Illustrative Math Lesson

Stretching and Shrinking: Exploring Dilations on the Coordinate Plane

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8th GradeBTC Style / Thinking Classrooms40 min

Learning Objective

Students will apply dilations centered at the origin and at other points to figures on the coordinate plane, identify scale factors from pre-image/image pairs, and describe the properties preserved and changed under dilation.

Lesson Overview

Students progress from identifying scale factors to applying dilations centered at the origin, then at non-origin centers, building toward composing dilations with other transformations. Tasks change one variable at a time across five thin-sliced problems.

Materials

Vertical whiteboards or chart paper
Dry-erase markers (multiple colors)
Pencils and paper for scratch work
Basic calculator or phone calculator

Scaffolded Task Progression

1Task 1

Point

A

is at

(3, 5)

. A dilation centered at the origin has a scale factor of

2

. Find the image A'.

Then do the same for point

B = (1, 4)

and point

C = (0, 6)

.

What rule describes what happens to any point

(x, y)

under this dilation?

2Task 2

Triangle

P QR

has vertices

P = (2, 4)

Q = (6, 4)

R = (6, 8)

.

A dilation centered at the origin has scale factor

\frac{1}{2}

.

Find P', Q', R'. Plot the pre-image and image on the same coordinate grid. Is the image larger or smaller? By how much?

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