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Coordinate Geometry

Essential content for elementary teachers

  1. Understand distance on a line.
  2. Understand the coordinate plane.
    1. Coordinates
    2. Origin
    3. Quadrants
    4. Identify and plot points
  3. Use coordinate geometry to investigate properties of shapes and relationships such as congruence, similarity, and the Pythagorean relationship.

Essential content for students grades K-3

  1. Specify locations and describe spatial relationships using coordinate geometry.10
    1. Describe, name, and interpret relative positions on a line and on a plane.
    2. Describe, name, and interpret direction and distance in navigating on a line or on a plane and apply ideas about direction and distance.
    3. Find and name locations with simple relationships such as "near to" and in coordinate systems such as maps.

Essential content for students grades 4-5

  1. Maintain and expand on concepts introduced in primary grades.
  2. Specify locations and describe spatial relationships using coordinate geometry.11
    1. Describe location and movement using common language and geometric vocabulary.
    2. Make and use coordinate systems to specify locations and to describe paths.
    3. Find the distance between points along horizontal and vertical lines of a coordinate system.

See Appendix A for a list of sample state standards for mathematics.

Instructional activities and lesson plans for coordinate geometry

The brief activities and lesson plans listed here (by grade level) are described more extensively in Instructional Activities and Lesson Plans, where they are listed alphabetically.

Activity Description
Mixed-up Pictures
grades K-2
Showing pictures where some of the items are upside-down and some are right-side-up, have students identify the proper orientation of each item.
Calendar Locations
grades 1-3
Have students use a calendar to locate relative positions in a plane.
Number Line Message
grades 1-3
Have students place specially chosen letters above a series of numbers on the number line, and have them read the message that emerges.
Traveling on a Grid
grades 2-3
Have students use large block graph paper to draw city streets and buildings. Have them describe how to get from one location to another.
Graphing Points on a Line
grades 2-4
Have students identify points on a number line. This activity also includes negatives, scale, a glossary, and links.
Using Maps
grades 3-5
Have students use road maps to find the distances between cities. Have them describe how to get from one city to another.
Coordinate Games
grades 4-5
Have students play games such as Battleship, Coordinate Tic-Tac-Toe, Hurkle, or Grid Football.
The Plane
grades 4-5
Help students learn to plot points on the coordinate plane. Concepts included in this activity are: the plane, finding points, graphing points, and scale.
Plotting Pictures
grades 4-5
Have students plot and connect sets of coordinates that create shapes and images.
Playground Grids
grades 4-5
Mark off a grid on the playground with X- and Y-axes. Have students walk to points on the grid by traveling along the grid lines. (This can also be done in a classroom that has square floor tiles.)
Lesson Plans Description
Traveling around Our Town
grades 1-2
Students learn to specify locations on a grid by using the words right, left, up, and down and find different paths from one location to another.
Find the Shape
grades 4-5
Students play a game similar to the game Battleship. They practice identifying ordered pairs and plotting ordered pairs in the first quadrant. (This lesson can be extended to include the entire coordinate plane.)
  1. National Council of Teachers of Mathematics, Principles and Standards for School Mathematics, p. 396.
  2. Ibid.

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