Application of Enlargement and Similarity

Grade 12 · Mathematics

Semester 2 | Period 5 | Week 29

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Subject: Mathematics

Semester: 2

Period: 5

Week: 29

WEEK 29

Class: Grade 12
Age: 17 years
Duration: 40 minutes × 5 periods
Subject: Mathematics
Topic: Application of Enlargement and Similarity
Focus: Applying enlargement to complex figures and solids, calculating areas and volumes under enlargement, and real-life applications.

 

SPECIFIC OBJECTIVES

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

  1. Apply enlargement to complex plane figures and solid shapes.
  2. Calculate the areas and volumes of images under enlargement.
  3. Use scale factors to determine side lengths, areas, and volumes.
  4. Solve word problems involving enlargement and similarity.
  5. Identify real-life applications of enlargement and similarity (architecture, engineering, geography, models, etc.).

 

INSTRUCTIONAL TECHNIQUES

  • Guided discovery
  • Practical demonstration
  • Question and answer
  • Group discussion
  • Problem-solving approach

 

INSTRUCTIONAL MATERIALS

  • Rulers, compasses, protractors, graph paper
  • Cardboard cutouts of 2-D and 3-D shapes
  • Whiteboard and markers
  • Models/maps/scale drawings

 

PERIOD 1 & 2: Enlargement of Complex Plane Figures

PRESENTATION

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Reviews basic enlargement and scale factor (positive and negative).

Students respond with definitions and examples.

Step 2 - Demonstration

Shows enlargement of polygons (rectangles, trapeziums, hexagons).

Students observe and take notes.

Step 3 - Application

Guides students in enlarging irregular shapes on graph paper.

Students perform enlargements step by step.

Step 4 - Practice

Assigns exercises on enlarging composite plane figures.

Students solve in groups and compare results.

NOTE ON BOARD:

  • Enlargement affects all dimensions by the scale factor k.
  • If scale factor = k,
    • Length ratio = k
    • Area ratio = k²

EVALUATION (5 Exercises):

  1. Define enlargement.
  2. State the relationship between linear scale factor and area.
  3. Enlarge a rectangle of sides 2 cm × 4 cm by scale factor 3.
  4. Find the new area.
  5. Enlarge a triangle with sides 3, 4, 5 by factor 2. Write new side lengths.

CLASSWORK (5 Questions):

  1. Enlarge a square of side 5 cm by scale factor 2. Find its new area.
  2. A triangle has area 12 cm². If enlarged by factor 3, find the new area.
  3. Enlarge a trapezium with bases 4 cm, 6 cm, height 5 cm by factor 2.
  4. If the scale factor = 4, what happens to the area?
  5. Draw a hexagon and enlarge it by scale factor ½.

HOMEWORK (5 Tasks):

  1. Enlarge a rectangle of sides 3 cm × 7 cm by factor 5. Find its new area.
  2. The area of a triangle is 20 cm². If enlarged by scale factor 2, what is the new area?
  3. Enlarge a trapezium with area 15 cm² by factor 3. Find new area.
  4. If k = ½, what is the relationship between original and enlarged areas?
  5. Draw and enlarge a kite with diagonals 4 cm and 6 cm by factor 2.

 

PERIOD 3: Enlargement of Solids (Volumes)

PRESENTATION

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Recalls area ratio = k². Extends to volume ratio = k³.

Students recall and note.

Step 2 - Demonstration

Uses cube/cuboid models to explain volume enlargement.

Students compare enlarged solid shapes.

Step 3 - Application

Shows calculations of volume ratios.

Students work through guided examples.

Step 4 - Practice

Assigns exercises with cubes, cones, and spheres.

Students calculate enlarged volumes.

NOTE ON BOARD:

  • Linear ratio = k
  • Area ratio = k²
  • Volume ratio = k³

EVALUATION (5 Exercises):

  1. If two cubes are similar with side ratio 2:3, find their volume ratio.
  2. A cube has volume 64 cm³. Enlarged by factor 2, find new volume.
  3. A cone of radius 3 cm and height 4 cm is enlarged by factor 3. Find new volume.
  4. If radius of a sphere doubles, what happens to its volume?
  5. A cuboid has dimensions 2 cm × 3 cm × 4 cm. Enlarge by factor 2. Find new volume.

CLASSWORK (5 Questions):

  1. A cube has side 5 cm. Enlarge by factor 3. Find the new volume.
  2. If linear scale factor = 4, what is volume ratio?
  3. Two cones are similar, heights 5 cm and 10 cm. Find ratio of volumes.
  4. A sphere has radius 7 cm. Enlarged by factor 2. Find new volume.
  5. If volume ratio = 1:8, what is the scale factor?

HOMEWORK (5 Tasks):

  1. A cuboid has volume 125 cm³. Enlarged by factor 2. Find new volume.
  2. Two spheres are similar with radii 2 cm and 6 cm. Find volume ratio.
  3. If area ratio = 9, what is linear scale factor?
  4. A cone has height 6 cm. Enlarged by factor ½. Find new height and volume ratio.
  5. If linear scale factor = 5, what are the ratios of area and volume?

 

PERIOD 4 & 5: Problem-Solving and Real-Life Applications

PRESENTATION

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Discusses practical uses of enlargement in real life.

Students mention maps, architecture, models.

Step 2 - Demonstration

Shows examples: scale maps, building plans, models of cars/aircraft.

Students observe.

Step 3 - Application

Guides problem-solving with word problems.

Students attempt and present solutions.

Step 4 - Practice

Assigns real-life application tasks.

Students solve and explain.

NOTE ON BOARD:

  • Applications of enlargement and similarity:
  1. Maps and scale drawings.
  2. Architecture and engineering.
  3. Models and prototypes.
  4. Photography and art.

EVALUATION (5 Exercises):

  1. Give two real-life uses of enlargement.
  2. A map scale is 1:1000. If distance on map = 2 cm, what is actual distance?
  3. A model of a car is built to scale 1:20. If car length = 4 m, what is model length?
  4. A building plan uses scale 1:100. If room length = 8 m, what is length on plan?
  5. A photograph enlargement has scale factor 3. If original height = 6 cm, find new height.

CLASSWORK (5 Questions):

  1. A model ship is made to scale 1:50. If actual ship length = 200 m, what is model length?
  2. A room is 5 m wide. On a plan drawn to 1:100, find its width.
  3. A globe is a scale model of Earth. If Earth’s radius = 6371 km and globe radius = 20 cm, what is the scale?
  4. A photo is enlarged by factor 4. Original area = 15 cm². Find enlarged area.
  5. A pyramid has height 9 cm. Enlarged by factor 2. Find new height and volume ratio.

HOMEWORK (5 Tasks):

  1. A toy aeroplane is made to scale 1:30. If real length = 15 m, find toy length.
  2. A map scale is 1:50000. If two towns are 6 cm apart on map, find actual distance.
  3. A model cube has volume 27 cm³. If enlarged by factor 3, find new volume.
  4. A plan of a house is drawn to scale 1:200. If plan length = 4 cm, what is real length?
  5. Write three real-life applications of enlargement and similarity.