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MAFS.912.G-CO.1.2

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 versus horizontal stretch).
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Congruence
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Experiment with transformations in the plane. (Geometry - Supporting 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: TI item(s)
  • Also assesses:

    MAFS.912.G-CO.1.4

  • 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 represent transformations in the plane.

    Students will describe transformations as functions that take points in
    the plane as inputs and give other points as outputs.

    Students will compare transformations that preserve distance and
    angle to those that do not.

    Students will use definitions of rotations, reflections, and translations
    in terms of angles, circles, perpendicular lines, parallel lines, and line
    segments.

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

    Items may ask the student to determine if a transformation is rigid.

    Items may ask the student to determine if steps that are given can be
    used to develop a definition of an angle, a circle, perpendicular lines,
    parallel lines, or line segments by using rotations, reflections, and
    translations.

  • Response Attributes :
    Items may require the student to give a coordinate of a transformed
    figure.

    Items may require the student to use a function, e.g.,
    y equals k left parenthesis f left parenthesis x plus a right parenthesis right parenthesis plus b , to describe a transformation.

    Items may require the student to determine if a verbal description of
    a definition is valid.

    Items may require the student to determine any flaws in a verbal
    description of a definition.

    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 give a line of reflection and/or a
    degree of rotation that carries a figure onto itself.

    Items may require the student to draw a figure using a description of
    a translation.

SAMPLE TEST ITEMS (1)

  • Test Item #: Sample Item 1
  • Question:

    Nicole, Jeremy, and Frances each perform a transformation on the triangle RST. Each recorded his or her transformation and the location of S' in the table. Point S of the triangle is located at *5,-7).

    Complete the table to determine the values of a and b that make the algebraic descriptions of each person's transformation true.

  • Difficulty: N/A
  • Type: TI: Table Item