Foundations Of Geometry: Not Just Your Ordinary Plane Geometry

Name of Participant(s): Aimee McLane, Teresa Niles

Overview of purpose: Using the Geometer’s Sketchpad, SMARTBoard Interactive Whiteboard and software, RM math Framework Edition content and activities such as Kaleidos and Easiteach math tools, the Airliner Wireless Slate, and the online textbook (Holt Math Course Three Pre-Algebra), we will provide both our regular and special education students with the opportunity to use technological devices already found in the math classroom to master the concepts and vocabulary of plane geometry. The structure of this inclusion class will allow technology to provide multiple opportunities for both differentiated instruction and cooperative groups.

length of instructional time for unit: 3-4 weeks

grade/level of audience: middle school mathematics

NYS Learning Standards to be addressed:

MST

Standard 3:Geometry and Algebra strands

PCSD Standards:

  • Critical thinker- All students will capable of problem solving, decision making and risk taking enabling them to function in an efficient, productive way in society.
  • Effective Communicator- All students will develop the skills necessary to communicate effectively.
  • Lifelong Learner- All students will develop the skills of self-evaluation and inquiry to engage in the process of lifelong learning.

Understanding:

Students will understand that. . .

  • they will master the concepts of plane geometry if they can interpret and then apply the necessary mathematical language
  • they must often explore a variety of learning styles to be successful.

Essential Questions:

  • What do problem solvers do?
  • How does mastery of a language effectively communicate the essence of a concept?
  • How might we show the measure of angles formed by or contained in parallel lines cut by a transversal and by intersecting lines?
  • How do the properties of transformations of plane figures relate?

Content Knowledge

Declaratory:

Students will know/understand the language of mathematics as it relates to geometry, such as a point, line, plane, angle, ray, segment, etc.

Procedural

Students will be able to. . .

  • Apply algebra to determine the measure of angles formed by or contained in parallel lines cut by a transversal and by intersecting lines.
  • Identify pairs of vertical angles a congruent.
  • Identify pairs of supplementary and complementary angles.
  • Calculate the missing angle measurements when given two parallel lines cut by a transversal.
  • Calculate the missing angle measurements when given two intersecting lines and an angle.
  • Describe and identify transformations in the plane, suing proper function notation.
  • Draw the image of a figure under rotations of 90 and 180 degrees.
  • Draw the image of a figure under a reflection over a given plane.
  • Draw the image of a figure under a translation.
  • Identify the properties preserved and not preserved under a reflection, rotation, translation and dilation.