Geometric Transformations: Enlargement

Active learning helps students visualize how shapes change under enlargement, making abstract scale factor ideas concrete. Working with grids, transparencies, and vectors lets students test their own predictions and correct mistakes in real time.

• Secondary 4
• Mathematics
• 4 activities
• 25 min–45 min

Learning Objectives

1. Calculate the coordinates of the image of a point or shape after an enlargement, given the center of enlargement and scale factor.
2. Construct the image of a plane shape under an enlargement, using a given center and scale factor, including fractional and negative scale factors.
3. Analyze the effect of the scale factor and the position of the center of enlargement on the size and position of the resulting image.
4. Compare and contrast the properties of an object and its image under an enlargement, identifying corresponding points and lengths.
5. Explain the geometric relationship between the center of enlargement, the object, and the image using vector notation or geometric reasoning.

Experiential Learning

⏱ 30 min·Pairs

Pair Construction: Grid Paper Enlargements

Pairs select a simple shape and center on dot paper, then use rulers to mark image points by multiplying distances by k. They verify similarity by measuring sides and angles. Switch roles for a second enlargement with negative k.

Prepare & details

Analyze how the scale factor and center of enlargement affect the size and position of the image.

Facilitation Tip: During Pair Construction, circulate to ensure students measure distances from the center to original vertices before scaling to the image.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Experiential Learning

⏱ 45 min·Small Groups

Small Groups: Transparency Overlays

Groups trace shapes onto transparencies, mark centers, and enlarge by sliding and scaling over base sheets. They test fractional k by adjusting transparencies and note position shifts. Present findings to class.

Prepare & details

Differentiate between positive and negative scale factors in terms of their effect on the image.

Facilitation Tip: During Transparency Overlays, remind groups to verify equal scaling by measuring corresponding sides on the overlay and original.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Experiential Learning

⏱ 35 min·Whole Class

Whole Class: Digital Demo Relay

Project GeoGebra with a shape; students call out centers and k values for teacher to input, predicting image changes. Class votes on predictions, then discusses matches. Follow with individual digital practice.

Prepare & details

Construct an enlargement of a shape given a center and a scale factor, including fractional scale factors.

Facilitation Tip: During Digital Demo Relay, pause after each volunteer to ask the class to predict the next step before revealing the solution.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Experiential Learning

⏱ 25 min·Individual

Individual: Vector Method Challenge

Students plot shapes on axes, express vertices as vectors from center, multiply by k, and plot images. They describe transformations in vector terms and check with compasses.

Prepare & details

Analyze how the scale factor and center of enlargement affect the size and position of the image.

Facilitation Tip: During Vector Method Challenge, emphasize vector direction and magnitude by having students label each vector with its scale factor component.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Teaching This Topic

Teach enlargement by starting with hands-on constructions so students experience the physical meaning of scale factor. Encourage students to verbalize each step as they work, which builds precision in describing transformations. Avoid rushing to formulas; let students discover that negative scale factors combine rotation and scaling through repeated practice.

What to Expect

Students will confidently describe size and position changes, apply scale factors accurately for any k value, and justify their constructions with precise measurements and vocabulary. Success looks like clear sketches with labeled coordinates and scale factors, supported by group discussions.

Watch Out for These Misconceptions

Common Misconception

During Pair Construction: watch for students assuming enlargement always makes shapes larger.

What to Teach Instead

Have pairs compare their shapes for k=0.5 and k=2 on the same grid, then measure side lengths to confirm reduction and enlargement before moving to negative k.

Common Misconception

During Transparency Overlays: watch for students missing the rotation effect of negative k.

What to Teach Instead

Ask each group to rotate their transparency 180 degrees around the center and observe how the image aligns with a negative k construction to make the rotation visible.

Common Misconception

During Pair Construction: watch for students placing the image center incorrectly when the center is outside the original shape.

What to Teach Instead

Require students to draw rays from the center through each vertex and mark the image vertex along the same ray at the scaled distance before sketching the final image.

Assessment Ideas

Quick Check

After Grid Paper Enlargements, collect student sketches and calculations for a shape enlarged by k=2 or k=0.5. Look for accurate coordinate shifts and proportional side lengths in their final images.

Exit Ticket

After Transparency Overlays, give students a diagram with an image and original shape. Ask them to write the scale factor and explain how they used corresponding points to find it, then identify one pair of matching vertices.

Peer Assessment

During Vector Method Challenge, have partners trade constructions and verify each other’s work by measuring two corresponding sides and the distance between the center and a vertex in both shapes.

Extensions & Scaffolding

• Challenge students who finish early to create a complex shape with holes and apply a fractional negative scale factor, then describe the transformation in detail.
• For students who struggle, provide pre-labeled grids with the center marked and a scale factor written as a fraction to simplify calculations.
• Deeper exploration: Have students research how architects use enlargement in perspective drawing and present one real-world example to the class.

Key Vocabulary

Center of Enlargement	A fixed point from which all distances to the object are scaled by the scale factor to produce the image.
Scale Factor (k)	The ratio of the distance from the center of enlargement to a point on the image to the distance from the center of enlargement to the corresponding point on the object. It determines the size change.
Image	The resulting shape after a geometric transformation, in this case, an enlargement.
Object	The original shape before the geometric transformation is applied.
Corresponding Points	Points on the object and its image that are related by the enlargement transformation; they lie on the same ray from the center of enlargement.