G.1.1

Verify experimentally the properties of rotations, reflections, and translations:

a.  Lines are taken to lines, and line segments to line segments of the same length.

b.  Angles are taken to angles of the same measure.

c. Parallel lines are taken to parallel lines.

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Formative Assessments
Formative Assessments
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CPALMS: Students are given the opportunity to experimentally verify the properties of angle transformations (translations, reflections, and rotations).

Angle Transformations

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CPALMS: Students are given the opportunity to experimentally verify the properties of parallel line transformations (translations, reflections, and rotations).

Parallel Line Transformations

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CPALMS: Students are given the opportunity to experimentally verify the properties of segment transformations (translations, reflections, and rotations).

Segment Transformations

Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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CPALMS: This manipulative is an interactive visual presentation of the rotation of a point around the origin of the coordinate system. The original point can be dragged to different positions and the angle of rotation can be changed with a 90° increment.

Rotation of a Point

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CPALMS: Using this resource, the user can demonstrate or explore translation of shapes created with pattern blocks, using or not using a coordinate axes and lattice points background, by changing the translation vector.

Transformations – Translation

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A translation is explained as moving a shape, nothing else. Every point of the shape moves the same distance, in the same direction. Students virtually translate shapes by determining angle degrees, as well as deciding the exact distance for the move. Writing the x- and y- expression for the shape’s move is modeled.

Transformations – Virtual Translations by Math is Fun

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CPALMS: The user clicks and drags a shape they have constructed to view its reflection across a line. A background grid and axes may or may not be used. The reflection may by examined analytically using coordinates. Symmetry may be displayed.

Transformations – Reflections

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In this virtual manipulative, students read the definition of a rotation, watch a model rotate in a coordinate plane based on the student's decided number of degrees, and then answer a series of multiple choice questions with pictorial representations. Answers are explained.

Transformations – Virtual Rotations by Math is Fun

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In this virtual activity, students use their existing understanding of rigid transformations in order to complete a round of virtual transformation golf. Using a coordinate grid, they are challenged to use one or more transformations to transform the pre-image onto the image.

“Transformation Golf: Rigid Motion” – by Desmos

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CPALMS: Using this resource, the student is able to rotate shapes and their images with or without a background grid and axes.

Transformations – Rotation

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Students see the definition of reflection and how it is a flip and that each point on the shape is the same distance from the central line. Mirror image is explained and modeled. Students can then choose different virtual mirror lines and watch exactly how a shape is reflected.

Transformations – Virtual Reflections by Math is Fun

Assessment Questions
Assessment Questions
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Multiple Choice 
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Multiple Choice
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Multi-Select
Videos of Expert Instruction
Videos of Expert Instruction
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In this Khan Academy video (approx. 7:22 min) students will learn what the ``image`` of a transformation is, what are the rigid transformations, and which are not rigid. The shapes are shown and manipulated on the coordinate plane.

“Rigid Transformations Introduction” by Khan Academy

Hook/Performance Tasks
Hook/Performance Tasks
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Illustrative Mathematics: This prepares students for formal definition of dilations and similarity transformations. Their engagement in a context that's not typical (random curves) leads to focus on the properties of transformations rather than the figure.

A Scaled Curve

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Illustrative Mathematics: Students experience applying and reasoning about reflections of geometric figures using understanding of properties of rigid motions. Reflecting a rectangle over a diagonal, the image is still a rectangle and it shares 2 vertices with the original rectangle.

Reflecting a Rectangle Over a Diagonal

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Illustrative Mathematics: The goal is to apply geometry in order analyze the shape of a rectangle obtained by folding paper. The central geometric ideas involved are reflections, analysis of angles in triangles, and the Pythagorean Theorem.

Origami Silver Rectangle

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Illustrative Mathematics: The goal is for students to apply a wide range of ideas from geometry and algebra in order to show that a given quadrilateral is a rectangle. Working on task helps students see multiple constructions unified to achieve a common purpose. Connects to HS geometry ideas.

Is this a Rectangle?

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Illustrative Mathematics: The purpose is to help students transition from the informal notion of congruence as ``same size, same shape`` that they learn in elementary school and begin to develop a definition of congruence in terms of rigid transformations.

Same Size, Same Shape?

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Illustrative Mathematics: The goal is to use technology to visualize what happens to angles and side lengths of a polygon (a triangle in this case) after a reflection, rotation, or translation. GeoGebra files are attached with triangles already constructed as shown in the images.

Reflections, Rotations, and Translations

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Illustrative Mathematics: The purpose of this task is for students to find a way to decompose a regular hexagon into congruent figures. This is meant as an instructional task that gives students some practice working with transformations.

Partitioning a Hexagon

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Illustrative Mathematics: Students gather knowledge and skills from 7th grade in context which prepares for important 8th grade similarity. Ideas: scaled shapes have the same angle measures and corresponding segments of scaled shapes have proportional lengths.

Scaling Angles and Polygons