Translations, Reflections, and Rotations

Abstract

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

The activities and discussions in this lesson address the following NCTM standards:

Geometry

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

  • precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties
  • understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects
  • create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship
Apply transformations and use symmetry to analyze mathematical situations
  • describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling
  • examine the congruence, similarity, and line or rotational symmetry of objects using transformations
Links to other standards.

Student Prerequisites

  • Arithmetic: Students must:
    • 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 such as Netscape for experimenting with the activities

Teacher Preparation

Students will need:

Lesson Outline

  1. Focus and Review

    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.

  2. 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 talk about these ideas and show you a little about this program first.

  3. 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.

  4. Guided Practice

    • After answering all questions that the students might have regarding the use of The TransmoGrapher, pass out the Translations, Reflections, and Rotations Worksheet .

    • 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.

  5. 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.

  6. Closure

    You may wish to bring the class back together for a discussion of the findings. 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 Outlines

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.

Suggested Follow-Ups or Extensions

This lesson can be followed by: