II. Geometry and Measurement

 
  1. Shape and Shape Relationships
  2. Position
  3. Measurement

 

Additional Links to General Mathematics Sites

 

2. Position

High School

  1. Benchmark 1. "Locate and describe objects in terms of their position, including polar coordinates, three-dimensional Cartesian coordinates, vectors and limits."
    1. Conic Sections - Position (II.2.HS.1,2&4)
      This is an informative site for Algebra teachers who like to conduct experiments in their classroom. Directions are given for creating things like an ellipse board and using a light to make the four conic sections.
    2. Graphing Vector Calculator - Position (II.2.HS.1)
      Outstanding - Learn about Vectors and Vector Operations by sketching and playing with them. Java script needed.
    3. Vectors - Position (II.2.HS.1&3)
      This site ia a tutorial on the properties of vectors including a definition, addition and multiplication. Students can read the properties, try practice questions, and check their answers. A computer-scored quiz completes the lesson.
  2. Benchmark 2. "Locate and describe objects in terms of their orientation and relative position, including displacement (vectors), phase shift, maxima, minima and inflection points; give precise mathematical descriptions of symmetries."
    1. Conic Sections - Position (II.2.HS.1,2&4)
      This is an informative site for Algebra teachers who like to conduct experiments in their classroom. Directions are given for creating things like an ellipse board and using a light to make the four conic sections.
    2. Ellipse Game  - Position (II.2.HS.2&4)
      You will be given an ellipse of random dimensions and you will have to try to click on one of the foci. Should you fail in this mission at first, you will be given some clues. Helps student get a feel for where the foci of a ellipse are located.
    3. Symmetry Around the World - Position (II.2.HS.2)
      Students can read a lot of useful information about the various types of symmetry. Many pictures are included. The reading is easy and the pictures are interesting. It includes a worksheet that teachers can print and students can complete as they work through the site.
  3. Benchmark 3. "Give precise mathematical descriptions of transformations and describe the effects of transformations on size, shape, position and orientation."
    1. Reflect on This - Position (II.2.HS.3)
      This site, by NCTM (Illuminations) provides a lesson on symmetry for high school geometry students. In this lesson, the student will build a kaleidoscope and use reflection to create and measure polygons. Reproducible activity masters can be downloaded by the teacher.
    2. Totally Tessellated - Position (II.2.HS.3)
      Outstanding - This site uses tessellations to explore transformations and symmetry. It includes high school quality animated examples and hands-on activities for students.
    3. Vectors - Position (II.2.HS.1&3)
      This site ia a tutorial on the properties of vectors including a definition, addition and multiplication. Students can read the properties, try practice questions, and check their answers. A computer-scored quiz completes the lesson.
  4. Benchmark 4. "Describe the locus of a point by a rule or mathematical expression; trace the locus of a moving point."
    1. Conic Sections - Position (II.2.HS.1,2&4)
      This is an informative site for Algebra teachers who like to conduct experiments in their classroom. Directions are given for creating things like an ellipse board and using a light to make the four conic sections.
    2. Ellipse Game  - Position (II.2.HS.2&4)
      You will be given an ellipse of random dimensions and you will have to try to click on one of the foci. Should you fail in this mission at first, you will be given some clues. Helps student get a feel for where the foci of a ellipse are located.
    3. Exploring Functions through Parametric Equations - Position (II.2.HS.4)
      This is a lesson plan and handout on parametric equations.  It has the students trace the path of a baseball after it has been hit.  They are asked to find the distance of the ball in relation to time and vice versa.
  5. Benchmark 5. "Use concepts of position, direction and orientation to describe the physical world and to solve problems."
    1. Sketchpad v.3 Gallery - Projectile Motion - Position (II.2.HS.5)
      This sketch show the path of a projectile computed interactively. Buttons give you control over showing the focus and direction and over an illustration of how to find the focus of the parabolic path using light rays. An animation button allows you to animate a ball along the path. A Time Trace button shows dynamic locus of the balls at uniform time intervals. Requires the program Gometer's Sketchpad

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