II. Geometry and Measurement

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

 

Additional Links to General Mathematics Sites

 

1. Shape and Shape Relationship

Middle School

  1. Benchmark 1. "Distinguish among shapes and differentiate between examples and non-examples of shapes based on their properties; generalize about shapes of graphs and data distributions."
    1. Geometry -Shape and Shape Relationships (II.1.MS.1&2)
      This is a good site for reviewing basic geometric terms, shapes and shape relationships. It includes animations and some interactivity.
    2. Geometry from the land of the Incas - Pentagons & Pentagrams - Shape and Shape Relationships (II.1 MS.1,2,3&4)
      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.
    3. Hidden Polygons - Shape and Shape Relationships (II.1.MS.1)
      This site contains information on finding shapes on a triangle grid paper. This is a teacher lesson plan.
    4. Math.Com (Geometry) - Shape and Shape Relationships   (II.1.MS.1,2,3,4,6&7)
      An informational site for teachers and students.  There is some interaction for students in the lessons.  Students can participate in quizes at the end of each section.  This is the general site for geometry.  You will need to choose the area of interest.  Great site for middle school geometry.
    5. MATHO - Shape and Shape Relationships (II.1.MS.1&2)
      Fun way to allow students to review geometry terms. Students may need some simple direction before they begin. Several versions of the game board available.
  2. Benchmark 2. "Generalize the characteristics of shapes and apply their generalizations to classes of shapes."
    1. Geometry -Shape and Shape Relationships(II.1.MS.1&2)
      This is a good site for reviewing basic geometric terms, shapes and shape relationships. It includes animations and some interactivity.
    2. Geometry from the land of the Incas - Pentagons & Pentagrams - Shape and Shape Relationships (II.1 MS.1,2,3&4)
      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
    3. Geometric Terms - Shape and Shape Relationships (II.1.MS.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. Learning about Length, Perimeter, Area, and Volume of Similar Objects - Shape and Shape Relationships  (II.1.MS.2,3&4)
      Students experiment with different ratios of side lengths to interpret the changes in perimeter, area, surface area, and volume.  They use their data from perimeter and area to make a line graph and then interpret the reasons for differences in the graphs.  They also create tables to organize and easily analyze their volume and surface area data to study the relationship between changes in length in both volume and surface area.
    5. Links For Geometry - Shape and Shape Relationships (II.1.MS.2&3)
      Students will explore shapes, shape relationships and position. This is a student activity.
    6. Math.Com (Geometry) - Shape and Shape Relationships   (II.1.MS.1,2,3,4,6&7)
      An informational site for teachers and students.  There is some interaction for students in the lessons.  Students can participate in quizes at the end of each section.  This is the general site for geometry.  You will need to choose the area of interest.  Great site for middle school geometry.
    7. MATHO - Shape and Shape Relationships (II.1.MS.1&2)
      Fun way to allow students to review geometry terms. Students may need some simple direction before they begin. Several versions of the game board available.
    8. Native American Geometry - Shape and Shape Relationships (II.1.MS.2&3)
      This site describes who Native Americans used geometry is creating there artifacts.  Could be used as a lesson in Social Studies as well.  Several other links are included.  Go to education and then hexagon parts.
    9. Paper Pool Games - Shape and Shape Relationships (II.1.MS.2)
      This site allows the student to interact directly with the activity. It is a review of rectangular patterns, beginning skills on gathering data and looking for patterns.
    10. Quadrilateral Quest - Shape and Shape Relationships (II.1.MS.2)
      Students assess their skills at matching quadrilaterals with their properties. This is a student interactive site that also includes a quiz.
    11. Sorting Activities for Polygons - Shape and Shape Relationships (II.1.MS.2)
      In this activity, students identify and classify polygons according to various attributes.
    12. Surface Area and Volume - Shape and Shape Relationships (II.1.MS.2,3&4)
      An interactive site for students to compare surface area and volume of different prisms.  Student worksheet and teacher lesson plans are included.
    13. Waldo's Interactive Math Site - Shape and Shape Relationships (II.1.MS.2)
      This interactive site allows students to manipulate lines, angles and triangles to discover some basic geometric rules. The site is easy for students to use and allows students to discover the rules.
  3. Benchmark 3. "Derive generalizations about shapes and apply those generalizations to develop classifications of familiar shapes."
    1. Brainwave Puzzles - Shape and Shape Relationships (II.1.MS.3)
      This interactive site allows students to look at different shapes and shape clusters and make conclusions of which shapes do not fit in each puzzle. The site has ten puzzles and in each puzzle the student needs to pick which shape/shape clusters is the odd one out. May be a little difficult for Middle School students.
    2. Exploring Geometric Solids andTheir Properties - Shape and Shape Relationships (II.1.MS.3&4) Outstanding
      Geometric solids are all around us.  This site starts out by explaining the parts of a solid and gradually builds to constructing similar solids.
    3. Geometry from the land of the Incas - Pentagons & Pentagrams - Shape and Shape Relationships (II.1 MS.1,2,3&4)
      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. Learning about Length, Perimeter, Area, and Volume of Similar Objects - Shape and Shape Relationships  (II.1.MS.2,3&4)
      Students experiment with different ratios of side lengths to interpret the changes in perimeter, area, surface area, and volume.  They use their data from perimeter and area to make a line graph and then interpret the reasons for differences in the graphs.  They also create tables to organize and easily analyze their volume and surface area data to study the relationship between changes in length in both volume and surface area.
    5. Links For Geometry - Shape and Shape Relationships (II.1.MS.2&3)
    6. Math.Com (Geometry) - Shape and Shape Relationships   (II.1.MS.1,2,3,4,6&7)
      An informational site for teachers and students.  There is some interaction for students in the lessons.  Students can participate in quizes at the end of each section.  This is the general site for geometry.  You will need to choose the area of interest.  Great site for middle school geometry.
      Students will explore shapes, shape relationships and position. This is a student activity.
    7. Native American Geometry - Shape and Shape Relationships (II.1.MS.2&3)
      This site describes who Native Americans used geometry is creating there artifacts.  Could be used as a lesson in Social Studies as well.  Several other links are included.  Go to education and then hexagon parts.
    8. Surface Area and Volume - Shape and Shape Relationships (II.1.MS.2,3&4)
      An interactive site for students to compare surface area and volume of different prisms.  Student worksheet and teacher lesson plans are included.
  4. Benchmark 4. "Construct familiar shapes using coordinates, appropriate tools (including technology), sketching and drawing two- and three-dimensional shapes."
    1. A Review of Basic Geometry: Space the Final Frontier - Shape and Shape Relationships (II.1.MS.4)
      Planes, Cylindric solids/surfaces, Conic solids/surfaces, Spheres, Platonic Solids, Archimedian Solids, Pentominoes, Symmetry, Views, and Nets, Map Coloring, and Link to Flatland.
    2. Cool Math - Shape and Shape Relationships (II.1.MS.4)
      Middle school problem solving activity to construct non congruent triangle in a dot grid.  More of an activity to do off line.  You print out a sheet of dots. You can't create them online, although solutions are given.
    3. Exploring Geometric Solids andTheir Properties - Shape and Shape Relationships (II.1.MS.3&4) Outstanding
      Geometric solids are all around us.  This site starts out by explaining the parts of a solid and gradually builds to constructing similar solids.
    4. Fractal Tool - Shape and Shape Relationships  (II.1.MS.4)
      Tool to create and change shapes.
    5. Geometric Constructions - Shape and Shape Relationships (II.1.MS.4)
      The purpose of this web site is to give students complete directions for using The Geometer's Sketchpad® software to construct the basic geometry constructions encountered in an introductory geometry course. Each sketch is followed by an interactive Java applet. Try dragging various points in the sketch to explore additional cases. The Geometer's Sketchpad® software is available from Key Curriculum Press. Angles, Circles, Inscribed-Circumscribed , Lines, Polygons, Triangles.
    6. Geometry from the land of the Incas - Pentagons & Pentagrams - Shape and Shape Relationships (II.1 MS.1,2,3&4)
      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
    7. Learning about Length, Perimeter, Area, and Volume of Similar Objects - Shape and Shape Relationships  (II.1.MS.2,3&4)
      Students experiment with different ratios of side lengths to interpret the changes in perimeter, area, surface area, and volume.  They use their data from perimeter and area to make a line graph and then interpret the reasons for differences in the graphs.  They also create tables to organize and easily analyze their volume and surface area data to study the relationship between changes in length in both volume and surface area.
    8. Math.Com (Geometry) - Shape and Shape Relationships   (II.1.MS.1,2,3,4,6&7)
      An informational site for teachers and students.  There is some interaction for students in the lessons.  Students can participate in quizes at the end of each section.  This is the general site for geometry.  You will need to choose the area of interest.  Great site for middle school geometry.
    9. MathsNet Interactive Geometry - Solids - Shape and Shape Relationships (II.1.MS.4) Outstanding! This interactive site includes a variety of activities to cover solid geometry. Level of difficulty and topic can be changed by the user.
    10. Soda Constructor - Shape and Shape Relationships (II.1.MS.4&7)
      This is a very interactive site in which the students will have the opportunity to actually construct shapes. The teacher must give directions of what shape the students are to construct and the teacher can also request the shape to be something that represents something in our physical world. The shapes can also be two and three dimensional shapes.
    11. Surface Area and Volume - Shape and Shape Relationships (II.1.MS.2,3&4)
      An interactive site for students to compare surface area and volume of different prisms.  Student worksheet and teacher lesson plans are included.
  5. Benchmark 5. "Combine, dissect and transform shapes."
    1. Bathroom Tiles - Shape and Shape Relationships (II.1.MS.5)
      Outstanding - Students use an interactive game to perform transformations using reflections and rotations. Three levels of activities are given as well as solutions and hints.
    2. Constructing Your Own Set of Tangrams - Shape and Shape Relationships (II.1.MS.5)
      Directions for constructing your own tangram. Extension activities with the pieces are available in which students will produce other shapes (http://forum.swarthmore.edu/trscavo/tangrams/activities.html) and gain a better understanding of area (http://forum.swarthmore.edu/trscavo/tangrams/area.html) with out formulas. These activities seem to be all linked together.
    3. Inversions by Scott Kim - Shape and Shape Relationships (II.1.MS.5)
      This site has several examples of symmetry using inversions of people's names.  It contains teacher lesson plans as well as several examples of various symmetries and unusual tesselations.
    4. Study Works! Online - Shape and Shape Relationships (II.1.MS.5)
      This site is student interactive. Students can see different types of symmetry (vertical, horizontal, and rotational) demonstrated visually.
    5. Welcome To Symmetry - Shape and Shape Relationships (II.1.MS.5)
      This unit is designed to recognize the MCTM Curriculum and Evaluation Standards for School Mathematics concerning the need to give increased attention to "Coordinate and Transformation Approaches in Geometry at the secondary level. The lesson also demonstrates increased attention to: The active involvement of students in constructing and applying mathematical ideas; the use of a variety of instructional formats; and the use of computers for learning and doing mathematics.  This has links to teacher resources and a student page dealing with symmetry (rotational, reflectional, translational).
    6. World of Escher - Shape and Shape Relationships (II.1.MS.5)
      This is a commercial site selling MC Escher tesselations.  It would be useful as a reference and has many examples of his art as well as those sent in by others.  Check out "gallery" for Escher's work and "contest" for other people.
  6. Benchmark 6. " Generalize about the common properties of similar, congruent, parallel and perpendicular shapes and verify their generalizations informally."
    1. A Fractals Unit for Middle School Students - Shape and Shape Relationships (II.1.MS.6)
      This site is for kids. It teaches them about dimension of objects and the drawing and measuring of them. Also congruent, parallel and perpendicular lessons.
    2. Learning About Length, Perimeter, Area and Volume - Shape and Shape Relationships (II.1.MS.6)
      The student learns about length, perimeter, area, and volume of similar objects using interactive figures. This site contains two different interactive components. These activities help the students to learn about geometric relationships among similar objects.
    3. Math.Com (Geometry) - Shape and Shape Relationships   (II.1.MS.1,2,3,4,6&7)
      An informational site for teachers and students.  There is some interaction for students in the lessons.  Students can participate in quizes at the end of each section.  This is the general site for geometry.  You will need to choose the area of interest.  Great site for middle school geometry.
  7. Benchmark 7. "Use shape, shape properties and shape relationships to describe the physical world and to solve problems."
    1. Figure This! Math Challenges for Families - Shape and Shape Relationships (II.1.MS.7)
      Figure This! Mathematics Challenges for Families provides interesting math challenges that middle-school students can do at home with their families. Each challenge features a description of the important math involved, a note on where the math is used in the real world, a hint to get started, complete solutions, a "Try This" section, additional relational related problems with answers, questions to thinks about, fun facts related to the math, and resources for further exploration. Math Challenges #3 and 4 are examples of problems that would help teach this particular objective.
    2. Math.Com (Geometry) - Shape and Shape Relationships   (II.1.MS.1,2,3,4,6&7)
      An informational site for teachers and students.  There is some interaction for students in the lessons.  Students can participate in quizes at the end of each section.  This is the general site for geometry.  You will need to choose the area of interest.  Great site for middle school geometry.
    3. Shape Explorer - Shape and Shape Relationships (II.1.MS.7)
      Students can interact with area and perimeter on various shapes. Students will enjoy interacting with various shapes and observing how perimeter and area are both calculated and relate.
    4. Soda Constructor - Shape and Shape Relationships (II.1.MS.4&7)
      This is a very interactive site in which the students will have the opportunity to actually construct shapes. The teacher must give directions of what shape the students are to construct and the teacher can also request the shape to be something that represents something in our physical world.

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