Download Cluster: Understand similarity in terms of similarity transformations

Progressive Mathematics Initiative
www.njctl.org
Mathematics Curriculum
Unit Plan # 3
Title: Transformations
Subject: Geometry
Length of Time: 2 weeks
Unit Summary:
In this unit several different transformations will be explored and their properties will be
compared. Function notation will be used to describe transformations and more rigorous
definitions will be developed for these transformations. A variety of tools (tracing paper,
Geometry software, etc.) will be used to show the effect of a transformation upon a figure.
Students will learn to predict the effect of a transformation upon a given figure, find
transformations or sequences of transformations that map one figure onto another.
Learning Targets
Domain: Congruence
Cluster: Experiment with transformations in the plane
Standard#:
G-CO.2
G-CO.3
G-CO.4
Standard:
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 rectangle, parallelogram, trapezoid, or regular polygon, describe
the rotations and reflections that carry it onto itself.
Develop definitions of rotations, reflections, and translations in terms of
angles, circles, perpendicular lines, parallel lines, and line segments.
G-CO.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.
Cluster: Understand congruence in terms of rigid motions
G-CO.6
G-CO.7
Use geometric descriptions of rigid motions to transform figures and to
predict the effect of a given rigid motion on a given figure; given two figures,
use the definition of congruence in terms of rigid motions to decide if they
are congruent.
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.
G-CO.8
Explain how the criteria for triangle congruence (ASA, SAS, and SSS)
follow from the definition of congruence in terms of rigid motions.
Domain: Similarity, Right Triangles, & Trigonometry
Cluster: Understand similarity in terms of similarity transformations
Standard#:
Standard:
Verify experimentally the properties of dilations given by a center and a
G-SRT.1
scale factor:
Given two figures, use the definition of similarity in terms of similarity
G-SRT.2
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.
G-SRT.3
Use the properties of similarity transformations to establish the AA criterion
for two triangles to be similar.
Unit Essential Questions:
Unit Enduring Understandings:
 What types of transformations
 Rigid motions: translation, reflection, rotation and
are rigid motions?
glide reflection
 Dilations
 How can you represent a
 Reflectional and rotational symmetry
transformation in the coordinate
 Compositions of Transformations
plane?
 Congruence and Similarity Transformations
 How do recognize symmetry in
a figure?
 What does it mean for two
figures to be congruent? To be
similar?
 Which sequence of
transformations can map one
figure onto the other?
Unit Objectives:
 Students will be able to identify rigid motions and images
 Students will be able to describe transformations in the coordinate plane
using function notation.
 Students will be able to translate, reflect, rotate and dilate a figure using a
variety of tools
 Students will be able to identify reflectional or rotational symmetry of a figure
if it exists.
 Given congruent figures or similar figures, students will be able to find a
sequence of transformations that moves one figure onto the other
Evidence of Learning
Formative Assessments:
 SMART Response questions at the end of each section throughout the unit.
 2 Labs
 2 Quizzes
Summative Assessment:
 Performance Task
 Unit Test
Lesson Plan
Topics
Topic #1: Transformations
Topic #2: Translations
Lab: Reflections Activity
Topic #3: Reflections
Lab: Rotations Activity
Topic #4: Rotations
Quiz 1: Reflections and Translations
Topic #5: Composition of Transformations
Topic #6: Congruence Transformations
Topic #7: Dilations
Topic #8: Similarity Transformations
Quiz 2: Rotations and Glide Reflections
Unit Review
Performance Task / Unit Test
Curriculum Resources
https://njctl.org/courses/math/geometry/
Video: Drawing Reflections Demo
Video: Drawing Rotations Demo
Class Periods
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