Oakland Terrace Elementary School

Rotation on a coordinate grid, completed on an online geoboard

Ms. Lyons's Class used the online geoboard to rotate designs on a coordinate grid. The geoboard shows the ordered pair for each point on the design when the cursor is placed on the point. (3,1) is one point on the light blue triangle in quadrant 1. Rotating the triangle 90º clockwise , the point becomes (1, -3) in quadrant 4. Rotated again, the point becomes (-3, -1). Finally, rotated the last time, the point becomes (-1, 3). When the four points are connected, they form a square.


Indicators: 2.5.4.1 identify transformations in a tessellation. 2.6.4.2 locate, give coordinates of, and graph plane figures that are the results of rotations (multiples of 90 degrees).	Students in Ms. Kondelis's fifth grade class use geoboards to make a design. They record the design in one quadrant of the coordinate grid. They then rotate the geoboard 90 degrees and record the design again. They continue rotating the geoboard and recording the design. Look at the design below to see what happens when you connect the same four points in each of the quadrants.


After completing the 90 degree rotations about the origin (0,0), students in Ms. Lyons's class choose one point on their design and identify the ordered pair in quadrant one; in the example above point (1, 3). The students then label the corresponding point in each of the other three quadrants. When students connect the four points, they will always find a square.	Labeling the points in all four quadrants prepares students for identifying both positive and negative values on the x and y axes. The students can also make generalizations about what happens to the coordinate pairs when rotating 90 degrees. In the example above, the student sees that (3, 2) rotated 90 degrees clockwise becomes (2, -3). Rotated again, the point becomes (-3, -2). The x and y values are switched, and the y value is multiplied by a value of -1.

Ms. Lyons's Class used the online geoboard to rotate designs on a coordinate grid. The geoboard shows the ordered pair for each point on the design when the cursor is placed on the point. (3,1) is one point on the light blue triangle in quadrant 1. Rotating the triangle 90º clockwise , the point becomes (1, -3) in quadrant 4. Rotated again, the point becomes (-3, -1). Finally, rotated the last time, the point becomes (-1, 3). When the four points are connected, they form a square.	Many students have to rely on the coordinates to figure out how to rotate the figure, reversing the x and y values and the positive to negative (this is a good time to discuss absolute value) when rotating by 90º. This student, however, was able to rotate the figures in her head before manipulating them on the geoboard.
These students first rotated a fairly simple design.	They continued rotating figures, making their design much more sophisticated.