Standard #: MAFS.912.G-CO.1.5 (Archived Standard)


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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.


General Information

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Congruence
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 - Archived
Assessed: Yes

Test Item Specifications

    also assesses:
    MAFS.912.G-CO.1.3

    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 apply two or more transformations to a given figure to
    draw a transformed figure.

    Students will specify a sequence of transformations that will carry a
    figure onto another.

    Students will describe rotations and reflections that carry a geometric
    figure onto itself.

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

    Items may require the student to provide a sequence of
    transformations.

    Items may require the student to determine if an attribute of a figure
    is the same after a sequence of transformations has been applied. 

    Response Attributes :
    Items may require the student to use a function, e.g.,
    begin mathsize 12px style y equals k left parenthesis f left parenthesis x plus a right parenthesis right parenthesis plus b end style , to describe a transformation.

    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 transformation.

    Items may require the student to graph a figure using a description of
    a rotation and/or reflection.

    In items in which the student has to 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 write a line of reflection that will
    carry a figure onto itself.

    Items may require the student to give a degree of rotation that will
    carry a figure onto itself.



Related Courses

Course Number1111 Course Title222
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206300: Informal Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0101340: Three-Dimensional Studio Art 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0101350: Three-Dimensional Studio Art 3 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0104340: Drawing 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0104350: Drawing 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0104360: Drawing 3 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0104370: Painting 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0104380: Painting 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0104390: Painting 3 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0109310: Portfolio Development: Drawing-Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0109320: Portfolio Development: Two-Dimensional Design Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0109330: Portfolio Development: Three-Dimensional Design Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0114800: Florida's Preinternational Baccalaureate Art 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
0114810: Florida's Preinternational Baccalaureate Art 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912060: Access Informal Geometry (Specifically in versions: 2014 - 2015 (course terminated))
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912065: Access Geometry (Specifically in versions: 2015 - 2022, 2022 and beyond (current))


Related Resources

Educational Software / Tools

Name Description
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.

Free Graph Paper A variety of graph paper types for printing, including Cartesian, polar, engineering, isometric, logarithmic, hexagonal, probability, and Smith chart.

Formative Assessments

Name Description
Reflect a Semicircle

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

Two Triangles

Students are asked to describe the transformations that take one triangle onto another.

Rotation of a Quadrilateral

Students are asked to rotate a quadrilateral around a given point.

Indicate the Transformations

Students are asked to describe the transformations that take one triangle onto another.

Lesson Plans

Name Description
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.

Transformations in the Coordinate Plane

In this exploration activity of reflections, translations, and rotations, students are guided to discover general algebraic rules for special classes of transformations in the coordinate plane. This lesson is intended to be used after the development of formal definitions of rotations, translations, and reflections.

Reflecting on the Commute

Students are given a set of coordinates that indicate a specific triangle on a coordinate plane. They will also be given a set of three reflections to move the triangle through. Students will then perform three other sequences of reflections to determine if the triangle ends up where it started.

Sequence of Transformations

This lesson will assist students in performing multi-step transformations. Students will follow a sequence of transformations on geometric figures using translations, reflections, and rotations.

Isometries with GeoGebra

In this lesson, students explore transformations with GeoGebra and then apply concepts using a straightedge on paper. Students apply rules for each isometry. There is a teacher-driven opening followed by individual student activity.

How Did It Get There? A Series of Transformation Events

Students will perform a series of transformations in order to determine how the pre-image will map onto the final image of a given figure. Students will use patty paper to manipulate their pre-image onto the image. Students will also work in collaborative groups to discuss their findings and will have the opportunity to share their series of transformations with the class. The class discussion will be used to demonstrate that there are several ways for the students to map their pre-image onto the final image.

Dancing For Joy

We have danced our way through reflections, rotations, and translations; now we are ready to take it up a notch by performing a sequence of transformations. Students will also discover the results when reflecting over parallel lines versus intersecting lines.

Product of Two Transformations

Students will identify a sequence of steps that will translate a pre-image to its image. Students will also demonstrate that the sequence of two transformations is not always commutative.

How to Land Your Spaceship

Teach your students to maneuver a "spaceship" through a sequence of transformations that will successfully carry it onto its landing pad. GeoGebra directons are provided.

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.

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.

Reflections Hands On

Students will use a protractor/ruler to construct reflections and a composite of reflections. They will create transformations using paper cut-outs and a coordinate plane. For independent practice, students will predict and verify sequences of transformations. The teacher will need an LCD Projector and document camera.

Flipping Fours

Students will translate, rotate and reflect quadrilaterals (Parallelogram, Rectangle, Square, Kite, Trapezoid, and Rhombus) using a coordinate grid created on the classroom floor and on graph paper. This activity should be used following guided lessons on transformations.

Let's Reflect On This...

Students will use parallel and intersecting lines on the coordinate plane to transform reflections into translations and rotations.

Rotation of Polygons about a Point

Students will rotate polygons of various shapes about a point. Degrees of rotation vary but generally increase in increments of 90 degrees. Points of rotation include points on the figure, the origin, and points on the coordinate plane. The concept of isometry is addressed.

Transform through the Maze

In this fun activity, students will use rigid transformations to move a triangle through a maze. The activity provides applications for both honors and standard levels. It requires students to perform rotations, translations, and reflections.

Perspectives Video: Expert

Name Description
The Geometry of DNA Replication

A discussion of the applications of Knot Theory, replication of DNA, enzymes, and fluid dynamics.

Perspectives Video: Professional/Enthusiast

Name Description
Reflections, Rotations, and Translations with Additive Printing

Transform your understanding of 3D modeling when you learn about how shapes are manipulated to arrive at a final 3D printed form!

Tutorial

Name Description
Points after rotation

Students will see what happens when a figure is rotated about the origin -270 degrees. Having a foundation about right triangles is recommended before viewing this video.

Virtual Manipulative

Name Description
Combining Transformations

In this manipulative activity, you can first get an idea of what each of the rigid transformations look like, and then get to experiment with combinations of transformations in order to map a pre-image to its image.

Student Resources

Educational Software / Tool

Name Description
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.

Tutorial

Name Description
Points after rotation:

Students will see what happens when a figure is rotated about the origin -270 degrees. Having a foundation about right triangles is recommended before viewing this video.

Virtual Manipulative

Name Description
Combining Transformations:

In this manipulative activity, you can first get an idea of what each of the rigid transformations look like, and then get to experiment with combinations of transformations in order to map a pre-image to its image.



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