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Coordinate Plane Transformations

Grade Focus
Grade 6, Grade 7, Grade 8, Grade 9, Grade 10, Grade 11, Grade 12
Age Level
11, 12, 13, 14, 15, 16, 17
Subject
Math
Technology Integration Activity
Digital Ethics, Imaging
Estimated Time of Completion
2-3 days
Author: Chris Jones, Virginia Beach City Public Schools Last modified: 05/01/2010

Coordinate Plane Transformations

Downloads for this lesson plan

Introduction

High school geometry students will superimpose real-world images on to a coordinate plane, then transform them (translation, rotation, dilation, and reflection).  The students will create an activity to share with middle school students.  Middle school students will plot given points, determine the type of transformation that took place, and then discuss results with the high school creators via a Skype video conference. 

Prerequisite Experience

Prerequisite Knowledge for High School Students:

·       Manipulating images using technology

·       Plotting points on a coordinate plane

Prerequisite Knowledge for Middle School Students:

·       Plotting ordered pairs on a coordinate plane

·       Identifying transformations

Prerequisite Knowledge for Teachers:

·       Sharing information through a collaborative workspace such as Sharepoint and Google Docs

·       Video conferencing using Skype

·       Manipulating images in Microsoft Word

·       Emailing attachments

Teacher Prep Time

1 hour (this includes time to accomplish the following tasks):

·       Make copies of any handouts (middle school teachers only)

·       Obtain a laptop and ensure Skype is downloaded and in working condition.

·       Obtain a webcam for the video conference

·       Email activities to the middle school teacher (high school teachers only)

Project

Middle school students will plot points on a coordinate plane given to them by high school students.  Based on the information provided by the high school students, the middle school students will determine the type of transformation that the high school students modeled and guess the name of the image that was transformed.  Students will discuss their results with each other through a video conference using Skype.

Assessment/Grading

Rubric

Time Management Tips

High School Teachers:

·       1-2 days prior to video conferencing, share the assignment guidelines with students via a collaborative workspace such as Sharepoint.

·       Allow students time to research the types of transformations, locate, capture, and manipulate an image to transform on a coordinate plane.

·       High school teachers, email the activities students create to the middle school teachers no later than 1 day before the video conference.          
  • This will ensure that there is enough time to communicate with the middle school teacher on grouping strategies for the conference. 

 Middle School Teachers:

·       1 day before video conferencing, obtain the activities created by the high schoolers.  Group students into groups of 2-3 and distribute one activity to each group.  

·       Allow the groups 15-20 minutes to complete the activity by plotting the given points.

Lesson Plan Details

Engage

 

  • Show students several real world images that have been transformed: translated, rotated, dilated, and reflected.
  • Ask students to describe what they think happened to each image.  Discuss ideas.
  • Show the same images again, with a coordinate plane superimposed over each image.  Ask students to describe, again, what they think happened to each figure using the coordinate plane as a point of reference.
  • Use student ideas to introduce vocabulary:
    • Translation
    • Rotation
    • Reflection
    • Dilation
  • Distribute copies of the assignment via a collaborative web space such as Sharepoint, or use hard copies if an online workspace is unavailable.
  • Review the guidelines and expectations with the students.
  • Tell students that they will be researching the various types of transformations, creating their own transformations with real-world images, and then generating an activity that they will share with middle school students. 

 

 

Explore

  • Allow students time to research the 4 types of transformations.
  • Students should choose a real world image and use the copy/paste and layout tools in Microsoft word to transform their images over the coordinate plane.
  • Students should create an answer key that displays the points of the pre-image and post-image along with hints as to the name of the object that was transformed.  These will be shared with middle school students. 

Explain

  • Students should develop a translation rule
    • Ex: (x + 2, y -1) 
  • Students should develop a rotation rule
    • Ex: rotate 90 degrees clockwise about the origin
  • Students should develop a reflection rule
    • Ex: reflect about the x-axis
  • Students should develop a dilation rule
    •  Ex: (2x, 3y)

Elaborate

After high school students have researched and generated original transformations of real world figures they should:

  • Create a set of instrucions for plotting the coordinates of the pre-image and post-image.
  • Offer a list of hints for determining the name of the original figure that was transformed.
    • These will be shared with middle school students.

After middle school students have receievd the above activities, students should:

  • Plot the given points.
  • Identify the type of transformation.
  • Describe the rule for the type of transformation.
  • Hypothesize the name of the figure that was transformed.

Evaluate

High school students will be graded based upon criteria defined in a rubric.  The following criteria will be used to evaluate and assess students:

·       Mathematical Understanding: Student displays a clear, in-depth understanding of all types of transformations.  

·       Images:  Images are accurately transformed on the coordinate plane with no mistakes. 

·       Creativity:  A unique and creative approach to choosing images to transform.  Information is presented in a unique and viewer-friendly manner.  Extra & informative details are included.

·       Discussion:  All students hold a confident & professional discussion appropriate to the assignment.  Students guide thinking rather than reveal answers in a straightforward manner.  The discussion does not stray from the topic of transformations.  Misconceptions are recognized & addressed with a clear explanation. 

 

 Middle school students will be graded based upon criteria defined in a rubric.  The following criteria will be used to evaluate and assess students:

 

·       Mathematical Understanding:  Students have a strong understanding of accurately locating points on the coordinate plane.  Students accurately identify the transformation.

·       Discussion:  Students hold a confident & professional discussion appropriate to the assignment.  Students accurately express their knowledge verbally and convey their ideas clearly.  Misconceptions are recognized & addressed with a clear explanation.  All group members participate in the discussion.

Provide students with a copy of the rubric when this project is introduced so that they are familiar with the expectations for succeeding in this assignment.  Before submitting their final products, have students reflect on the rubric and circle the scores that they feel best describe their final work products. 

Extend

  •  After high school students have researched transformations and created four transformed figures along with directions for plotting the images, hold a video conference with middle school students.

    ·       High school teachers should email the final projects for the middle school teachers to print and distribute to their students.

    ·       Middle school teachers will have their students plot the given points and identify the various transformations.

    ·       Middle school students will come to the webcam one group at a time to discuss their results with the group that created their assignment.  High school students should be able to accurately discuss whether or not the middle school students correctly plotted and transformed the images.  The teacher will then reveal the true solution to check student work.  Students should discuss any questions or misconceptions that occurred when completing the assignment.