Sixth Grade

 
  1. Number and Operations (N)
  2. Algebra (A)
  3. Measurement (M)
  4. Geometry (G)
  5. Data and Probability (D)

 

Additional Links to General Mathematics Sites

 

4. Geometry (G)

 

Sixth Grade

Understand and Apply Basic Properties

  1. G.GS.06.01 Understand and apply basic properties of lines, angles, and triangles, including:
    • triangle inequality
    • relationships of vertical angles, complementary angles, supplementary angles
    • congruence of corresponding and alternate interior angles when parallel lines
    _ are cut by a transversal, and that such congruencies imply parallel lines
    • locate interior and exterior angles of any triangle, and use the property that an exterior
    _angle of a triangle is equal to the sum of the remote (opposite) interior angles
    • know that the sum of the exterior angles of a convex polygon is 360o.
    1. A Fractals Unit for Middle School Students
      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
      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)
      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.

Understand the Concept of Congruence and Basic Transformations

  1. G.GS.06.02 Understand that for polygons, congruence means corresponding sides and angles have equal measures.
    1. A Fractals Unit for Middle School Students
      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
      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)
      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.
  2. G.TR.06.03 Understand the basic rigid motions in the plane (reflections, rotations, translations), relate these to congruence, and apply them to solve problems.
    1. About a Line and a Triangle
      This site is about rotation of a line around a fixed point. This is a student activity.
    2. Bridges to Math Comprehension
      Students will collect bridge statistics to use for geometry identification and measurement calculations. They will collect statistics about 2-4 famous bridges to use in calculating geometric computations of area, parallel and intersecting lines. Results will be compared using less than, greater than or equal to skills. Extensions include exploring other web sites to see student works and illustrations, projects done with toothpicks and other materials to build bridges and more. This unit was primarily created for grades 4-6, but could also be used in basic math grades 7-8.
    3. Bathroom Tiles
      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.
    4. Classification of Patterns
      This site contains a complete lesson plan which could be used to introduce geometric transformation. A teacher's guide and some reproducible materials are included. Some of the lesson could be done in and interactive manner on the computer.
    5. Constructing Your Own Set of Tangrams
      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.
    6. Count On
      Worm Hunt is great for practicing the coordinate grid.  The students choose a coordinate pair to try to find a worm.  They get a response to let them know how far they are from the worm, thus the students have to practice figuring distances between points on the grid.  This would be an excellent game for 5th and 6th graders.
    7. Dilations
      An interactive site to experiment with dilations.
    8. Interactive Transformations
      This site allows the student to interact with the computer to discover the difference between translations, rotations, and reflections.  It also allows them to make an object larger and do a combination of transformations.
    9. Inversions by Scott Kim
      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.
    10. Math Files
      Outstanding - This is a student game where students need to decide how to rotate, reflect, and translate one object to another object. Students can get hints from the computer and can click on "key ideas" to learn more about the various transformations. This is a very interactive site for students.
    11. Math Forum
      This sight gives detailed explanations of tessellation, using history, vocabulary of geometric shapes and the use of symmetry.  There are several other links of tessellations including software information.
    12. MathsNet Interactive
      This site includes a variety of activities and information that cover reflections, enlargements, rotations and translations. Activities increase in difficulty so the site is actually appropriate for a wide range of grade levels.
    13. NCTM Translations,Reflection,Transformations
      Interactive Site that reviews Reflections, Transformations, and Translations. Students can see the shape go through theses topics.
    14. Quilts
      Students have to decide which type of symmetry is used in a quilt and then replicate that quilt by clicking on the appropriate squares. Because the different types of symmetry used are denoted by H, M, S, and B, this is probably best used in grades 5-6. Teachers should teach students the correct transformational language. This activity involves spatial visualization.
    15. Symmetries and Their Properties
      This "Illuminations" site describes and illustrates rotational symmetry, reflections, translations, and glide reflections. Although the investigation is coded for grades 9 - 12 this is appropriate and applicable for Middle School.
    16. The Mathematics of Seminole Patchwork
      This site provides background information on the symmetry of the designs contained in the Seminole Patchwork. Examples and explanations of the types of transformations that are used in the designs are given. An excellent resource for integrating art, history, and multicultural mathematics.
    17. Waldo's Interactive Math
      This interactive sites includes an activity allowing students to manipulate practice reflections and rotations on a coordinate plane. It allows for practice and/or testing of skills. Some teacher direction may be needed initially although the directions are clear. This site uses JAVA applets.
    18. Welcome To Symmetry
      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).
    19. World of Escher
      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.
  3. G.TR.06.04 Understand and use simple compositions of basic rigid transformations, e.g., a translation followed by a reflection.
    1. About a Line and a Triangle
      This site is about rotation of a line around a fixed point. This is a student activity.
    2. Bathroom Tiles
      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.
    3. Classification of Patterns
      This site contains a complete lesson plan which could be used to introduce geometric transformation. A teacher's guide and some reproducible materials are included. Some of the lesson could be done in and interactive manner on the computer.
    4. Constructing Your Own Set of Tangrams
      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.
    5. Dilations
      An interactive site to experiment with dilations.
    6. Interactive Transformations
      This site allows the student to interact with the computer to discover the difference between translations, rotations, and reflections.  It also allows them to make an object larger and do a combination of transformations.
    7. Inversions by Scott Kim
      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.
    8. Math Files - Bathroom Tiles
      Outstanding - This is a student game where students need to decide how to rotate, reflect, and translate one object to another object. Students can get hints from the computer and can click on "key ideas" to learn more about the various transformations. This is a very interactive site for students.
    9. Math Forum
      This sight gives detailed explanations of tessellation, using history, vocabulary of geometric shapes and the use of symmetry.  There are several other links of tessellations including software information.
    10. MathsNet Interactive
      This site includes a variety of activities and information that cover reflections, enlargements, rotations and translations. Activities increase in difficulty so the site is actually appropriate for a wide range of grade levels.
    11. NCTM Translations,Reflection,Transformations
      Interactive Site that reviews Reflections, Transformations, and Translations. Students can see the shape go through theses topics.
    12. Quilts
      Students have to decide which type of symmetry is used in a quilt and then replicate that quilt by clicking on the appropriate squares. Because the different types of symmetry used are denoted by H, M, S, and B, this is probably best used in grades 5-6. Teachers should teach students the correct transformational language. This activity involves spatial visualization.
    13. Symmetries and Their Properties
      This "Illuminations" site describes and illustrates rotational symmetry, reflections, translations, and glide reflections. Although the investigation is coded for grades 9 - 12 this is appropriate and applicable for Middle School.
    14. The Mathematics of Seminole Patchwork
      This site provides background information on the symmetry of the designs contained in the Seminole Patchwork. Examples and explanations of the types of transformations that are used in the designs are given. An excellent resource for integrating art, history, and multicultural mathematics.
    15. Waldo's Interactive Math
      This interactive sites includes an activity allowing students to manipulate practice reflections and rotations on a coordinate plane. It allows for practice and/or testing of skills. Some teacher direction may be needed initially although the directions are clear. This site uses JAVA applets.
    16. Welcome To Symmetry
      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).
    17. World of Escher
      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.

Construct Geometric Shapes

  1. G.SR.06.05 Use paper folding to perform basic geometric constructions of perpendicular lines, midpoints of line segments and angle bisectors; justify informally.
    1. A Review of Basic Geometry: Space the Final Frontier
      Planes, Cylindric solids/surfaces, Conic solids/surfaces, Spheres, Platonic Solids, Archimedian Solids, Pentominoes, Symmetry, Views, and Nets, Map Coloring, and Link to Flatland.
    2. Classification of Patterns
      This site contains a complete lesson plan which could be used to introduce geometric transformation. A teacher's guide and some reproducible materials are included. Some of the lesson could be done in and interactive manner on the computer.
    3. Cool Math
      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.
    4. Exploring Geometric Solids andTheir Properties
      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.
    5. Fractal Tool
      Tool to create and change shapes.
    6. Geometric Constructions
      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.
    7. Geometry from the land of the Incas - Pentagons & Pentagrams
      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
    8. I Took a Trip on a Train
      Students are shown an overhead view of a circular train track as well as photos "taken" from the train's perspective.  They must put the photos in chronological order.  This deals with different perspectives and positions as related to time.
    9. Learning about Length, Perimeter, Area, and Volume of Similar Objects
      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.
    10. Math.Com (Geometry)
      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.
    11. Math Forum
      This sight gives detailed explanations of tessellation, using history, vocabulary of geometric shapes and the use of symmetry.  There are several other links of tessellations including software information.
    12. MathsNet Interactive Geometry - Solids
      Outstanding      ! This interactive site includes a variety of activities to cover solid geometry. Level of difficulty and topic can be changed by the user.
    13. Math to Build On
      This page provides links to information on the same website. There are lessons on parallel, perpendicular, collinear, and more. Good general site for geometry. This site contains teacher lesson plans.
    14. Soda Constructor
      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.
    15. Stem and Leaf Plots
    16. Stem and leaf plots explained.
    17. Stem and Leaf Plots
      Stem and leaf plots explained.
    18. Stem and Leaf Plots
      Stem and Leaf Plots that build and compare the line plot of the data set to the stem-and-leaf plot.
    19. Surface Area and Volume
      An interactive site for students to compare surface area and volume of different prisms.  Student worksheet and teacher lesson
      plans are included.
    20. Symmetries and Their Properties
      This "Illuminations" site describes and illustrates rotational symmetry, reflections, translations, and glide reflections. Although thei nvestigation is coded for grades 9 - 12 this is appropriate and applicable for Middle School.

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