6-GM-4-2


6.GM.4.2 Recognize that translations, reflections, and rotations preserve congruency and use them to show that two figures are congruent.

In a Nutshell

Transforming a two-dimensional figure through translation, reflection, rotation or a combination of these transformations preserves congruency, which means the image is exactly the same as the preimage except for its location and orientation in the plane. Two figures are congruent if one of the figures can be mapped onto the other using a sequence of transformations including translation, reflection, or rotation.

Student Actions

Teacher Actions

  • Develop a deep and flexible conceptual understanding of congruency using translations, reflections, and rotations to prove two figure are congruent.

  • Develop the ability to communicate mathematically through discussion and writing about strategies used to determine two figures are congruent using translations, reflections, and rotations.

 

  • Implement tasks that promote problem solving which involve proving two figures are congruent using translations, reflections, and rotations. For example, the task could be cutting out the original figure and performing the necessary transformations to show the resulting figure is congruent to the original figure.

  • Pose purposeful questions about congruency and how translations, reflections, and rotations preserve congruency.  For example, is the preimage congruent to the image shown in the coordinate plane below? If so, what transformation or sequence of transformations can be used to prove that the preimage and image are congruent?

 

                                   

 

Key Understandings

Misconceptions

  •  Translations, reflections, and rotations preserve congruency.

  • How to show two figures are congruent by mapping one figure onto the other using translations, reflections, and rotations.

 

 
  • Not recognize congruent figures if they are oriented differently in the plane. For example, students may say these parallelograms are not congruent because of their orientation.

 

                                                           

 

OKMath Framework Introduction

6th Grade Introduction