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MAFS.912.G-CO.2.6

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.
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Congruence
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Understand congruence in terms of rigid motions. (Geometry - Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes

TEST ITEM SPECIFICATIONS

  • Item Type(s): This benchmark may be assessed using: MC item(s)
  • Also assesses:

    MAFS.912.G-CO.2.7

    MAFS.912.G-CO.2.8

  • Assessment Limits :
    Items may require the student to be familiar with using the algebraic
    description begin mathsize 12px style left parenthesis x comma y right parenthesis rightwards arrow left parenthesis x plus a comma y plus b right parenthesis end style for a translation, and
    begin mathsize 12px style left parenthesis x comma y right parenthesis rightwards arrow left parenthesis k x comma k y right parenthesis end style for a dilation when given the center of dilation.

    Items may require the student to be familiar with the algebraic
    description for a 90-degree rotation about the origin,
    begin mathsize 12px style left parenthesis x comma y right parenthesis rightwards arrow left parenthesis negative y comma x right parenthesis end style for a 180-degree rotation about the origin,
    begin mathsize 12px style left parenthesis x comma y right parenthesis rightwards arrow left parenthesis negative x comma negative y right parenthesis end style and for a 270-degree rotation about the origin,
    begin mathsize 12px style left parenthesis x comma y right parenthesis rightwards arrow left parenthesis y comma negative x right parenthesis end style

    Items that use more than one transformation may
    ask the student to write a series of algebraic descriptions.

    Items must not use matrices to describe transformations.

    Items must not require the student to use the distance formula.

    Items may require the student to find the distance between two
    points or the slope of a line.

    In items that require the student to represent transformations, at
    least two transformations should be applied

  • Calculator :

    Neutral

  • Clarification :
    Students will use rigid motions to transform figures.

    Students will predict the effect of a given rigid motion on a given
    figure.

    Students will use the definition of congruence in terms of rigid
    motions to determine if two figures are congruent.

    Students will explain triangle congruence using the definition of
    congruence in terms of rigid motions.

    Students will apply congruence to solve problems.

    Students will use congruence to justify steps within the context of a
    proof.

  • Stimulus Attributes :
    Items may be set in a real-world or mathematical context.

    Items may require the student to determine the rigid motions that
    show that two triangles are congruent.

  • Response Attributes :
    Items may ask the student to name corresponding angles and/or
    sides.

    Items may require the student to use a function, e.g.,

    y=k(f(x+a))+b , to describe a transformation.


    In items in which the student must write the line of reflection, any
    line may be used.

     

    Items may require the student to be familiar with slope-intercept
    form of a line, standard form of a line, and point-slope form of a line.

    Items may require the student to name corresponding angles or
    sides.

     

    Items may require the student to determine the transformations
    required to show a given congruence.

    Items may require the student to list sufficient conditions to prove
    triangles are congruent.

    Items may require the student to determine if given information is
    sufficient for congruence.

    Items may require the student to give statements to complete formal
    and informal proofs.



     

SAMPLE TEST ITEMS (1)

  • Test Item #: Sample Item 1
  • Question:

    Evelyn is designing a pattern for a quilt using polygon EQFRGSHP shown.

    Evelyn transforms EQFRGSHP so that the impage of E is at (2,0) and the image of R is at (6,-7). Which transformation could Evelyn have used to show EQFRGSHP and its image are congruent?

  • Difficulty: N/A
  • Type: MC: Multiple Choice