In this lesson, students use coordinate transformation notation such as . This notation supports the understanding of transformations as functions while also providing a novel context to have students examine rigid transformations, similarity transformations, and transformations that do not fit any vocabulary that students have learned. Students compute the result of transformation rules starting with one point at a time. Then they complete a table of inputs and outputs. In the final activity, students transform a figure using function rules. Throughout the lesson, students generate hypotheses about how to predict the outcome of a rule before trying it on a figure.
Students reason abstractly (MP2) as they translate back and forth between concrete diagrams and abstract rules.
Technology isn’t required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.
Learning Goals
Describe (using words and other representations) transformations as functions that take points in the plane as inputs and give other points as outputs.
Student-Facing Goal
Let’s compare transformations to functions.
Student-Facing Targets
I can use coordinate transformation notation to take points in the plane as inputs and give other points as outputs.
Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
