Dilations
Dilations
Objectives
In this lesson, students will apply dilation factors to a geometric figure in the coordinate plane. Students will:
- stretch geometric figures by multiplying the coordinates by a factor greater than 1.
- shrink geometric figures by multiplying the coordinates by a factor between 0 and 1.
Essential Questions
- How can you use coordinates and algebraic techniques to represent, interpret, and verify geometric relationships?
Vocabulary
- Dilation: A linear transformation that enlarges or shrinks objects by a scale factor that is the same in all directions. [IS.1 - Struggling Learners and ELL Students] [IS.2 - All Students]
- Parallel Lines: 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.
- Perpendicular Lines: 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.
- 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 or equal to 180 degrees. A polygon is concave if it is not convex.
- Scale Factor: The multiple by which a geometric object is enlarged or reduced; scale factors >1 enlarge the linear dimensions of the object and scale factors <1 reduce the linear dimensions of the object.
- Shrink: To become smaller in size; in geometry, a dilation with a scale factor < 1.
- Slope: The angle of inclination; for a straight line, the tangent of the angle that the line makes with the positive x-axis.
- Stretch: To make something wider or longer; in geometry, a dilation.
- 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.
Duration
60–90 minutes/1–2 class periods [IS.3 - All Students]
Prerequisite Skills
Prerequisite Skills haven't been entered into the lesson plan.
Materials
- One of These Things is Not Like the Other (M-G-5-3_One of These Things.doc)
- Lesson 3 Graphic Organizer (M-G-5-3_Lesson 3 Graphic Organizer.doc and M-G-5-3_Lesson 3 Graphic Organizer KEY.doc) [IS.4 - Struggling Learners and ELL Students]
- Lesson 3 Exit Ticket (M-G-5-3_Lesson 3 Exit Ticket.doc and M-G-5-3_Lesson 3 Exit Ticket Key.docx)
- colored pencils
- rulers
- graph paper
Related Unit and Lesson Plans
Related Materials & Resources
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Formative Assessment
Suggested Instructional Supports
Instructional Procedures
Related Instructional Videos
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DRAFT 10/13/2011