| Code |
Description |
| MAFS.912.G-CO.1.1: | Know precise definitions of angle, circle, perpendicular line, parallel
line, and line segment, based on the undefined notions of point, line,
distance along a line, and distance around a circular arc. |
| 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). |
| MAFS.912.G-CO.1.3: | Given a rectangle, parallelogram, trapezoid, or regular polygon,
describe the rotations and reflections that carry it onto itself. |
| MAFS.912.G-CO.1.4: | Develop definitions of rotations, reflections, and translations in terms
of angles, circles, perpendicular lines, parallel lines, and line segments. |
| 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. |
This cluster includes the following access points.
Vetted resources educators can use to teach the concepts and skills in this topic.
| 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. |
| Coding Geometry Challenge # 12 & 13: | This set of geometry challenges focuses on creating circles and calculating area/circumference as 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. |
| Basic Definitions in Geometry: | A set of basic definitions in geometry (line segment, ray, angle, perpendicular lines, and parallel lines) is addressed. The notation used in naming each defined term is also emphasized. |
| 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. |
| Regular Polygon Transformation Investigation: | This is an introductory lesson on regular polygon transformation for congruency using a hands-on approach. |
| Musical Chairs with Words and a Ball: | This lesson introduces students to concepts and skills that they will use throughout the year. Students will learn that the terms point, and line are considered "undefined." Students will play musical chairs while learning to develop precise definitions of circle, angle, parallel line, and perpendicular line, using counterexamples at different classroom stations. Students will identify models, use notation, and make sketches of these terms. |
| 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. |
| Rotations of Regular Polygons: | This lesson guides students through the development of a formula to find the first angle of rotation of any regular polygon to map onto itself. Free rotation simulation tools such as GeoGebra, are used. |
| 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. |
| Pick Your Words Precisely!: | Students will develop precise definitions of the terms angle, circle, line segment, parallel line and perpendicular line by completing a graphic organizer under the Frayer model through small and whole group discussion. |
| I Am Still Me Transformed.: | Students explore ways of applying, identifying, and describing reflection and rotation symmetry for both geometric and real-world objects, for them to develop a better understanding of symmetries in transformational geometry. |
| 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. |
| Rotations and Reflections of an Equilateral Triangle: | Students will apply simple transformations (rotation and reflection) to an equilateral triangle, then determine the result of the action of two successive transformations, eventually determining whether the action satisfies the commutative and associate properties. |
| 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. |
| Sage and Scribe - Points, Lines, and Planes: | Students will practice using precise definitions while they draw images of Points, Lines, and Planes. Students will work in pairs taking turns describing an image while their partner attempts to accurately draw the image. |
| 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. |
| Fundamental Property of Reflections: | This lesson helps students discover that in a reflection, the line of reflection is the perpendicular bisector of any segment connecting any pre-image point with its reflected image. |
| 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. |
| Building Blocks of Geometry: | Students will be introduced to the undefinable concepts of points, lines, and planes that are the building blocks of geometry and recognize that these three terms become the basis for many other geometric definitions. Students will participate in a Building Block Scavenger Hunt, using cameras to photograph examples of specified terms that they find outside of the math classroom. The students will compose a power point to display their photographs of the required terms.
This lesson is adapted from a presentation that included an activity by Dianne Olix, 1995. |
| Virtually Possible: | This is a ray drawing activity to aid students in their understanding of how virtual images are formed by plane mirrors, and how the image size and distance from the mirror compare to those of the object. |
| Rotations and Reflections of an Equilateral Triangle: | Students will apply simple transformations (rotation and reflection) to an equilateral triangle, then determine the result of the action of two successive transformations, eventually determining whether the action satisfies the commutative and associate properties. |
| Name |
Description |
| Developing a Definition of a Reflection: | Click "View Site" to open a full-screen version. In this tutorial, the development of a formal definition of a reflection is presented. |
| Developing a Definition of a Rotation: | Click "View Site" to open a full-screen version. In this tutorial, the development of a formal definition of a rotation is presented. |
| Developing a Definition of a Translation: | Click "View Site" to open a full-screen version. In this tutorial, the development of a formal definition of a translation is presented. |
| Rotational Symmetries of Regular Polygons: | Click "View Site" to open a full-screen version. The world contains many examples of figures with rotational symmetry. Some of these occur in art, others occur in nature. Knowledge of rotational symmetry can be helpful in understanding both the human and the natural world. In this tutorial, rotations that carry a regular polygon onto itself are explored and suggestions for teaching this topic are offered. |
| Rotating polygons 180 degrees about their center: | Students will investigate symmetry by rotating polygons 180 degrees about their center.
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| Line of reflection: | Students are shown, with an interactive tool, how to reflect a line segment. Students should have an understanding of slope and midpoint before viewing this video. |
| Line of reflection: | This tutorial uses the midpoint of two lines to find the line of reflection. |
| 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. |
| Specifying planes in three dimensions: | In this tutorial, students are introduced to the concept that three non-collinear points are necessary to define a unique plane. |
| The language of geometry: | Before learning any new concept it's important students learn and use common language and label concepts consistently. This tutorial introduces students to th point, line and plane. |
| Identifying parallel and perpendicular lines: | This tutorial is great practice for help in identifying parallel and perpendicular lines. |
| Basic Geometry Language and Labels: | In this tutorial we will learn the basics of geometry, such as identifying a line, ray, point, and segment. |
Vetted resources students can use to learn the concepts and skills in this topic.
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