Translation Coordinates

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Resource ID#: 64654 Primary Type: Formative Assessment

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Students are asked to translate two-dimensional figures in the coordinate plane and identify the coordinates of the vertices of the images.

General Information

Subject(s): Mathematics

Grade Level(s): 8

Intended Audience: Educators

Keywords: MFAS, translation, coordinates, transformation

Instructional Component Type(s): Formative Assessment

Resource Collection: MFAS Formative Assessments

Attachments

MFAS_TranslationCoordinates_Worksheet.docx

Formative Assessment Task

Instructions for Implementing the Task

This task can be implemented individually, with small groups, or with the whole class.

The teacher asks the student to complete the problems on the Translation Coordinates worksheet.
The teacher asks follow-up questions, as needed.

TASK RUBRIC

Getting Started

Misconception/Error

The student is unable to correctly perform translations.

Examples of Student Work at this Level

The student:

Only identifies the coordinates of the vertices of the preimage.
Attempts to translate the figure but does so incorrectly. The student:
- Only translates the y-coordinate.
- Is unable to correctly calculate the coordinates of the vertices of the image.

Questions Eliciting Thinking

What is a translation? How are the vertices of the original image related to the vertices of the translated image?

Can you describe the translation in words? What happens to the vertices of the figure?

I see that you listed the coordinates of the vertices of triangle IJK as the coordinates of the vertices of triangle $begin mathsize 12px style I apostrophe J apostrophe K apostrophe end style$ ? Would you expect these to be the same after the translation?

How can you calculate the coordinates of the vertices of the translated figure from the coordinates of the vertices of the original triangle?

What is the x-coordinate of point I? What is its y-coordinate?

Instructional Implications

Review the definition of translation as a transformation of the plane. Explain that a translation along a vector, v, assigns to each point, P, in the plane an image point, $begin mathsize 12px style P apostrophe end style$ , so that the distance from $begin mathsize 12px style P apostrophe end style$ to P corresponds to the magnitude (length) of vector, v, and the direction of $begin mathsize 12px style P apostrophe end style$ from P corresponds to the direction of vector, v. Guide the student to understand how the rule given in the first problem describes the translation in terms of a horizontal component (e.g., x – 3) and a vertical component (e.g., y + 5). Use grid paper to illustrate translations of points and to demonstrate the relationship between a point, its image, and the vector that defines the translation. Then illustrate translations of more complex figures such as segments, angles, and polygons.

Emphasize the basic properties of rigid motions:

Lines are taken to lines, and line segments to line segments of the same length.
Angles are taken to angles of the same measure.
Parallel lines are taken to parallel lines.

Discuss how these properties ensure that the image of a figure under a rigid motion is always congruent to the preimage.

To develop an intuitive understanding of transformations, allow the student to experiment with a variety of transformations using transparent paper or interactive websites such as: http://www.mathopenref.com/translate.html.

Provide opportunities to perform translations of figures in the coordinate plane described algebraically and by vectors.

Making Progress

Misconception/Error

The student incorrectly labels or calculates a value of an ordered pair.

Examples of Student Work at this Level

The student:

Uses a counting method to locate the vertices of the translated figure but makes an error in identifying the coordinates.
Reverses the order of the coordinates in one ordered pair but writes all other ordered pairs correctly.
Incorrectly calculates one coordinate but all other coordinates are calculated correctly.

Questions Eliciting Thinking

How did you translate the figure? Did you calculate the coordinates of the vertices of the image or did you use a counting method?

I think you may have made a small error when you determined the coordinates of the vertices of the translated figure. Can you check your work to find the error?

Instructional Implications

Provide specific feedback to the student concerning any error made. Allow the student to revise his or her work to correct any errors. Provide additional opportunities to perform translations of figures in the coordinate plane described algebraically and by vectors.

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 describes and labels the coordinates of the images of triangle IJK. The student may or may not plot the images.

$begin mathsize 14px style I apostrophe end style$ (1, 5) $begin mathsize 14px style J apostrophe end style$ (-1, 1), $begin mathsize 14px style K apostrophe end style$ (-5, 9)
$begin mathsize 14px style I apostrophe end style$ (-4, 6) $begin mathsize 14px style J apostrophe end style$ (-6, 2), $begin mathsize 14px style K apostrophe end style$ (-10, 10)

Questions Eliciting Thinking

What would the image look like on the coordinate grid if you graphed it?

Can you determine a rule for the translation using the vector in the second problem?

Instructional Implications

Introduce the concept of congruence in terms of rigid motions. Ask the student to determine if two figures are congruent by describing a sequence of rigid motions that map one figure onto the other.

Consider implementing the MFAS tasks Dilation Coordinates, Rotation Coordinates, and Reflection Coordinates (8.G.1.3).

Accommodations & Recommendations

Special Materials Needed:
- Translation Coordinates 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

* Please note that examples of resources are not intended as complete curriculum.

Aligned Standards

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