Download Resource ID#: 9924

Transformations Using Technology
Resource ID#: 9924
Primary Type: Educational Software / Tool
This document was generated on CPALMS - www.cpalms.org
This virtual manipulative can be used to demonstrate and explore the effect of translation,
rotation, and/or reflection on a variety of plane figures. A series of transformations can be
explored to result in a specified final image.
Subject(s): Mathematics
Grade Level(s): 8, 9, 10, 11, 12
Intended Audience: Educators
, Students
Suggested Technology: Computer for Presenter, Computers for Students, Internet Connection,
LCD Projector, Adobe Flash Player, Java Plugin
Instructional Time: 20 Minute(s)
Freely Available: Yes
Keywords: Reflection, rotation, translation, transformations
Instructional Component Type(s): Educational Software / Tool, Virtual Manipulative,
Instructional Design Framework(s): Demonstration, Learning Cycle (e.g., 5E)
Resource Collection: iCPALMS
Related Standards
Name
MAFS.8.G.1.1:
MAFS.8.G.1.2:
Description
Verify experimentally the properties of rotations, reflections,
and translations:
a. Lines are taken to lines, and line segments to line
segments of the same length.
b. Angles are taken to angles of the same measure.
c. Parallel lines are taken to parallel lines.
Understand that a two-dimensional figure is congruent to
another if the second can be obtained from the first by a
MAFS.8.G.1.3:
MAFS.8.G.1.4:
MAFS.912.G-CO.1.2:
MAFS.912.G-CO.1.3:
MAFS.912.G-CO.1.4:
MAFS.912.G-CO.1.5:
MAFS.912.G-CO.2.6:
sequence of rotations, reflections, and translations; given two
congruent figures, describe a sequence that exhibits the
congruence between them.
Describe the effect of dilations, translations, rotations, and
reflections on two-dimensional figures using coordinates.
Understand that a two-dimensional figure is similar to another if
the second can be obtained from the first by a sequence of
rotations, reflections, translations, and dilations; given two
similar two-dimensional figures, describe a sequence that
exhibits the similarity between them.
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 rectangle, parallelogram, trapezoid, or regular polygon,
describe the rotations and reflections that carry it onto itself.
Develop definitions of rotations, reflections, and translations in
terms of angles, circles, perpendicular lines, parallel lines, and
line segments.
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.
Use geometric descriptions of rigid motions to transform figures
and to predict the effect of a given rigid motion on a given
figure; given two figures, use the definition of congruence in
terms of rigid motions to decide if they are congruent.
Attached Resources
Virtual Manipulative
Name
Description
This virtual manipulative is an interactive visual presentation of
the rotation of a point around the origin of the coordinate
Rotation of a Point:
system. The original point can be dragged to different positions
and the angle of rotation can be changed with a 90° increment.
Students use a slider to explore dilation and scale factor.
Transformations - Dilation:
Students can create and dilate their own figures. (source:
NLVM grade 6-8 "Transformations - Dilation")
The user clicks and drags a shape they have constructed to view
its reflection across a line. A background grid and axes may or
Transformations - Reflections:
may not be used. The reflection may by examined analytically
using coordinates. Symmetry may be displayed.
Rotate shapes and their images with or without a background
Transformations - Rotation:
grid and axes.
The user can demonstrate or explore translation of shapes
created with pattern blocks, using or not using a coordinate axes
Transformations - Translation: and lattice points background, by changing the translation
vector.
(source: NLVM grade 6-8 "Transformations - Translation")
Lesson Plan
Name
Rotations and Reflections of
an Equilateral Triangle:
Description
Students will apply simple transformations (rotation and
reflection) to an equilateral triangle, then determine the result of
the action of two successive transformations, eventually
determining whether the action satisfies the commutative and
associate properties.