This lesson is designed to introduce students to translations, reflections, and rotations.

Objectives

Upon completion of this lesson, students will:

have been introduced to the concepts of translation, reflection, and rotation.

have practiced translating, reflecting, and rotating two-dimensional objects on the coordinate plane.

Standards Addressed:

Grade 10

Geometry

The student demonstrates an understanding of geometric relationships.

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

The student demonstrates understanding of position and direction when solving problems (including real-world situations).

The student demonstrates a conceptual understanding of geometric drawings or constructions.

Grade 3

Geometry

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

The student demonstrates understanding of position and direction.

The student demonstrates a conceptual understanding of geometric drawings or constructions.

Grade 4

Geometry

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

The student demonstrates understanding of position and direction.

The student demonstrates a conceptual understanding of geometric drawings or constructions.

Grade 5

Geometry

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

The student demonstrates understanding of position and direction.

The student demonstrates a conceptual understanding of geometric drawings or constructions.

Grade 6

Geometry

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

The student demonstrates understanding of position and direction.

Grade 7

Geometry

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

The student demonstrates understanding of position and direction.

Grade 8

Geometry

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

The student demonstrates understanding of position and direction.

Grade 9

Geometry

The student demonstrates an understanding of geometric relationships.

The student demonstrates conceptual understanding of similarity, congruence, symmetry, or transformations of shapes.

The student demonstrates understanding of position and direction when solving problems (including real-world situations).

The student demonstrates a conceptual understanding of geometric drawings or constructions.

Eighth Grade

Geometry

Understand congruence and similarity using physical models, trans- parencies, or geometry software.

Geometry

Congruence

Experiment with transformations in the plane

Understand congruence in terms of rigid motions

Grades 6-8

Geometry

Apply transformations and use symmetry to analyze mathematical situations

Grades 9-12

Geometry

Apply transformations and use symmetry to analyze mathematical situations

Use visualization, spatial reasoning, and geometric modeling to solve problems

Pre-Calculus

Number and Operations

Competency Goal 1: The learner will describe geometric figures in the coordinate plane algebraically.

Technical Mathematics I

Algebra

Competency Goal 3: The learner will describe the transformation of polygons in the coordinate plane algebraically.

Geometry and Measurement

Competency Goal 2: The learner will measure and apply geometric concepts to solve problems.

Technical Mathematics II

Geometry and Measurement

Competency Goal 1: The learner will use properties of geometric figures to solve problems.

3rd Grade

Geometry

The student will demonstrate through the mathematical processes an understanding of the connection between the identification of basic attributes and the classification of two-dimensional shapes.

4th grade

Geometry

Standard 4-4: The student will demonstrate through the mathematical processes an understanding of the relationship between two- and three-dimensional shapes, the use of transformations to determine congruency, and the representation of location and movement within the first quadrant of a coordinate system.

5th grade

Geometry

The student will demonstrate through the mathematical processes an understanding of congruency, spatial relationships, and relationships among the properties of quadrilaterals.

6th Grade

Geometry

The student will demonstrate through the mathematical processes an understanding of shape, location, and movement within a coordinate system; similarity, complementary, and supplementary angles; and the relationship between line and rotational symmetry.

Intermediate Algebra

Algebra

The student will demonstrate through the mathematical processes an understanding of functions, systems of equations, and systems of linear inequalities.

4th Grade

Geometry

4.17.c The student will investigate congruence of plane figures after geometric transformations such as
reflection (flip), translation (slide) and rotation (turn), using mirrors, paper
folding, and tracing.

5th Grade

Geometry

5.15a The student, using two-dimensional (plane) figures (square, rectangle, triangle, parallelogram, rhombus, kite, and trapezoid) will recognize, identify, describe, and analyze their properties in order to develop definitions of these figures

5.15e The student, using two-dimensional (plane) figures (square, rectangle, triangle, parallelogram, rhombus, kite, and trapezoid) will recognize the images of figures resulting from geometric transformations such as
translation (slide), reflection (flip), or rotation (turn).

7th Grade

Geometry

7.13 The student, given a polygon in the coordinate plane, will represent transformations - rotation and translation - by graphing the coordinates of the vertices of the transformed polygon and sketching the resulting figure.

8th Grade

Geometry

8.8 The student will apply transformations (rotate or turn, reflect or flip, translate or slide, and dilate or scale) to geometric figures represented on graph paper. The student will
identify applications of transformations, such as tiling, fabric design, art, and scaling.

Reason for Alignment: The Translations, Reflections, and Rotations lesson contains a discussion of the basics of transformations, along with a good worksheet that could be used as a supplement to the text.

Student Prerequisites

Arithmetic: Student must be able to:

be able to identify the basic two-dimensional shapes of a square, a triangle, and a parallelogram.

have a small amount of knowledge about the cartesian coordinate system.

Technological: Students must be able to:

perform basic mouse manipulations such as point, click and drag

use a browser for experimenting with the activities

Teacher Preparation

Access to a browser

Pencil and paper

Access to a calculator (optional)

Copies of supplemental materials for the activities:

Remind students what has been learned in previous lessons that will be pertinent to this lesson
and/or have them begin to think about the words and ideas of this lesson:

Can someone tell me where you might see a reflection in everyday life? Students may point out
that we see our reflection in a mirror or in a still pond.

Can anyone tell me what it means to rotate an object? Students may describe this as turning an
object.

Can anyone guess what it might mean to translate an object? Students may not have an answer to
this question, in which case you may let them know that they will learn what it means to
translate an object in today's lesson.

Objectives

Let the students know what it is they will be doing and learning today. Say something like this:

Today, class, we will learn what translations, reflections, and rotations are to a
mathematician.

We are going to use the computers to learn about these three concepts, but please do not turn
your computers on or go to this page until I ask you to. I want to talk about these ideas and
show you a little about this program first.

Teacher Input

First, entertain a discussion about translations, reflections, and rotations with the class. You
have a couple of options of how to do this:

Explain to the students how to do the assignment. You should model or demonstrate it for the
students, especially if they are not familiar with how to use the computer applets on the
Project Interactivate site.

Open your browser to
The TransmoGrapher in order to demonstrate this activity to the students.

Show the class how to choose the shape they wish to translate, rotate, or reflect using the
buttons at the top of the applet.

Explain that they must pay close attention to the color of each side of the shape in order to
see that the shape has been rotated, translated, or reflected.

Show the class how to enter a distance to translate, a degree by which to rotate, or a line of
symmetry over which to reflect the object.

Walk the students through the first problem on the sheet. Help them by reminding them as you
walk around the room what "rotate", "fourth quadrant", and "reflect" mean. Predict what they
should see by drawing it on the board before the students try the steps.

If the students needed a lot of help with the first problem, walk them through the second
problem on triangles as well.

Independent Practice

Allow the students to work on their own and to complete the worksheet, should you choose to
provide one. Monitor the room for questions and to be sure that the students are on the
correct web site.

Have each student choose a figure and apply 2 transformations to it (noting what he or she
did). Then have students change places and try to determine how to undo each transformation.

Closure

Allow students to explain the concepts of translation, reflection, and rotation. The students
should share about the places where the activity was difficult. Ensure that all students
understand the three concepts before moving on to another lesson.

Alternate Outline

This lesson can be rearranged in several ways.

When discussing and explaining the concepts of translation, reflection, and rotation, students
may choose to physically act out the movements in order to understand them better.

You may invent your own way of using this lesson to suit the needs of your students.