<p>In this lesson, students will learn about rigid transformations. Students will:<br>- translate geometric figures in the coordinate plane.<br>- rotate a geometric figure.<br>- reflect a geometric figure.</p>

<p>- How can you use coordinates and algebraic approaches to represent, interpret, and validate geometric relationships?</p>

<p>- 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.<br>- 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.<br>- Geometric Figure: Any combination of points, lines, planes.<br>- Polygon: A closed-plane figure consisting of points called <i>vertices</i> and segments called <i>sides</i>, 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.<br>- 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.<br>- Rigid: An ideal body such that the distance between every pair of points of the body remains unchanged.<br>- 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.<br>- 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.<br>- Translation: In Euclidean geometry, the moving of every point a constant distance in a specified direction.</p>

<p>- graph paper<br>- colored pencils/markers<br>- Connect the Dots Activity (M-G-5-2_Connect the Dots Activity and KEY)<br>- Lesson 2 Graphic Organizer (M-G-5-2_Lesson 2 Graphic Organizer and KEY)<br>- Partner Narrating Activity (M-G-5-2_Partner Narrating Activity)<br>- Narrating Activity Grid (M-G-5-2_Narrating Activity Grid)<br>- Lesson 2 Extension Activity (M-G-5-2_Lesson 2 Extension Activity)</p>

<p>- The Connect the Dots Activity evaluates student performance in transferring ordered pairs to the correct coordinate locations, as well as understanding and selecting appropriate transformations to follow precise directed instructions.&nbsp;<br>- The Partner Narrating Activity tests listening skills and using listening to transfer ordered pair data to locations on the coordinate plane. Some students will perform better with auditory numerical information than written numerical data, and vice versa.&nbsp;<br>- The Lesson 2 Exit Ticket evaluates students' abilities to use transformations and differentiate between specific transformations in order to make suitable choices.</p>

<p>Active Engagement, Explicit Instruction<br>W: The lesson starts with a fun review of graphing coordinates on the coordinate plane. Students quickly realize they only have half the picture. In today's lesson, students will learn how to take the given coordinates to complete the picture. They've probably heard the terms <i>reflect</i> and <i>rotate</i> before, so the familiarity of the terminology may stimulate their curiosity, as well as the question of why they need to know these words in mathematics.&nbsp;<br>H: Most students are familiar with coloring books and color-by-number activities. Today the lesson begins with a "connect-the-dots" activity. Students are curious about what the coordinates will create in the coordinate plane. When students understand it doesn't make a complete picture, they know they need to pay attention in order to find out how to complete it later.&nbsp;<br>E: The graphic organizer helps students enhance their note-taking skills. After filling it out, students will have the necessary information to complete today's narrating activity. Students are paired up and describe the transformations required to move from one image to the next. They must be careful in how they describe the transformations and use details so that their partner knows what to draw.&nbsp;<br>R: Effective learning requires students to be able to teach and describe what they are learning. Today's activity challenges students to consider the vocabulary they use to describe transformations of geometric figures in the coordinate plane. To ensure that their partner draws the correct image, they must understand the difference between reflection and rotation. When students believe they have a complete picture, they must look and see how close they were to the original figure. This exercise is similar to the telephone game. Sometimes what someone sees or hears is different from what is said. This activity provides numerous opportunities for students to modify and develop their thought processes relating to transformations.&nbsp;<br>E: When students compare their drawings to their partner's, they must evaluate the language used in the narration. They may need to utilize their graphic organizer to avoid confusion with the vocabulary. Students who are listening must also ensure that they are not hearing one thing while acting on another.&nbsp;<br>T: All students can master the material in this lesson. The opening activity and graphic organizer need visual learning. The narrating activity is great for auditory learners, while the extension activity is ideal for kinesthetic learners.&nbsp;<br>O: This lesson begins with an entertaining review practice (plotting coordinates in the plane) before introducing new content. 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 contains good transitions from the beginning activity to taking notes, the partner activity, and finally completing the opening activity.<br>&nbsp;</p>

<p><strong>Part 1</strong></p><p>Distribute the Connect the Dots Activity (M-G-5-2_Connect the Dots Activity and KEY). Make sure that students use colored pencils or markers. Discuss the worksheet questions with the class, then distribute the Lesson 2 Graphic Organizer (M-G-5-2_Lesson 2 Graphic Organizer and KEY). <strong>"Check out the title of your graphic organizer. What do you think 'Rigid Transformations' means?"</strong> Hopefully, students understand what it means for something to be rigid and what it means for something to transform.</p><p><strong>Part 2</strong></p><p>Pair students and have one sit with his or her back to the whiteboard, while the other sits across (facing the whiteboard). Place the Partner Narrating Activity (M-G-5-2_Partner Narrating Activity) in the overhead or document camera (only one at a time). To construct coordinate templates, use the Narrating Activity Grid (M-G-5-2_Narrating Activity Grid). <strong>"The partner facing the board will tell to the partner with his or her back to the board what to draw first and what changes are required to get to the final image. Make sure to use details, such as the coordinates, to help your partner understand what to draw. When you think you're finished, go over your partner's drawing and explain any confusions or differences in the pictures. Then switch places. You'll each get to draw twice."</strong> It makes no difference what students think is the original figure or image. They can begin with any one and then narrate to get to the other.</p><p><strong>Part 3</strong></p><p>For an exit ticket activity, have students write out the coordinates of the left side of the butterfly in the Connect the Dots Activity if they were to complete the picture. (Change the <i>x</i>-values to negative and keep the same <i>y</i>-values.) Then have them reflect the butterfly over the line <i>y</i> = 11, labeling the new coordinates.</p><p><strong>Extension:</strong></p><p>If students understand this lesson fast and have enough time, they can play a game similar to Battleship. Provide a copy of the Extension Activity (M-G-5-2_Lesson 2 Extension Activity). Students create circles, squares, rectangles, equilateral triangles, and isosceles triangles on their top grid. They must then guess the coordinates and location of their partner's shapes. Their companion must tell them if the coordinates were "hit" or "miss" and then provide ideas on how to rotate, translate, or reflect their shapes. When one person has mapped the other person's shapes, they win.</p>