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).
General Information
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
    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

Related Courses

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1206300: Informal Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
0101340: Three-Dimensional Studio Art 2 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
0101350: Three-Dimensional Studio Art 3 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
0104340: Drawing 1 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
0104350: Drawing 2 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
0104360: Drawing 3 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
0104370: Painting 1 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
0104380: Painting 2 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
0104390: Painting 3 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
0109310: Portfolio Development: Drawing-Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
0109320: Portfolio Development: Two-Dimensional Design Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
0109330: Portfolio Development: Three-Dimensional Design Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
0114800: Florida's Preinternational Baccalaureate Art 1 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
0114810: Florida's Preinternational Baccalaureate Art 2 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7912060: Access Informal Geometry (Specifically in versions: 2014 - 2015 (course terminated))
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7912065: Access Geometry (Specifically in versions: 2015 - 2022 (current), 2022 and beyond)
0104335: Drawing 1 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7967015: Access Drawing 1 (Specifically in versions: 2015 - 2018, 2018 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.912.G-CO.1.AP.2a: Represent transformations in the plane using, e.g., transparencies and geometry software.
MAFS.912.G-CO.1.AP.2b: Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Assessments

Sample 4 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grades.

Type: Assessment

Sample 2 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grade.

Type: Assessment

Educational Software / Tool

Transformations Using Technology:

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.

Type: Educational Software / Tool

Formative Assessments

Demonstrating Rotations:

Students are asked to rotate a quadrilateral 90 degrees clockwise.

Type: Formative Assessment

Transformations And Functions:

Students are given examples of three transformations and are asked if each is a function.

Type: Formative Assessment

Comparing Transformations:

Students are asked to determine whether or not dilations and reflections preserve distance and angle measure.

Type: Formative Assessment

Demonstrating Translations:

Students are asked to translate a quadrilateral according to a given vector.

Type: Formative Assessment

Demonstrating Reflections:

Students are asked to reflect a quadrilateral across a given line.

Type: Formative Assessment

Lesson Plans

Coding Geometry Challenge #23 & 24:

This set of geometry challenges focuses on using transformations to show similarity and congruence of polygons and circles. Students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Type: Lesson Plan

Triangles on a Lattice:

In this activity, students will use a 3x3 square lattice to study transformations of triangles whose vertices are part of the lattice. The tasks include determining whether two triangles are congruent, which transformations connect two congruent triangles, and the number of non-congruent triangles (with vertices on the lattice) that are possible.

Type: Lesson Plan

Transformations... Geometry in Motion:

Transformations... Geometry in Motion is designed for students to practice their knowledge of transformations. Students will represent transformations in the plane, compare transformations, and determine which have isometry. Students should have a basic understanding of the rules for each transformation as they will apply these rules in this activity. There is a teacher-led portion in this lesson followed by partner-activity. Students will be asked to explain and justify reasoning, as well.

Type: Lesson Plan

Perspectives Video: Experts

Mathematically Exploring the Wakulla Caves:

The tide is high!  How can we statistically prove there is a relationship between the tides on the Gulf Coast and in a fresh water spring 20 miles from each other?

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Knot Theory Entangled in Cellular Biology:

This FSU professor describes how knot theory and cellular biology are intertwined. Researchers are still trying to determine how enzyme bridges are able to un-knot long strands of DNA to mitigate potential cell destruction.

Type: Perspectives Video: Expert

MFAS Formative Assessments

Comparing Transformations:

Students are asked to determine whether or not dilations and reflections preserve distance and angle measure.

Demonstrating Reflections:

Students are asked to reflect a quadrilateral across a given line.

Demonstrating Rotations:

Students are asked to rotate a quadrilateral 90 degrees clockwise.

Demonstrating Translations:

Students are asked to translate a quadrilateral according to a given vector.

Transformations And Functions:

Students are given examples of three transformations and are asked if each is a function.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Educational Software / Tool

Transformations Using Technology:

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.

Type: Educational Software / Tool

Perspectives Video: Expert

Mathematically Exploring the Wakulla Caves:

The tide is high!  How can we statistically prove there is a relationship between the tides on the Gulf Coast and in a fresh water spring 20 miles from each other?

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.