# MAFS.912.G-CO.1.5

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
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.1.3

• Assessment Limits :
Items may require the student to be familiar with using the algebraic
description  for a translation, and
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,
for a 180-degree rotation about the origin,
and for a 270-degree rotation about the origin,

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.,
, 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

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)

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.912.G-CO.1.AP.5b: Create sequences of transformations that map a geometric figure on to itself and another geometric figure.

## Related Resources

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

## Assessments

Sample 3 - High School Geometry State Interim Assessment:

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

Type: Assessment

Sample 2 - High School Geometry State Interim Assessment:

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

Type: Assessment

## Educational Software / Tools

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

Free Graph Paper:

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

Type: Educational Software / Tool

## Formative Assessments

Reflect a Semicircle:

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

Type: Formative Assessment

Two Triangles:

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

Type: Formative Assessment

Rotation of a Quadrilateral:

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

Type: Formative Assessment

Indicate the Transformations:

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

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

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.

Type: Lesson Plan

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 see whether the triangle ends up at the same location or not.

Type: Lesson Plan

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.

Type: Lesson Plan

Isometries with GeoGebra:

In this lesson, students explore transformations with GeoGebra 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.

Type: Lesson Plan

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 in order 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.

Type: Lesson Plan

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.

Type: Lesson Plan

Product of Two Transformations:

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

Type: Lesson Plan

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.

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

Reflections Hands On:

Students will use a protractor/ruler to construct reflections and 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.

Type: Lesson Plan

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.

Type: Lesson Plan

Let's Reflect On This...:

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

Type: Lesson Plan

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.

Type: Lesson Plan

Transform through the Maze:

In this fun activity, students will work with transformations to move a triangle through a maze. The activity has an honors level and standard level application. It requires students to perform rotations, translations, and reflections.

Type: Lesson Plan

## Perspectives Video: Expert

The Geometry of DNA Replication:

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

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiast

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!

Type: Perspectives Video: Professional/Enthusiast

## Tutorial

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.

Type: Tutorial

## Virtual Manipulative

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.

Type: Virtual Manipulative

## MFAS Formative Assessments

Indicate the Transformations:

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

Reflect a Semicircle:

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

Rotation of a Quadrilateral:

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

Two Triangles:

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

## 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

## Tutorial

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.

Type: Tutorial

## Virtual Manipulative

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.

Type: Virtual Manipulative

## Parent Resources

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