MathematicsTransformations in the Coordinate Plane

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Unit Information

Content Map: Transformations in the Coordinate Plane

EOCT STUDY GUIDE - UNIT 5

CCGPS Overview and Unit Standards or Troup County Version (TCV):

  • MCC9-12.G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

  • MCC9-12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

  • MCC9-12.G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

  • MCC9-12.G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

  • MCC9-12.G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

Prerequisites: As identified by the CCGPS Frameworks

It is expected that students will have prior knowledge/experience related to the concepts and skills identified below. It may be necessary to pre-assess in order to determine if time needs to be spent on conceptual activities that help students develop a deeper understanding of these ideas.

·         - plotting points on a coordinate plane

·         - congruence of geometric figures and the correspondence of their vertices, sides, and angles

·         - recognizing line and rotational symmetry

·         - interpreting and sketching views from different perspectives

·         - calculate the perimeter and area of fundamental geometric plane figures

·         - use the concepts of ratio, proportion, and scale factor to demonstrate the relationships between similar plane figures

 

Unit Length: 15-20 days

Unit Essential Questions:

  • What are the undefined terms essential to any study of geometry?

    Does location in a plane matter?

    How do you determine the type of transformation that has occurred?

    Does a transformation change an object's position and/or size?

    How do we define and create geometric transformations?

    How does the transformation of a geometric figure and a function compare?

    What effects do transformations have on geometric figures?

    Which tansformations create isometries?

    How do we know which transformations have created the mapping of an image?

    How can a reflection be loke a rotation?

    How can the coordinate plane help me understand properties of reflections, translations, and rotations?

    What is the relationship between reflections, translations, and rotations?

     

Unit Vocabulary and Symbols: Transformations in the Coordinate Plane

State recommended resources: Internet Resources

Resources by Concept: (click on a concept)

Concept 1: Experiment with transformations in the plane.
Resources:CCGPS Frameworks:
  • Discovering Geometry, 2.1, 2.4, 4.2, 4.4, 7.1, 7.5-7.7, 8.1
  • America's Choice, Math I, Geometry Gallery, Lesson 3
  • ABC Passing the GA Geometry EOCT (ISBN 1-59807-071-7) 1.1-1.10, 3.4, 9.1-9.6
  • Holt, Algebra 1, 5.6
  • Patty Paper Geometry, Investigation Set 9
  • McDougal Passports to Alg and Geometry (ISBN 0-395-87988-4) Sections 11.3-11.5
Tasks:  How the state recommends that we use the TASKS
These tasks were taken from the CCGPS Frameworks. The tasks cover multiple standards and may be used as teaching strategies or as culminating activities.
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