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Transformations

Lesson Plan

Transformations

Objectives

In this lesson, students are going to learn about the rigid transformations. Students will: [IS.2 - Struggling Learners and ELL Students]

  • translate a geometric figure in the coordinate plane.
  • rotate a geometric figure.
  • reflect a geometric figure.

Essential Questions

  • How can you use coordinates and algebraic techniques to represent, interpret, and verify geometric relationships?

Vocabulary

  • Clockwise: Motion that proceeds as the hands of a clock, from the top to the right, then down and to the left, and back to the top. [IS.1 - Preparation]
  • Counterclockwise: Motion that proceeds in the opposite direction from clockwise; from the top to the left, then down and to the right, and back to the top.
  • Geometric Figure: Any combination of points, lines, planes.
  • Polygon: A closed-plane figure consisting of points called vertices and segments called sides, which have no common point except for end points. A polygon is convex if each interior angle is less than 180 degrees. A polygon is concave if it is not convex.
  • Reflection: In a line, replacing each point in the reflected configuration by a point symmetric to the given point with respect to the line; in a plane, replacing each point in the reflected configuration by point symmetric to the given point with respect to the plane.
  • Rigid: An ideal body such that the distance between every pair of points of the body remains unchanged.
  • Rotation: Rigid motion about a line or a point; for a point, rigid motion in a circular path, in a plane about the point. Rotation about a line is of a kind such that every point in the figure moves in a circular path about the line in a plane perpendicular to the line.
  • Transformation: A passage from one figure or expression to another as a correspondence or mapping of one space on another or on the same space.
  • Translation: In Euclidean geometry, the moving of every point a constant distance in a specified direction.

Duration

90–120 minutes/1–2 class periods [IS.3 - All Students]

Prerequisite Skills

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Materials

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Formative Assessment

  • View
    • The Connect the Dots Activity assesses student performance on transferring ordered pairs to correct coordinate locations, and understanding and selecting appropriate transformations to follow specific directional instructions.
    • The Partner Narrating Activity assesses listening skills and using listening to transfer ordered pair data to locations on the coordinate plane. Some students will show greater skill using auditory numerical information than using written numerical data, and vice versa.
    • The Lesson 2 Exit Ticket assesses students’ ability to use transformations and discriminate between specific transformations to make appropriate selections.

Suggested Instructional Supports

  • View
    Active Engagement, Explicit Instruction
    W: This lesson begins with an enjoyable review of plotting coordinates in the coordinate plane. Students soon realize that they only have half of the picture. In today’s lesson they learn how to take the given coordinates and change them to complete the picture. They have probably heard the words reflect and rotate, so the familiarity of the language may pique their interest as well as the question of why they need to know these words in mathematics.  
    H: Most students have seen or used coloring books as well as color-by-numbers activities. Today the lesson begins with a sort of “connect-the-dots” activity. Students are curious as to what the coordinates are going to create in the coordinate plane. When they realize that it doesn’t make a complete picture, they know they have to pay attention in order to figure out how to complete the image later on. 
    E: The graphic organizer is a great way for students to improve their note-taking skills. Having filled it out, they are then in possession of the information they need to complete today’s narrating activity. Students are paired up and describe to one another what transformations need to be made to get from one image to the next. They must be careful with how they describe the transformations, and they have to use details in order for their partner to figure out what to draw.  [IS.7 - All Students]
    R: Students learn best when they are able to teach and describe what they are learning. Today’s activity forces students to think about the language they use when describing transformations of geometric figures in the coordinate plane. [IS.8 - All Students] They have to know the difference between reflection and rotation in order for their partner to draw the correct image. When students think they have a complete picture, they must look and see how close they were to the original figure and its image. This activity is similar to the telephone game. Sometimes what someone sees or hears is different from what is said. This activity gives students many opportunities to revise and refine their thought processes relating to transformations.  
    E: When students turn around and see what they were supposed to have drawn and what their partner actually drew, they have to evaluate the language they used in their narration. They may need to have their graphic organizer out so that they don’t confuse any of the vocabulary. Students who are listening also have to make sure that they aren’t hearing one thing and doing another.  
    T: All students have opportunities to master the material in this lesson. The opening activity and the graphic organizer involve visual learning. The narrating activity is great for the auditory learner, and the extension activity is perfect for the kinesthetic learner. 
    O: This lesson has an engaging review activity (plotting coordinates in the plane) to begin introducing new material. Students likely know the words reflection and rotation. This part of the lesson puts the words to use as concepts that are quantified. The lesson has good transitions from the opening activity to taking notes to the partner activity to ending the class with completing the opening activity.  

     

    IS.1 - Preparation
    Consider using graphic organizers (e.g., Frayer Model, Verbal Visual Word Association, Concept Circles) to review key vocabulary prior to or during the lesson. Consider posting these words son a word wall in the classroom and/or having students keep vocabulary notebooks with “student friendly definitions”  
    IS.2 - Struggling Learners and ELL Students
    For struggling students or ELL students , be sure they have an understanding of these terms- allow them to manipulate objects or paper figures to understand these terms.  
    IS.3 - All Students
    Consider pre-teaching the concepts critical to this lesson, including the use of hands-on materials. Throughout the lesson (based upon the results of formative assessment), consider the pacing to be flexible to the needs of the students. Also consider the need for re-teaching and/or review both during and after the lesson as necessary.  
    IS.4 - Struggling Learners and ELL Students
    Consider assessing student background knowledge as struggling students and/or students who are ELLs may have difficulty understanding this or connecting this to prior learning. Be certain to help all groups of learners make connections and see value in this learning intention.  
    IS.5 - All Students
    Consider having these students assigned as partner   pairs ahead of time to save time during the lesson. Review partner work and norms of working with partners prior to this activity. This will be helpful for all learners.  
    IS.6 - All Students
    As an exit ticket activity, use this information as formative assessment and as focus for review, re-teaching or reinforcement if necessary for all students.  
    IS.7 - All Students
    Partnering activities are important to help all students stay engaged during a lesson.  
    IS.8 - All Students
    Working together is an excellent way to collect data for self and peer assessment of learning activities for all students.  

Instructional Procedures

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    Part 1

    Hand out the Connect the Dots Activity (M-G-5-2_Connect the Dots Activity.doc and M-G-5-2_Connect the Dots Activity KEY.doc). Make sure students use colored pencils or markers. Discuss the questions on the worksheet with the class and then hand out the Lesson 2 Graphic Organizer (M-G-5-2_Lesson 2 Graphic Organizer.doc and M-G-5-2_Lesson 2 Graphic Organizer KEY.doc). “Look at the title of your graphic organizer. What do you think ‘Rigid Transformations’ means?” Hopefully students know what it means for something to be rigid and what it means for something to transform. [IS.4 - Struggling Learners and ELL Students]

    Part 2

    Pair students up and have one student sit with his/her back to the whiteboard with the other student sitting across (facing the whiteboard). Place the Partner Narrating Activity (M-G-5-2_Partner Narrating Activity.doc) on the overhead or document camera (only showing one at a time). [IS.5 - All Students] Use the Narrating Activity Grid (M-G-5-2_Narrating Activity Grid.doc) to create coordinate templates. “The partner facing the board is going to describe to the other partner who has his/her back to the board what to draw to begin with and what transformations need to be done to get to the final image. Make sure you use details, such as the coordinates, to help your partner get a good idea of what to draw. When you think you are done, check your partner’s drawing and describe any confusions or differences in the pictures. Then switch places. You will each get to draw twice.” It doesn’t matter what students think is the original figure and what is the image. They can start with either one and then narrate to get to the other.

    Part 3

    For an exit ticket activity, have students list what the coordinates of the left-side of the butterfly in the Connect the Dots Activity would be if they were to complete the picture. (Change the x-values to negative and have the same y-values.) Then have them reflect the butterfly over the line y = 11 and have them label the new coordinates. [IS.6 - All Students]

    Extension:

    • If students catch on quickly to this lesson and there is time, they can play a game similar to Battleship. Give them a copy of the Extension Activity (M-G-5-2_Lesson 2 Extension Activity.doc). Students draw a circle, a square, a rectangle, an equilateral triangle and an isosceles triangle on their top grid. They then have to guess the coordinates/location of their partner’s shapes. Their partner needs to tell them “hit” or “miss” for the coordinates and then give hints as to how to rotate, translate, or reflect their shapes. When one person has mapped the shapes of the other person, s/he wins.

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DRAFT 10/13/2011
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