Getting Started

The student does not demonstrate an understanding of reflections and rotations.

The student:

• Attempts to perform the reflections or rotations but is unable to do so correctly.
  
  
  
  
• Says the triangle cannot be reflected since line m does not coincide with one of the sides of the triangle or that it cannot be rotated since the direction of rotation was not given.
• Indicates that he or she does not understand.
  
  

Did you attempt to reflect the figure? What happened?

Did you attempt to rotate the figure? How did you start? Where was the figure after the first rotation?

What does it mean to reflect a figure across a line?

What does it mean to rotate a figure 90° around a point?

Review the definitions of reflections and rotations. Allow the student to experiment with reflections and rotations by using transparent paper or interactive websites such as http://tinyhttp://tinyurl.com/pxzmw5ourl.com/pxzmw5o and http://www.mathopenref.com/reflect.html.

Consider using MFAS tasks Define A Reflection (G-CO.1.4), Define A Rotation (G-CO.1.4), and Rotation of a Quadrilateral (G-CO.1.5) if not previously used.

Ask the student to perform each indicated transformation. Guide the student to observe that the triangle returns to its original position after two reflections and then again after four 90 degree rotations. Provide additional opportunities for the student to experiment with repeated reflections and rotations. Ask the student to first predict the effect on the figure and then perform the transformations. Eventually, ask the student to predict the location and orientation of the final image without having to perform the transformations.

Making Progress

The student’s explanation is unclear, incomplete, or contains an error.

The student understands that the triangle will return to its original position but provides an explanation that:

• Is unclear.
  
  
  
  
• Is incomplete.
  
  
  
  
• Includes notational errors.
  
  

Where would the triangle be located after it is reflected twice across line m?

Where would the triangle be located after it is rotated around point C four times in succession?

What degree rotation produces the same result as four successive 90° rotations?

Assist the student in clearly and completely explaining why the given transformations return the triangle to its original position. Allow the student to read model explanations written by his or her classmates.

Consider implementing MFAS tasks Transform This (G-CO.2.6) and Congruent Trapezoids (G-CO.2.6) if not used previously.

Got It

The student provides complete and correct responses to all components of the task.

The student states that after the reflections and rotations,  will return to its original position. Reflecting the triangle across the line m twice will bring it back to its original position. Four 90 degree rotations are the same as one 360 degree rotation which will again bring the triangle back to its original position.

Does it make a difference whether you rotate the triangle clockwise or counterclockwise?

Did you have to perform the reflections and rotations to determine what would happen?

Challenge the student to describe a sequence that includes exactly one rotation, one reflection, and one translation that returns the figure to its original position.

Consider implementing MFAS tasks Transform This (G-CO.2.6) and Congruent Trapezoids (G-CO.2.6) if not used previously.