Dilations 1

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Objective

SWBAT understand dilations with the origin as the center of dilation.

Big Idea

Biggie or Smalls? Set the foundation for students' understanding of dilations, and use Geogebra to illustrate.

Lesson Author

Jeff Li MTP

New York, NY

Grade Level

Eighth grade

Subjects

Math

dilation (stretches and shrinks)

Geometry

Standards

8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations:

8.G.A.1a

Lines are taken to lines, and line segments to line segments of the same length.

8.G.A.1b

Angles are taken to angles of the same measure.

8.G.A.1c

Parallel lines are taken to parallel lines

8.G.A.2

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

8.G.A.3

Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.

8.G.A.4

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

MP2

Reason abstractly and quantitatively.

MP6

Attend to precision.

Warm Up

10 minutes

Each day, students complete a warm-up that usually consists of spiraling the previous day's material, in addition to older material. Warm-up problems also sometimes extend lessons that students have encountered before to more unfamiliar contexts.

For a video narrative about how I structure each lesson, and how the warm-up fits in, click here.

Play of the Day

40 minutes

Huddle

10 minutes

For the huddle in this lesson, I like to review #4, since it has a scale factor that is not a whole number. It gets kids to move away from just their instincts (double or triple is easy) to apply the idea of image over original, which yields a scale factor of 3/2. It's also 1.5 times larger, which is a relatively simple concept for kids to master. This sets the stage for even more fractions as scale factors.