Series of Transformations that Lead to Congruence

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Objective

SWBAT understand what happens when a series of translations, reflections, and/or rotations is performed on a figure.

Big Idea

Unlock students' creativity by pushing them to use different series of multiple transformations to create two congruent figures.

Lesson Author

Jeff Li MTP

New York, NY

Grade Level

Eighth grade

Subjects

Math

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.

MP1

Make sense of problems and persevere in solving them.

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

Student work samples - creativity!

8 - 15 student work sample compound transformations 3.pdf

8 - 15 student work sample compound transformations congruence 2.pdf

8 - 15 student work sample compound transformations congruence 4.pdf

8 - 15 student work sample compound transformations of congruence 1.pdf

For the huddle in this lesson, I ask kids to come up with multiple ways to demonstrate compound transformations, and it's really cool the kinds of things they come up with.

See the student samples for some ideas.

I push kids also to be VERY precise about their explanations... how much of a translation? In which direction? Reflection over what line, exactly? This is really, really important.