Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 70583
Rotation of a Quadrilateral
Students are asked to rotate a quadrilateral around a given point.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, rotation, transformation, rigid motion
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_RotationOfaQuadrilateral_Worksheet.docx
MFAS_RotationOfaQuadrilateral_Worksheet.pdf
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problem on the Rotation of a Quadrilateral worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not demonstrate an understanding of a rotation.
Examples of Student Work at this Level
The student:
Is unable to rotate the quadrilateral.
Attempts to reflect or translate the quadrilateral.
Questions Eliciting Thinking
What does it mean to rotate a figure?
page 1 of 3 Can you explain how you found the image?
What should the shape of the image be?
Instructional Implications
Be sure the student understands that a rotation is a transformation of the plane. Each point in the plane is rotated a specified number of degrees (given by the degree of
rotation) either clockwise or counterclockwise (indicated by the sign of the degree of rotation) about a fixed point called the center of rotation. Use a unit circle to illustrate
rotations of points about the origin. Then illustrate rotations of more complex figures such as segments, angles, and polygons. Discuss the basic properties of rotations [e.g.,
1) rotations map lines to lines, rays to rays, and segments to segments; 2) rotations are distance preserving; and 3) rotations are degree preserving] and how these
properties ensure that the image of a figure under a rotation is always congruent to the preimage.
Provide the student with additional opportunities to rotate polygons using patty paper and/or dynamic geometry software. Include rotations that vary in terms of the
location of the center (inside, on, or outside the preimage) and the direction and degree of the rotation. Guide the student to always check the image to ensure that it is
congruent to the preimage.
Consider using the MFAS task Demonstrating Rotations (G-CO.1.2) if not previously used.
Making Progress
Misconception/Error
The student makes an error when rotating the figure.
Examples of Student Work at this Level
The student:
Rotates the image counterclockwise.
Rotates about a point other than A.
Locates a vertex incorrectly.
Questions Eliciting Thinking
Which direction were you asked to rotate the figure? Is that what you did?
About which point were you asked to rotate the figure? Is that what you used?
Instructional Implications
Review with the student the difference between a clockwise rotation and a counterclockwise rotation. Provide feedback on any notational errors (such as not labeling the
vertices of the image or labelling them incorrectly). Allow to student to correct his or her error.
Remind the student that the center of rotation may be a point on the preimage, outside the preimage, or inside the preimage. Make sure that the student understands
that each pair of corresponding vertices of the preimage and image will be equidistant from the center of rotation. Also, that the angle formed by a point on the preimage,
the center of rotation, and the corresponding image point must have a measure equal to the degree of the rotation. Provide the student with additional opportunities to
rotate polygons given a center, direction, and degree of rotation using patty paper and/or dynamic geometry software. Include rotations that vary in terms of the center
(inside, on, or outside the preimage) and the direction and degree of the rotation. Guide the student to always check the image to ensure that it is congruent to the
preimage.
Consider using the MFAS task Demonstrating Rotations (G-CO.1.2) if not previously used.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student correctly rotates the preimage
about point A. The student correctly labels the vertices of the rotated quadrilateral B"C"D"E".
Questions Eliciting Thinking
Can you think of a different rotation that would result in the same image?
What properties of the quadrilateral are preserved in a rotation? Is this true for reflections? Translations? Dilations?
Instructional Implications
Challenge the student to make a conjecture about the relationship between clockwise and counterclockwise rotations that result in the same image (e.g.,
the same as
clockwise is
counterclockwise).
page 2 of 3 Consider using the MFAS task Repeated Reflections and Rotations (G-CO.2.6).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Rotation of a Quadrilateral worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.G-CO.1.5:
Description
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.
page 3 of 3