II. Geometry and Measurement

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

 

Additional Links to General Mathematics Sites

 

2. Position

Middle School

  1. Benchmark 1. "Locate and describe objects in terms of their position, including compass directions, Cartesian coordinates, latitude and longitude and midpoints."
    1. Coordinates Game - Position (II.2.MS.1)
      Interactive site to plot points on a coordinate grid. This is a student activity.
    2. Coordinate Graphing - Position (II.2.MS.1)
      Students will become familiar with plotting and locating points on the coordinate plane. This lesson will give students the opporunity to practice plotting points with immediate feedback. Lesson Plan and Student Projects are included.
    3. Latitude, Longitude, and Mapmaking - Position (II.2.MS.1&4)
      This lesson requires students to review the concepts of latitude and longitude and to use these concepts to create maps of different countries on the computer. They'll conclude by discussing the reasons why it's important to understand latitude and longitude and by creating quizzes in which other students can locate "mystery" places that they map on the computer. The Crack the Code activity has students using a map and latitude/longitude to track down some theives.
    4. Math Forum - Position (II.2.MS.1)
      This site contains a lesson plan that uses "Claris Works" to create graphs of linear equations. Step-by-step instructions are given with accompanying diagrams.
    5. Maths Online - Position (II.2.MS.1)
      This site offers an applet of the Cartesian Plane that can be manipulated to show how the x and y values change as a point is moved. It also lets students see that the y-value on the x-axis is always zero and the x-value on the y-axis is always zero.
    6. What's the Point - Position (II.2.MS.1)
      This is a game where students must use their knowledge of an X-Y coordinate plane.  There are 3 levels of difficulty.
  2. Benchmark 2. "Locate and describe objects in terms of their orientation and relative position, including coincident, collinear, parallel, perpendicular; differentiate between fixed (e.g., N- S- E- W) and relative (e.g., right-left) orientations; recognize and describe examples of bilateral and rotational symmetry."
    1. Classification of Patterns - Position (II.2.MS.2&3)
      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.
    2. I Took a Trip on a Train - Position (II.2.MS.2)
      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.
    3. Math Forum - Position (II.2.MS.1,2,3,4&5)
      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.
    4. Math to Build On - Position (II.2.MS.2)
      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.
    5. Stem and Leaf Plots -Position (II.2.MS.2)
      Stem and leaf plots explained.
    6. Stem and Leaf Plots - Position (II.2.MS.2)
      Stem and leaf plots explained.
    7. Stem and Leaf Plots - Position (II.2.MS.2)
      Stem and Leaf Plots that build and compare the line plot of the data set to the stem-and-leaf plot.
    8. Symmetries and Their Properties - Position (II.2.MS.2&3)
      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.
  3. Benchmark 3. "Describe translations, reflections, rotations and dilations using the language of transformations and employ transformations to verify congruence of figures."
    1. About a Line and a Triangle - Position (II.2.MS.3)
      This site is about rotation of a line around a fixed point. This is a student activity.
    2. Classification of Patterns - Position (II.2.MS.2&3)
      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. Dilations - Position (II.2.MS.3)
      An interactive site to experiment with dilations.
    4. Interactive Transformations - Position  (II.2.MS.3)
      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.
    5. Math Files - Bathroom Tiles - Position (II.2.MS.3)
      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.
    6. Math Forum - Position (II.2.MS.1,2,3,4&5)
      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.
    7. MathsNet Interactive - Transformations - Position (II.2.MS.3)
      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.
    8. NCTM Translations,Reflection,Transformations - Position (II.2.MS.3)
      Interactive Site that reviews Reflections, Transformations, and Translations. Students can see the shape go through theses topics.
    9. Quilts - Position (II.2.MS.3)
      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.
    10. Symmetries and Their Properties - Position (II.2.MS.2&3)
      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.
    11. The Mathematics of Seminole Patchwork - Positon (II.2.MS.3)
      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.
    12. Waldo's Interactive Math - Position (II.2.MS.3)
      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.
  4. Benchmark 4. "Locate the position of points or objects described by two or more conditions; locate all the points (locus) that satisfy a given condition."
    1. Count On - Position (II.2.MS.4&5)
      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.
    2. Latitude, Longitude, and Mapmaking - Position (II.2.MS.1&4)
      This lesson requires students to review the concepts of latitude and longitude and to use these concepts to create maps of different countries on the computer. They'll conclude by discussing the reasons why it's important to understand latitude and longitude and by creating quizzes in which other students can locate "mystery" places that they map on the computer. The Crack the Code activity has students using a map and latitude/longitude to track down some theives.
    3. Taxicab Treasure Hunt - Position (II.2.MS.4)
      A treasure is hidden in the city. Students are given a map which shows the streets of the city. After picking an intersection, the computer will state how far it is to the treasure by using the shortest distance in blocks. Students need to use this new information, along with the old information, to determine where the treasure is. Students are then asked to write an explanation of the process that they used to locate the treasure. Although this explanation cannot be submitted to the creators of the site, the teacher could informally assess students' problem-solving skills by reading their explanations. Student can also read what other students have written in the past.
    4. Using Graphs to Convey Information - Position (II.2.MS.4)
      Students will use the given information to build graphs representing real world situations.
  5. Benchmark 5. "Use concepts of position, direction and orientation to describe the physical world and to solve problems."
    1. Bridges to Math Comprehension - Position (II.2.MS.5)
      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.
    2. Count On - Position (II.2.MS.4&5)
      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.

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