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Geometric Transformations Unit
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Geometric Transformations Unit

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Subject MathGeometry
Grade Level Grades 9-12
Resource Type Activity, Assessment, Handout, Lesson Plan
Standards Alignment
Common Core State Standards

About This Lesson

This unit plan is for a Transformations unit in High School Geometry. It introduces students to the four main transformations: translation, reflection, rotation, and dilation. The lessons focus on real-world connections, including video game and computer graphics, and a chance for students' to create their own fractal images using transformations. It presents both hands-on and algorithmic methods of transforming shapes, as well as chances for students to use GeoGebra to visually verify their work and experiment with different transformations.

The unit plan is for a two-week unit of 50 minute daily classes. It includes instructions for using the free software used in the plan, printouts for the students, and a unit exam for the last day of the unit.

Resources

Files

Geometric_Transformations_Unit_Plan.pdf

Lesson Plan
June 28, 2020
63.02 KB

Explanations_of_Activities.pdf

Activity
June 28, 2020
77.01 KB

Graph_Printout.pdf

Handout, Worksheet
June 28, 2020
126.76 KB

Transformations_Unit_Exam.pdf

Assessment
June 28, 2020
245.5 KB

Standards

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).
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.
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
Verify experimentally the properties of dilations given by a center and a scale factor:
A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

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