II. Geometry and Measurement

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

 

Additional Links to General Mathematics Sites

 

High School

  1. Benchmark 1. "Use shape to identify plane and solid figures, graphs, loci, functions and data distributions."
    1. Guessing Correlations - Shape and Shape Relationships (II.1.HS.1)
      This is an interactive site for students.  They are asked to look at a linear regression graph and decide an approximate value for the correlation coefficient.
    2. Mark Newbold's Animated Necker Cube - Shape and Shape Relationships (II.1.HS.1)
      Put your eyes in focus! This is a mind blowing animation of an opticial illusion.
    3. Properties of Circles - Shape and Shape Relationships (II.1.HS.1,2,3&4)
      Students measure circular objects to discover the ratio of the circumference of a circle to it's radius of a circle. This site is not student interactive but contains printable student worksheets and teacher reference materials.
    4. Studying Polyhedra - Shape and Shape Relationships (II.1.HS.1)
      Students take a look at several rotating polyhedra. Students can count the number of faces, edges, and vertices. There are many links to other sites that can add more depth to understanding polyhedras.
  2. Benchmark 2. "Determine necessary and sufficient conditions for the existence of a particular shape and apply those conditions to analyze shapes."
    1. 3-D Visualization Activity: Student Activity - Shape and Shape Relationships (II.1.HS.2)
      Students investigate the properties of three-dimensional figures including slicing and creating line drawings or nets. Java applets, student worksheets and teacher resources are included.
    2. Exterior Angles Conjectures - Shape and Shape Relationships (II.1.HS.2)
      Student interactive site which allows the student to see a demonstration of the exterior angles conjecture.
    3. Geometric Terms - Shape and Shape Relationships (II.1.HS.2)
      This is a concentration type game, where the student has to match up the term to the proper definition.  The geometric definitions and terms are excellent for refreshing and practice.
    4. Impossible Triangles - Shape and Shape Relationships (II.1.HS.2)
      Given properties of triangles, students will determine why it is impossible to create a triangle with the given dimensions. Students can enter answers and check them as they go.
    5. Isosceles Trapezoid - Shape and Shape Relationships (II.1.HS.2)
      An activity that always students to discover the properties of an isosceles trapezoid.  It provides a method to discover the properties using pencil and paper or geometer sketchpad.
    6. Parallelogram Conjectures - Shape and Shape Relationships (II.1.HS.2)
      An activity that always students to discover the properties of a parallelogram.  It provides a method to discover the properties using pencil and paper or geometer sketchpad.
    7. Polygon Sum Conjecture - Shape and Shape Relationships (II.1.HS.2)
      Student interactive site which allows the student to see a demonstration of the polygon sum conjecture.
    8. Properties of Circles - Shape and Shape Relationships (II.1.HS.1,2,3&4)
      Students measure circular objects to discover the ratio of the circumference of a circle to it's radius of a circle. This site is not student interactive but contains printable student worksheets and teacher reference materials.
    9. Quadrilateral Sum Conjecture - Shape and Shape Relationships (II.1.HS.2)
      Student interactive site which allows the student to see a demonstration of the quadrilateral sum conjecture.
    10. Rectangle Conjectures - Shape and Shape Relationships (II.1.HS.2)
      An activity that always students to discover the properties of rectangles.  It provides a method to discover the properties using pencil and paper or geometer sketchpad.
    11. Rhombus Conjectures - Shape and Shape Relationships (II.1.HS.2)
      An activity that always students to discover the properties of a rhombus.  It provides a method to discover the properties using pencil and paper or geometer sketchpad.
    12. Triangle Sum Conjecture - Shape and Shape Relationships (II.1.HS.2)
      Student interactive site which allows the student to see a demonstration of the triangle sum conjecture.
  3. Benchmark 3. "Use transformational, coordinate or synthetic methods to verify (prove) the generalizations they have made about properties of classes of shapes."
    1. Properties of Circles - Shape and Shape Relationships (II.1.HS.1,2,3&4)
      Students measure circular objects to discover the ratio of the circumference of a circle to it's radius of a circle. This site is not student interactive but contains printable student worksheets and teacher reference materials.
    2. Teacher Resources for Inversions - Shape and Shape Relationships (II.1.HS.3&4)
      This site provides several classroom activities based on inversions. Worksheets are appropriate for grades 3-12 for teaching symmetry, art, geometry, language arts, and creative thinking. Teacher lesson plans and printable worksheets are included.
    3. The Geometry Center - Shape and Shape Relationships (II.1.HS.3&5)
      This student interactive site explores symmetry, tiling, wallpaper groups, fractals and isometries. It includes animations of transformations.
    4. The Geometers Sketchpad (Three Labs)  - Shape and Shape Relationships (II.1.HS.3)
      Students use Geometer's Sketchpad to investigate properties of parallelograms, rectangles, and triangles.
  4. Benchmark 4. "Draw and construct shapes in two and three dimensions and analyze and justify the steps of their constructions."
    1. Designs With Circles - Shape and Shape Relationships (II.1.HS.4)
      A circle construction activity that explores reflectional and rotational symmetry.
    2. Geometry: From the Land of the Incas - Shape and Shape Relationships (II.1.HS.4)
      Students will find an eclectic mix of sound, science, and Incan history in order to raise interest in Euclidean geometry. Geometry problems, proofs, quizzes, puzzles, quotations and visual displays are included. The site also has a section on Geometry Theorems and Problems and quizzes in other areas mathematics.
    3. Geometry from the land of the Incas - Pentagons & Pentagrams - Shape and Shape Relationships (II.1.HS.4) New
      This dynamic geometry software provides an environment in which we can explore geometric relationships and make test conjectures. The site also has a section on Geometry Theorems and Problems and quizzes in other areas mathematics.
    4. Geometry from the land of the Incas - Platonic Solids - Shape and Shape Relationships (II.1.HS.4) New
      This dynamic geometry software provides views of Platonic Solids. Great animation as the five shapes rotate to show a three dimensional view of each shape.
    5. Geometry from the land of the Incas - Seven Circles Theorem - Shape and Shape Relationships (II.1.HS.4) New
      This dynamic geometry software provides views of multiple circles. Great animation as the six circles touch the original circle and their two neighbors.
    6. Glencoe Mathematics – Poster Project for “Who is behind this geometry idea anyway?” - Shape and Shape Relationships New
      Your school is having a Mathematics Appreciation Day. One event for the day is a competition for the best research project on a mathematical topic. Since you are currently studying geometry, your teacher wants each student in your class to research a topic in geometry. You will need to prepare a portfolio or poster to display the results of your research. If you prefer, you can prepare a Web page with this information that others can view.
    7. Hamilton's Math to Build On - Shape and Shape Relationships  (II.1.HS.4)
      This is a student interactive site that reviews the basics of angles from definitions to drawing.  It gives clear simple examples.  This would be extremely useful as a tutorial or for students who need extra help understanding this simple concept of geometry.  Suitable for the special needs student.
    8. Interactive Construction - Shape and Shape Relationships (II.1.HS.4)
      Students build shapes out of points, lines and circles. Basic constructions can be made using the foundation level while more involved constructions can be made using the advanced tools.
    9. MathsNet Interactive Construction -Shape and Shape Relationships (II.1.HS.4)
      Students are able to construct shapes from points, lines and circles. Shapes can then be manipulated to change size and orientation.
    10. Polyhedra Nets-Paper - Shape and Shape Relationships (II.1.HS.4)
      Students can print the net provided on this site to construct polyhedra.  This is not an interactive site.
    11. Properties of Circles - Shape and Shape Relationships (II.1.HS.1,2,3&4)
      Students measure circular objects to discover the ratio of the circumference of a circle to it's radius of a circle. This site is not student interactive but contains printable student worksheets and teacher reference materials.
    12. Rotations and Rotational Symmetry - Shape and Shape Relationships (II.1.HS.4&5)
      A nice 4 part lesson plan to use in 9th grade geometry to teach rotations and rotational symmetry. Interactive applets are included along with questions for reflection and understanding. Students are able to create their own designs.
    13. Square Twist - Shape and Shape Relationships (II.1.HS.4)
      Construction of square twist tessellation through the medium of paper folding.
    14. Symmetries and Their Properties: Glide Reflections - Shape and Shape Relationships (II.1.HS.4&5)
      A five part lesson plan including a student tutorial, interactive applets and questions for understanding. A good lesson for 9th grade geometry to reinforce the properties of glide relflections. Students are able to create their own designs.
    15. Symmetries and Their Properties- Reflections - Shape and shape Relationships (II.1.HS.4&5)
      A four part lesson plan with student interaction that helps to reinforce the properties of reflections through tutorials with applets included. Perfect for 9th grade geometry. Questions for understanding are included.
    16. Symmetries and Their Properties- Translations - Shape and Shape Relationships (II.1.HS.4&5)
      A 5 lesson activity on translations for 9th grade geometry. The activities include tutorials, interactive applets and questions for understanding. Student will be actively engaged in this lesson.
    17. Teacher Resources for Inversions - Shape and Shape Relationships (II.1.HS.3&4)
      This site provides several classroom activities based on inversions. Worksheets are appropriate for grades 3-12 for teaching symmetry, art, geometry, language arts, and creative thinking. Teacher lesson plans and printable worksheets are included.
  5. Benchmark 5. "Study transformations of shapes using isometries, size transformations and coordinate mappings."
    1. Rigid Motions in the Plane - Shape and Shape Relationships (II.1.HS.5)
      Need Geometer's Sketchpad or TI92. An exhaustive study of a variety of rigid isometrics using the previously named technology. This is a teacher lesson plan.
    2. Rotations and Rotational Symmetry - Shape and Shape Relationships (II.1.HS.4&5)
      A nice 4 part lesson plan to use in 9th grade geometry to teach rotations and rotational symmetry. Interactive applets are included along with questions for reflection and understanding. Students are able to create their own designs.
    3. Symmetries and Their Properties: Glide Reflections - Shape and Shape Relationships (II.1.HS.4&5)
      A five part lesson plan including a student tutorial, interactive applets and questions for understanding. A good lesson for 9th grade geometry to reinforce the properties of glide relflections. Students are able to create their own designs.
    4. Symmetries and Their Properties- Reflections - Shape and shape Relationships (II.1.HS.4&5)
      A four part lesson plan with student interaction that helps to reinforce the properties of reflections through tutorials with applets included. Perfect for 9th grade geometry. Questions for understanding are included.
    5. Symmetries and Their Properties- Translations - Shape and Shape Relationships (II.1.HS.4&5)
      A 5 lesson activity on translations for 9th grade geometry. The activities include tutorials, interactive applets and questions for understanding. Student will be actively engaged in this lesson.
    6. The Four Types of Symmetry in the Plane - Shape and Shape Relationships (II.1.HS.5&7)
      This site provides teacher notes on transformations of shapes in two dimensions. The site is not interactive but contains diagrams, sample questions and recommended projects.
    7. The Geometry Center - Shape and Shape Relationships (II.1.HS.3&5)
      Outstanding -This student interactive site explores symmetry, tiling, wallpaper groups, fractals and isometries. It includes animations of transformations.
  6. Benchmark 6. "Compare and analyze shapes and formally establish the relationships among them, including congruence, similarity, parallelism, perpendicularity and incidence."
    1. Angles and Parallel Lines - Shape and Shape Relationships (II.1.HS.6)
      This site has an interactive applet that allows geometry students to discover properties of parallel lines. Access the applet by clicking on "11-14" at the left side of the webpage. Locate "Angles and Parallel Lines" from the drop down menu to use the applet.
    2. Can a Geometric Mean be Nice? - Shape and Shape Relationships (II.1.HS.6)
      Outstanding - This lesson deals with proportions, right triangles, and the geometric mean. It also includes an interactive window for exploring different triangles. It also includes downloadable Geometer's Sketchpad files (optional).
    3. Circle Properties - Shape and Shape Relationships (II.1.HS.6)
      This site is a tutorial on various parts of a circle, for example, sectors, arcs, etc. Students can read the properties, answer questions, and check themselves. A computer-scored quiz completes the lesson.
    4. Geometry for High School - Shape and Shape Relationships (II.1.HS.6)
      This site contains over 40 applets for Geometry including Angles and Parallel Lines, Congruent Figures and Triangles, Quadrilaterals and Similar Figures.
    5. Isometric Drawing Tool - Shape and Shape Relationships (II.1.HS.6)
      Students are able to construct different geometric figures and then rotate them around to see all sides.
    6. Pantograph - Shape and Shape Relatiionships (II.1.HS.6)
      Students use a "Pantograph" to create similar figures and find the ratio of magnification when the lengths of the arms are defined. Although interactive, students could easily create their own pantograph in the classroom.
  7. Benchmark 7. "Use shape, shape properties and shape relationships to describe the physical world and to solve problems."
    1. Sketchpad Homework - Shape and Shape Relationships (II.1.HS.7)
      Teachers will find detailed instructions for several sketchpad applications. It begins with basic commands and advances to more difficult lessons.
    2. The Four Types of Symmetry in the Plane - Shape and Shape Relationships (II.1.HS.5&7)
      This site provides teacher notes on transformations of shapes in two dimensions. The site is not interactive but contains diagrams, sample questions and recommended projects.
    3. The Cylinder Problem - Shape and Shape Relationships (II.1.HS.7)
      This site poses a problem that involves comparing cylinders. It involves a number of mathematical concepts and problem-solving approaches that can lead to rich discourse in the classroom.
    4. The Moving Sofa Problem - Shape and Shape Relationships (II.1.HS.7)
      Outstanding! This "Study Works" site provides a complete set of lessons for upper middle school through high school. Students must determine whether couches, of varying shapes, can fit around a narrow corner. In addition, students calculate areas of different shaped furniture and explore properties of regular and irregular objects. Teacher notes, worksheets, and discussion topics are included.
    5. Visualizing Topography - Shape and Shape Relationships (II.1.HS.7)
      Visualizing Topography is an instructional tour that shows how to visualize topography in 3D. It contains Quick Time movies and questions that help students visualize two-dimensional topography in three dimensions. Student worksheets and teacher guides are included.

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