<p>In this lesson, students will use dilation factors on a geometric figure on the coordinate plane. The students will:&nbsp;<br>- stretch geometric figures by multiplying their coordinates by a factor greater than 1.&nbsp;<br>- shrink geometric figures, multiply their coordinates by a factor between 0 and 1.</p>

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

<p>- <strong>Dilation:</strong> A linear transformation that enlarges or shrinks objects by a scale factor that is the same in all directions.&nbsp;<br>- <strong>Parallel Lines:</strong> Equidistant, apart; if two lines are cut by a transversal, and the sum of the interior angles on one side of the transversal is less than a straight angle, the two lines will meet if produced, and will meet on that side of the transversal. Only one line can be drawn parallel to a given line through a given point not on the line.<br>- <strong>Perpendicular Lines:</strong> Two lines are perpendicular to each other if, in a plane, the slope of one of the lines is the negative reciprocal of the other; two straight lines that intersect such that they form a pair of equal adjacent angles.<br>- <strong>Polygon:</strong> 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 or equal to 180 degrees. A polygon is concave if it is not convex.<br>- <strong>Scale Factor:</strong> The multiple by which a geometric object is enlarged or reduced; scale factors &gt;1 enlarge the linear dimensions of the object and scale factors &lt;1 reduce the linear dimensions of the object.<br>- <strong>Shrink:</strong> To become smaller in size; in geometry, a dilation with a scale factor &lt; 1.<br>- <strong>Slope:</strong> The angle of inclination; for a straight line, the tangent of the angle that the line makes with the positive x-axis.<br>- <strong>Stretch:</strong> To make something wider or longer; in geometry, a dilation.<br>- <strong>Transformation:</strong> A passage from one figure or expression to another as a correspondence or mapping of one space on another or on the same space.</p>

<p>- One of These Things is Not Like the Other (M-G-5-3_One of These Things)<br>- Lesson 3 Graphic Organizer (M-G-5-3_Lesson 3 Graphic Organizer and KEY)&nbsp;<br>- Lesson 3 Exit Ticket (M-G-5-3_Lesson 3 Exit Ticket and KEY)<br>- colored pencils<br>- rulers<br>- graph paper</p>

<p>- The One of These Things Is Not Like the Other activity encourages students to separate the specific characteristics of shapes in a more general way than simply identifying which object is out of place. Because the characteristics of shapes include color, which is not affected by dilation, students must reason from the specific to the general in order to apply the scale factor, dilate, and evaluate the results.&nbsp;<br>- Student responses to the exit ticket activity will differ depending on their choice of shape, number of sides and vertices, length of sides, and location. First, conduct a qualitative review of the results: Is the scale factor 3 drawing larger or smaller than the original? Is the scale factor \(3 \over 4\) drawing larger or smaller than the original? Has the student used the scale factor consistently in all directions?<br>&nbsp;</p>

<p>Active Engagement, Explicit Instruction<br>W: This lesson teaches students about dilations, which are used to increase or decrease the size of shapes in the coordinate plane. They must learn about dilations because nothing is perfect on the first try. If students want to be cartoonists or animators, they must understand how to scale characters larger or smaller to fit the screen and the appropriate situation. Students must multiply coordinates by a value greater than 1 to make an object larger, or by a number between 0 and 1 to make an object smaller.&nbsp;<br>H: When discussing Sesame Street, students should be interested in the lesson's progression. Whether or not students have directly experienced it, they grasp the concept of things being out of place. They learn how to change the size of objects in the coordinate plane by multiplying the coordinates by a factor.&nbsp;<br>E: Students use the graphic organizer to learn about the topic before engaging in partner activities to explore it. This allows them to make mistakes and learn from those mistakes before proceeding to the individual exit ticket.&nbsp;<br>R: Working in pairs and having discussions about the topics allows students to learn how others process information and solve problems. This permits students to clarify any misconceptions regarding the content. Following the partner activity, students review their work in groups of four to revise it before it is collected.&nbsp;<br>E: Collaborating with partners allows students to review their work and make sure they are on the right track with the content. They check each other's arithmetic and ensure that they are plotting coordinates appropriately on the plane.&nbsp;<br>T: This lesson can be modified to each learner. It can be set to a slower pace to practice multiplication of whole numbers with fractions. It can be used to study plotting points in the coordinate plane. If students have already mastered these two skills, this lesson will not be too difficult. For students who may be exceeding the standards, the class can explore what negative dilation factors do to an image.&nbsp;<br>O: This lesson starts with an interesting topic (Sesame Street), progresses to a graphic organizer that students use during their partner activity, and then concludes with an individual exit ticket. The transition between activities is simple, and there is an extension exercise if students need more practice with dilations.</p>

<p><strong>"How many of you have seen </strong><i><strong>Sesame Street</strong></i><strong>?"</strong> Explain a little bit about the show to students. <strong>"There is a character named Grover who sings the song 'One of These Things is Not Like the Other.' I'm going to show you some pictures and you have to tell me which object does not belong and why it does not belong."</strong> Place the One of These Things activity sheet (M-G-5-3_One of These Things) in front of an overhead or document camera. Students have two options for #1. The blue square does not belong because it is the only one that is not red; similarly, the large square does not belong because it is not small. Students have two options for #2. The small face doesn't belong because it isn't big, and the teary face doesn't belong because it's not smiling. <strong>"Let's say we can't change the color or the face. What could we do so that we go from two objects not belonging to only one object?” </strong>Give students time to think. <strong>"Well, how can we do that?"</strong> Hopefully, students will say make the large square smaller and the small face larger.</p><p><strong>"Today, we will study how to make geometric figures larger or smaller in the coordinate plane. How many of you have seen an eye doctor before?"</strong> Allow the students to reply. <strong>"How many of you have had your pupils dilated for medical reasons? Does anyone know what it means for the pupils of your eyes to dilate?"</strong> Allow students to raise their hands and engage in a discussion regarding eye dilation. A similar discussion may include camera lenses that can be adjusted to allow more or less light in. <strong>"To allow the doctor to examine your eyes, certain drops are placed in your eyes, forcing your pupils (the black part of your eye) to remain open. So when you look at someone who has recently had his or her eyes dilated, the pupils are larger than usual. Today we will understand what dilation means in geometry."</strong></p><p>Hand out the Lesson 3 Graphic Organizer (M-G-5-3_Lesson 3 Graphic Organizer and KEY) and have students complete it.</p><p><strong>Part 1</strong></p><p>Students will be paired up and given four sheets of graph paper. Each student makes his or her own artwork using geometric figures. Tell students to keep things simple. For example, consider a house made up of a large square, a triangle for the roof, a rectangle for the door, and four square windows. When students have finished their pictures, they exchange them with their partner. They then use another piece of graph paper to dilate the picture by a factor of 3. When they're finished, have the pairs check each other's work. Then they design another picture and switch it. This time, they must dilate the picture by a \(1 \over 4\) (or \(1 \over 2\)). If there is time, students can perform it again, but this time dilate half of the shapes by a factor greater than one and the other half by a factor between 0 and 1. Display students' work in the classroom.</p><p><strong>Part 2</strong></p><p>Distribute the Lesson 3 Exit Ticket (M-G-5-3_Lesson 3 Exit Ticket and KEY) to determine whether students comprehend the dilation concept.</p><p><strong>Extension:</strong></p><p>Draw a birds-eye view diagram of your classroom. Direct students to measure objects around the room before measuring the ones in the diagram. They must determine the dilation factor of each object. For example, if their desk is 24 inches wide and the diagram shows a 1 inch wide desk, the dilation factor is \(1 \over 24\).&nbsp;<br>When students grasp a positive dilation factor, ask them what happens if the dilation factor is -2 or -\(1 \over 2\). After using a factor of -2, they can complete the exit ticket by determining the coordinates of their figure's image.</p>