Using Grid Boards with Rotations Topic Index | Geometry Index | Regents Exam Prep Center

Grid boards are constructed of a peg-board consistency and are perforated in a graph grid pattern.  One side of the board is a rectangular coordinate system and the other side is a unit circle style system (not a true polar coordinate system). 
 The grid boards shown here were manufactured by Energy Concepts, Inc. (Illinois).

The following activity can be used to help students understand the concept of rotations (and to help them understand angle size and location).  This activity is a good discovery activity prior to rotation of coordinates.

Make a transparent moveable marker from overhead transparency film.  With a permanent marker, draw a line segment down the center of the strip.  Attach the marker to the grid board with a clip at the origin.

Using clipart from your work processor, print various colored shapes. Laminating the shapes will keep them in good condition.  This will allow them to survive from year to year.

Attach the "bug" to the end of the moveable marker with scotch tape.  Students are now ready to start an investigation of angle sizes and the position of objects as they rotate with respect to the origin. Angles are labeled in degrees on the grid boards.

1.  Place the "figure" at 45 degrees.  Rotate the figure 90 degrees.  Record the new degree location.  Draw a sketch showing the position of the "figure" after the rotation.  Drawing a sketch of the actual figure will emphasize to the students that a rotation is not simply a "sliding" of the figure to a new position.

2.  Place the "figure" at 135 degrees.  Rotate the figure 180 degrees.  Record the new degree location.  Draw a sketch showing the position of the "figure" after the rotation.

3.  Place the "figure" at 270 degrees.  Rotate the figure 135 degrees.  Record the new degree location.  Draw a sketch showing the position of the "figure" after the rotation. 

4.  Place the "figure" as close to the coordinates (2,4) as possible.  Rotate the figure 90 degrees.  What are the x and y coordinates of the "figure" after the rotation?  This discovery question is only an investigation.  It could be revisited by the teacher (as a demonstration in front of the class) when the "rules" for rotating coordinates are discussed.

5.  Place the "figure" as close to the coordinates (-4,-6) as possible.  Rotate the figure 180 degrees.  What are the x and y coordinates of the "figure" after the rotation?