Lesson 3:
Standards Addressed:
MCC9-12.G.CO.2
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).
MCC9-12.G.CO.5
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.
Essential Question: How can we represent transformations of geometric objects in a graph using functions?
This lesson is structured into three parts, a launch activity used to engage the students in the lesson, the work period in which students will be
collaboratively working to discover concepts, and a closing in which students will share their thoughts, findings, and understanding of the concepts.
Launch: Working with their collaborative pair, students will complete a launch activity in which they will be shown a geometric object
on a graph and be asked to complete three transformations onto the object, a rotation, a reflection, and a translation. The class will discuss different
ways in which these can be represented.
Work Period: Working with their collaborative pair, students will investigate the concept of representing translations using functions. Students will sign onto the website www.textbooktactics.comand watch the following video tutorials: transformational geometry – rotations, transformational geometry – translations,
and transformational geometry –reflections. Students will learn and become familiar with the concept of transformational functions through these videos.
Once complete, students will use their knowledge of transformations and functions to transform a polygon in the coordinate grid. Students will need to perform the following transformations: reflection across the x and y-axes, reflections across the line y=x, 90 degree and 180 degree rotation through the origin, horizontal and vertical translation, diagonal translation. Each transformation will need to be represented both graphically and by writing a function.
Summary: To summarize the lesson, a geometric object and a transformation will be shown. A whole class discussion will be held on what
transformation has occurred, and how to represent the transformation using functions.
Engage: Students will engage in the lesson while being challenged to create multiple ways of representing a transformation.
Explore: Students will explore the concepts of transformations on the coordinate grid using the website www.textbooktactics.com.
Explain: Students will need to explain their thinking during the task. Students will be asked to justify their conclusions.
Elaborate: Students will elaboration on their understanding of functions by using the concept to represent transformations.
Evaluate: Students will have a chance to share and evaluate other students’ explanations. This will allow time for error correction.
Extend: Students will continue thinking about their final project, in which they will be creating an original logo for a company, band, or other group of their choosing.
Standards Addressed:
MCC9-12.G.CO.2
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).
MCC9-12.G.CO.5
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.
Essential Question: How can we represent transformations of geometric objects in a graph using functions?
This lesson is structured into three parts, a launch activity used to engage the students in the lesson, the work period in which students will be
collaboratively working to discover concepts, and a closing in which students will share their thoughts, findings, and understanding of the concepts.
Launch: Working with their collaborative pair, students will complete a launch activity in which they will be shown a geometric object
on a graph and be asked to complete three transformations onto the object, a rotation, a reflection, and a translation. The class will discuss different
ways in which these can be represented.
Work Period: Working with their collaborative pair, students will investigate the concept of representing translations using functions. Students will sign onto the website www.textbooktactics.comand watch the following video tutorials: transformational geometry – rotations, transformational geometry – translations,
and transformational geometry –reflections. Students will learn and become familiar with the concept of transformational functions through these videos.
Once complete, students will use their knowledge of transformations and functions to transform a polygon in the coordinate grid. Students will need to perform the following transformations: reflection across the x and y-axes, reflections across the line y=x, 90 degree and 180 degree rotation through the origin, horizontal and vertical translation, diagonal translation. Each transformation will need to be represented both graphically and by writing a function.
Summary: To summarize the lesson, a geometric object and a transformation will be shown. A whole class discussion will be held on what
transformation has occurred, and how to represent the transformation using functions.
Engage: Students will engage in the lesson while being challenged to create multiple ways of representing a transformation.
Explore: Students will explore the concepts of transformations on the coordinate grid using the website www.textbooktactics.com.
Explain: Students will need to explain their thinking during the task. Students will be asked to justify their conclusions.
Elaborate: Students will elaboration on their understanding of functions by using the concept to represent transformations.
Evaluate: Students will have a chance to share and evaluate other students’ explanations. This will allow time for error correction.
Extend: Students will continue thinking about their final project, in which they will be creating an original logo for a company, band, or other group of their choosing.