Enlargement - Movements and Perspective

Grade 12 · Mathematics

Semester 2 | Period 5 | Week 27

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Subject: Mathematics

Semester: 2

Period: 5

Week: 27

WEEK 27

Class: Grade 12
Age: 17 years
Duration: 40 minutes × 5 periods
Subject: Mathematics
Topic: Enlargement – Movements and Perspective
Focus: Movements combined with enlargement, perspective drawing using enlargement/reduction, identifying scale drawings, and practical exercises.

SPECIFIC OBJECTIVES

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

  1. Describe and perform enlargement combined with basic movements (translation, reflection, rotation).
  2. Apply enlargement and reduction in perspective drawing.
  3. Identify and interpret real-life scale drawings (e.g., maps, blueprints, models).
  4. Perform practical drawing exercises involving movement and enlargement.
  5. Recognize the role of enlargement and reduction in technical and artistic drawings.

 

INSTRUCTIONAL TECHNIQUES

  • Guided demonstration
  • Question and answer
  • Group work and collaboration
  • Hands-on practical drawing
  • Class discussion

 

INSTRUCTIONAL MATERIALS

  • Graph paper and plain drawing sheets
  • Ruler, compass, protractor, mathematical set
  • Whiteboard and markers
  • Models and pictures of scale drawings (maps, architectural sketches, perspective drawings)

 

PERIOD 1 & 2: Movements Combined with Enlargement

PRESENTATION

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Recalls the concept of enlargement and scale factors.

Students revise previous week’s work.

Step 2 - Explanation

Explains that enlargement can be combined with other transformations (translation, reflection, rotation).

Students listen attentively and take notes.

Step 3 - Demonstration

Shows how to enlarge a triangle by scale factor 2, then translate or reflect it.

Students follow teacher’s worked examples.

Step 4 - Practice

Gives guided tasks where students enlarge and then move figures.

Students work on graph paper.

NOTE ON BOARD:

  • Enlarged shapes can be:
  1. Translated (moved)
  2. Reflected (flipped)
  3. Rotated (turned)
  • Combination of transformations produces images of same shape but different positions.

EVALUATION (5 Exercises):

  1. Define movement in transformation.
  2. What transformation is performed when a shape is flipped across a line?
  3. Enlarge triangle (0,0), (1,0), (0,1) by scale factor 2, then translate it 3 units right.
  4. Enlarge square (1,1), (1,2), (2,2), (2,1) by scale factor –2 and reflect it in the y-axis.
  5. Explain the difference between enlargement and translation.

CLASSWORK (5 Questions):

  1. Enlarge triangle (0,0), (1,0), (0,2) by scale factor 3, then rotate it 90° about the origin.
  2. Enlarge square (0,0), (0,1), (1,1), (1,0) by scale factor 2, then translate 2 units up.
  3. Enlarge rectangle (0,0), (0,3), (2,3), (2,0) by scale factor 0.5, then reflect in x-axis.
  4. What is the result of combining enlargement with reflection?
  5. Distinguish between reflection and rotation.

ASSIGNMENT (5 Tasks):

  1. Enlarge triangle (–1,0), (–2,0), (–1,2) by scale factor 2, then translate 3 units down.
  2. Enlarge square (0,0), (0,2), (2,2), (2,0) by scale factor –1, then rotate 180° about the origin.
  3. Define enlargement, reflection, and rotation.
  4. State one real-life application of enlargement combined with movements.
  5. Draw and enlarge a pentagon, then reflect it in y-axis.

 

PERIOD 3 & 4: Perspective Drawing Using Enlargement/Reduction

PRESENTATION

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces perspective drawing as a way of showing 3D objects on 2D surfaces.

Students observe examples of perspective drawings.

Step 2 - Explanation

Explains how enlargement and reduction are used to create depth (near objects appear larger, far objects smaller).

Students listen attentively.

Step 3 - Demonstration

Demonstrates one-point and two-point perspective drawings using enlargement/reduction.

Students follow teacher’s step-by-step process.

Step 4 - Practice

Guides students to draw simple perspective diagrams of cubes and roads.

Students practice perspective drawings in groups.

NOTE ON BOARD:

  • Perspective Drawing: Method of representing 3D on 2D.
  • Enlargement = objects closer.
  • Reduction = objects farther.

EVALUATION (5 Exercises):

  1. Define perspective drawing.
  2. Why do objects appear smaller when farther away?
  3. Draw a simple one-point perspective of a cube.
  4. What role does scale factor play in perspective drawing?
  5. State one difference between one-point and two-point perspective.

CLASSWORK (5 Questions):

  1. Draw a road in one-point perspective (narrower as it moves away).
  2. Sketch a cube in two-point perspective.
  3. Show how enlargement and reduction apply in perspective drawing.
  4. Draw a railway track in perspective view.
  5. What is vanishing point in perspective drawing?

ASSIGNMENT (5 Tasks):

  1. Draw a building in one-point perspective.
  2. Draw a cube in two-point perspective.
  3. State one similarity between enlargement and perspective drawing.
  4. Explain why maps and photographs use reduction.
  5. Draw three objects showing perspective: a table, a box, and a ball.

 

PERIOD 5: Identifying Scale Drawings & Practical Exercises

PRESENTATION

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Explains concept of scale drawings in maps, blueprints, and models.

Students give real-life examples.

Step 2 - Demonstration

Shows examples of scale drawings (map of city, building plan).

Students observe carefully.

Step 3 - Practice

Guides students in drawing a simple room plan using given scale (e.g., 1 cm = 2 m).

Students work in pairs on practical drawing.

Step 4 - Discussion

Discusses applications of scale drawings in engineering and architecture.

Students participate actively.

NOTE ON BOARD:

  • Scale Drawing = representation of objects with reduced or enlarged measurements.
  • Example: Map scale 1:100 means 1 cm = 100 cm (1 m).

EVALUATION (5 Exercises):

  1. Define scale drawing.
  2. A line 2 cm long on a scale drawing represents 4 m. What is the scale?
  3. Why are scale drawings important in architecture?
  4. What is the difference between enlargement and scale drawing?
  5. Identify two real-life uses of scale drawings.

CLASSWORK (5 Questions):

  1. A map scale is 1:50,000. Find the actual distance represented by 5 cm.
  2. Draw a rectangle 2 cm × 3 cm to represent 4 m × 6 m at scale 1:200.
  3. Convert a scale of 1:20 to actual dimensions if the drawing shows 5 cm.
  4. A school field measures 120 m × 80 m. Represent it on a scale 1:4000.
  5. Define reduction in scale drawing.

ASSIGNMENT (5 Tasks):

  1. Draw a simple floor plan of your classroom using scale 1 cm = 1 m.
  2. A house plan has a wall of 10 cm on the paper, representing 20 m. Find the scale.
  3. State three careers where scale drawings are essential.
  4. Why is accuracy important in scale drawings?
  5. Sketch a tree in perspective view and label its enlarged and reduced parts.