Lesson 2

Transformations as Functions

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Lesson Narrative

In this lesson students use coordinate transformation notation such as \((x,y) \rightarrow (x+1, y+2)\). 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 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, they transform a figure with no scaffolding. Throughout the lesson, students generate hypotheses around 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

Teacher Facing

  • 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

  • Let’s compare transformations to functions.

Learning Targets

Student Facing

  • I can use coordinate transformation notation to take points in the plane as inputs and give other points as outputs.

CCSS Standards

Addressing

Building Towards

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