Lesson 2: Identify, create, describe sequence and effect of transformations (rotations, reflections, dialations, translations)
Duration of Days: 7
Lesson Objective
Students will be able to verify the properties of rotations, reflections, and translations, and describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
How do rigid transformations (translations, reflections, rotations) maintain the size and shape of a figure?
How can we use coordinates to describe the effect of a sequence of transformations, including dilations?
What is the difference between congruence (rigid transformations) and similarity (including dilations)?
Translation: A rigid transformation that slides a figure up, down, left, right, or a combination.
Reflection: A rigid transformation that flips a figure over a line of reflection.
Rotation: A rigid transformation that turns a figure clockwise or counterclockwise around a specified point.
Dilation: A transformation that makes a figure smaller or larger by a specific scale factor while maintaining its proportions.
Pre-image and Image: The original figure and the resulting figure after a transformation.
8.G.A.1a-c: Verify experimentally the properties of rotations, reflections, and translations.
8.G.A.2: Understand congruence through a sequence of rigid transformations.
8.G.A.3: Describe the effect of transformations on 2D figures using coordinates.
8.G.A.4: Understand similarity through a sequence of transformations, including dilations.
Description: Students explore transformations on the coordinate plane.
Purpose: To enable students to move beyond basic identification of shapes to proving congruence and similarity using mathematical rules and transformations.
DOK Level: Level 3 (Strategic Thinking) – Students describe sequences of transformations that exhibit congruence or similarity between figures.
Dilation Misconception: Students may believe dilations only enlarge figures; provide examples of reductions as well.
Negative Exponents: Confusing negative exponents in scale factors with making a figure negative rather than smaller.
Scaffolding: Provide tracing or parchment paper and mirrors for physical experimentation.
Visual Aids: Use Vocabulary Cards with visual representations of each transformation.
Quiz
Exit Ticket
Student Work