them to reduce it by a ratio of 1:3 using the radial line method. The teacher continues to supervise and assist pupils.
Pupils’ Activity: Pupils apply the reduction steps to construct the smaller quadrilateral on their drawing sheets.
Learning Point: Pupils gain practical experience in reducing plane figures.

Step 6: Application of Ratios

Time: 5 minutes
Teaching Skill: Explanation
Teacher’s Activity: The teacher explains how ratios are directly applied to determine the scale factor for enlargement or reduction. The teacher provides examples of how to interpret ratios like 2:1, 1:2, 3:2, and 2:3 for different figures (triangles, quadrilaterals, polygons) and how this affects the measurements.
Pupils’ Activity: Pupils listen and take notes on how to correctly apply given ratios to their constructions.
Learning Point: Pupils understand the direct relationship between given ratios and the scale factor for constructions.

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 enlargement and reduction in technical drawing.
Mention two methods used for enlarging or reducing plane figures.
Explain the main difference in applying a ratio for enlargement versus reduction.
If a figure is to be enlarged by a ratio of 3:1, what does this mean for its dimensions?

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 points of the lesson, reiterating the importance of accuracy in using drawing instruments and applying ratios. The teacher assigns homework which includes enlarging and reducing various figures to different ratios.
Pupils’ Activity: Pupils listen to the summary and copy down the homework assignment.
Learning Point: Pupils consolidate their understanding and prepare for further practice.

Lesson Keywords

Enlargement – Drawing a figure larger than its original size while maintaining its shape.
Reduction – Drawing a figure smaller than its original size while maintaining its shape.
Ratio – A comparison of two quantities, used to determine the scale factor for enlargement or reduction.
Scale – The ratio of the length in a drawing or model to the length of the actual object.
Radial Line Method – A geometric method for enlargement or reduction using a pole and radiating lines.
Grid Method – A method for enlargement or reduction involving copying a figure onto a scaled grid.

Differentiation

For pupils who grasp the concepts quickly, the teacher can provide more complex irregular figures or challenge them to use both the radial line and grid methods on the same figure. For pupils who are struggling, the teacher can provide simpler regular figures with whole number ratios and offer more one-on-one guidance and step-by-step instructions.

Note for teachers using this lesson plan

Ensure that pupils have a clear understanding of ratios before starting the practical exercises. Emphasize accuracy in measurement and drawing lines. Encourage pupils to use light construction lines initially and darken the final figure. Practical demonstration by the teacher is essential for this topic.