Lesson 2:
Exploring Translations of Geometric Shapes
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 vs 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 analyze two objects on a coordinate grid to determine the type of transformation, or combination of transformations, that can map one object onto the other?
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:
Students will use their working definitions of rotations and reflections from lesson 1 to analyze different shapes on a graph. A class discussion will be
held as to which shapes look like they are rotations or reflections of each other. This will engage students in the lesson for the day and lead into the
work period.
Work Period:
Students will work with a partner to explore the concepts of transformations on the coordinate plane. Students will be using the geometric software program
Geometer’s Sketchpad to explore these concepts. This will include activities such as creating geometric shapes and performing transformations on these
shapes that will include translations, reflections, and rotations. Specific activities include reflections across the axes, rotations about the origin, and
translations both horizontal and vertical.
Closing:
Students will complete a summary activity in which they will be given the coordinate of a geometric object and then instructed to reflect the object about
the y-axis, rotate the object 1800 about the origin, and translate the object -5 spaces in the horizontal direction. An example summary can be seen
below.
Engage: Students will use their working definitions to analyze geometric objects that have been transformed. This will be an extension of the previous lesson and will
challenge the students to expand their understanding of the last lesson’s concepts.
Explore: Students will explore the concepts of transformations on the coordinate grid using geometric software.
Explain: Students will need to explain their thinking during the task. Students will be asked to justify their conclusions.
Elaborate: Students will build upon their working definitions of rotation and reflection to include translations and specific characteristics of these on the coordinate
grid.
Evaluate: Students will have a chance to share and evaluate other students’ summaries. This will allow time for error correction.
Extend: Students will begin thinking about their final project, in which they will be creating an original logo for a company, band, or other group of their choosing.
Sample Student Summary Activity
Exploring Translations of Geometric Shapes
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 vs 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 analyze two objects on a coordinate grid to determine the type of transformation, or combination of transformations, that can map one object onto the other?
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:
Students will use their working definitions of rotations and reflections from lesson 1 to analyze different shapes on a graph. A class discussion will be
held as to which shapes look like they are rotations or reflections of each other. This will engage students in the lesson for the day and lead into the
work period.
Work Period:
Students will work with a partner to explore the concepts of transformations on the coordinate plane. Students will be using the geometric software program
Geometer’s Sketchpad to explore these concepts. This will include activities such as creating geometric shapes and performing transformations on these
shapes that will include translations, reflections, and rotations. Specific activities include reflections across the axes, rotations about the origin, and
translations both horizontal and vertical.
Closing:
Students will complete a summary activity in which they will be given the coordinate of a geometric object and then instructed to reflect the object about
the y-axis, rotate the object 1800 about the origin, and translate the object -5 spaces in the horizontal direction. An example summary can be seen
below.
Engage: Students will use their working definitions to analyze geometric objects that have been transformed. This will be an extension of the previous lesson and will
challenge the students to expand their understanding of the last lesson’s concepts.
Explore: Students will explore the concepts of transformations on the coordinate grid using geometric software.
Explain: Students will need to explain their thinking during the task. Students will be asked to justify their conclusions.
Elaborate: Students will build upon their working definitions of rotation and reflection to include translations and specific characteristics of these on the coordinate
grid.
Evaluate: Students will have a chance to share and evaluate other students’ summaries. This will allow time for error correction.
Extend: Students will begin thinking about their final project, in which they will be creating an original logo for a company, band, or other group of their choosing.
Sample Student Summary Activity