Enlargement - Basics

Grade 12 · Mathematics

Semester 2 | Period 5 | Week 26

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Subject: Mathematics

Semester: 2

Period: 5

Week: 26

WEEK 26
Class: Grade 12
Age: 17 years
Duration: 40 minutes × 5 periods
Subject: Mathematics
Topic: Enlargement – Basics
Focus: Concept of enlargement, magnification and reduction, positive and negative scale factors, and performing enlargement on plane shapes.

SPECIFIC OBJECTIVES

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

  1. Define enlargement as a type of transformation.
  2. Differentiate between magnification and reduction.
  3. Explain positive and negative scale factors.
  4. Perform enlargements of plane shapes using given scale factors.
  5. Identify properties of figures under enlargement.

 

INSTRUCTIONAL TECHNIQUES

  • Question and Answer
  • Guided Demonstration
  • Discussion
  • Group Work
  • Practice Exercises

 

INSTRUCTIONAL MATERIALS

  • Graph board and graph paper
  • Mathematical sets (compass, ruler, protractor)
  • Whiteboard and markers
  • Pre-drawn plane figures

 

PERIOD 1 & 2: Concept of Enlargement & Scale Factors

PRESENTATION

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces enlargement as a transformation that produces an image similar to the object but larger or smaller.

Students listen attentively and ask questions.

Step 2 - Magnification & Reduction

Explains that magnification occurs when the scale factor > 1, and reduction occurs when the scale factor is between 0 and 1.

Students write down notes and give examples.

Step 3 - Scale Factors

Explains positive scale factor (image on same side as object) and negative scale factor (image on opposite side of center).

Students observe diagrams and practice examples.

Step 4 - Practice

Demonstrates examples of enlargement on the board using coordinates and a given scale factor.

Students plot and enlarge figures on graph paper.

NOTE ON BOARD:

  • Enlargement: Transformation that increases/reduces size of an object.
  • Scale factor (k):
    • If k>1: magnification.
    • If 0<k<1: reduction.
    • If k<0: image is on opposite side of center.

 

EVALUATION (5 Exercises):

  1. Define enlargement.
  2. What happens when the scale factor is greater than 1?
  3. What is the meaning of a negative scale factor?
  4. State two properties preserved under enlargement.
  5. Distinguish between magnification and reduction.

CLASSWORK (5 Questions):

  1. State whether the enlargement is a magnification or reduction if the scale factor is:
    3, b. 0.5.
  2. What happens to a figure enlarged by a scale factor of –2?
  3. Write two differences between positive and negative scale factors.
  4. If a triangle with sides 3 cm, 4 cm, 5 cm is enlarged by a scale factor of 2, find the new lengths.
  5. A square of side 5 cm is enlarged by a scale factor of 0.5. What is the side length of the image?

ASSIGNMENT (5 Tasks):

  1. Define scale factor.
  2. A rectangle 2 cm × 5 cm is enlarged by scale factor 3. Find the new dimensions.
  3. What type of enlargement is produced by a scale factor of 0.25?
  4. A triangle is enlarged by scale factor –2. State the orientation of the image compared to the object.
  5. State one similarity and one difference between magnification and reduction.

 

PERIOD 3 & 4: Performing Enlargement on Plane Figures

PRESENTATION

Step

Teacher’s Activity

Student’s Activity

Step 1 - Revision

Reviews concept of scale factors.

Students recall and answer questions.

Step 2 - Demonstration

Shows how to enlarge a triangle with a given center and scale factor using graph paper.

Students follow step-by-step.

Step 3 - Practice

Guides students to enlarge quadrilaterals and polygons with different scale factors.

Students practice enlarging shapes individually and in groups.

Step 4 - Discussion

Discusses real-life applications of enlargement (e.g., maps, photographs, architectural drawings).

Students give more examples from daily life.

NOTE ON BOARD:

  • Enlargement requires:
  1. The object
  2. The center of enlargement
  3. The scale factor

 

EVALUATION (5 Exercises):

  1. What three things must be known to perform enlargement?
  2. Enlarge triangle (0,0), (1,0), (0,1) by scale factor 2 about the origin.
  3. Enlarge square (0,0), (0,2), (2,2), (2,0) by scale factor 3 about the origin.
  4. What happens when scale factor is 1?
  5. Why is enlargement considered a similarity transformation?

CLASSWORK (5 Questions):

  1. Enlarge triangle (0,0), (2,0), (1,1) by scale factor 2 about the origin.
  2. Enlarge square (1,1), (1,2), (2,2), (2,1) by scale factor 3 about the origin.
  3. Enlarge rectangle (0,0), (0,1), (2,1), (2,0) by scale factor 0.5 about the origin.
  4. Enlarge triangle (–1,0), (–2,1), (–1,2) by scale factor 2 about the origin.
  5. What is the image of point (2,3) under enlargement by scale factor –2 about the origin?

ASSIGNMENT (5 Tasks):

  1. Enlarge triangle (0,0), (1,0), (0,2) by scale factor 4 about the origin.
  2. Enlarge square (–1,–1), (–1,1), (1,1), (1,–1) by scale factor 0.5.
  3. What is the image of point (–2,4) under enlargement by scale factor –3?
  4. State one property preserved and one not preserved under enlargement.
  5. Enlarge rectangle (0,0), (0,2), (3,2), (3,0) by scale factor 2 about the origin.

 

PERIOD 5: Consolidation and Application

PRESENTATION

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Reviews all concepts of enlargement.

Students summarize and ask questions.

Step 2 - Mixed Problems

Provides problems involving both positive and negative scale factors.

Students solve individually and in groups.

Step 3 - Correction & Discussion

Discusses solutions and emphasizes key points.

Students correct mistakes and share findings.

NOTE ON BOARD:

  • Enlargement may produce a magnified or reduced image.
  • Enlargement preserves shape but changes size.
  • Negative scale factor places the image on the opposite side of the center.

 

EVALUATION (5 Exercises):

  1. What is the effect of enlarging with scale factor 0?
  2. Enlarge (2,1) by scale factor –2 about the origin.
  3. Enlarge triangle (0,0), (1,0), (0,1) by scale factor 1. What do you observe?
  4. State one real-life application of enlargement.
  5. Differentiate between similarity and congruence.

CLASSWORK (5 Questions):

  1. Enlarge square (0,0), (0,1), (1,1), (1,0) by scale factor 5 about the origin.
  2. Enlarge point (3,–2) by scale factor –3.
  3. Enlarge rectangle (0,0), (0,2), (4,2), (4,0) by scale factor 0.25.
  4. What happens when the scale factor is negative?
  5. Enlarge triangle (–1,–1), (–2,–1), (–1,–3) by scale factor 2 about the origin.

ASSIGNMENT (5 Tasks):

  1. Enlarge triangle (0,0), (1,2), (2,0) by scale factor –2 about the origin.
  2. Enlarge square (0,0), (0,2), (2,2), (2,0) by scale factor 4.
  3. A rectangle is 2 cm × 3 cm. If enlarged by scale factor 5, what are the new dimensions?
  4. What is the image of point (–3,4) under enlargement by scale factor –1?
  5. Enlarge trapezium (0,0), (1,2), (3,2), (4,0) by scale factor 2 about the origin.