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# 6-GM-4-1

last edited by 2 years, 6 months ago

6.GM.4.1 Predict, describe, and apply translations (slides), reflections (flips), and rotations (turns) to a two-dimensional figure.

In a Nutshell

A translation of a two-dimensional figure “slides” the figure left or right and up or down and can be described in terms of units when the figure is on a coordinate plane (Ex. The figure is translated 4 units to the right.) A reflection of a two-dimensional figure “flips” the figure across a given line creating a mirror image of the original figure. Reflections can be described in terms of the line that was used to reflect the figure (Ex. The figure was reflected across the y-axis). A two-dimensional figure can also be rotated or “turned” clockwise or counterclockwise. The description of a rotation of a two-dimensional figure includes the degree and direction of the turn (Ex. The figure was rotated 90 degrees counterclockwise.) The original figure before a transformation is called the preimage and the resulting figure after a transformation is called the image.  Making predictions about the image before applying a given transformation on a two-dimensional figure provides an opportunity to check the accuracy of the result.

## Teacher Actions

• Develop the ability to make predictions and draw conclusions about the results of a given translation, reflection, or rotation for two-dimensional figures by investigating these transformations using manipulatives, such as pattern blocks or shapes cut out of cardstock.

• Develop problem solving strategies by using multiple representations, like physical models in the form of manipulatives or graphical models on a coordinate plane for solving problems involving translations, reflections, and rotations.

• Develop the ability to communicate mathematically through writing and discussion about how a two-dimensional figure has been transformed from its original position to its current position using translations, reflections, or rotations.

• Implement tasks that promote reasoning about how a two-dimensional figure changes position when it is translated, reflected, or rotated.  For example, the task could be performing transformations using a two-dimensional shape cut out of cardstock.

• Pose purposeful questions to assess students’ understanding of how translations, reflections, and rotations transform two-dimensional figures. For example, what transformations or sequences of transformations can be used to map the preimage to its image in the coordinate plane below? ## Misconceptions

• Translations slide a two-dimensional figure left or right and up or down.

• Reflections create a mirror image of the original two-dimensional figure by flipping the figure across a given line.

• Rotations turn a two-dimensional figure clockwise or counterclockwise.

• The transformation of a two-dimensional figure can be described using different transformations or a combination of transformations.

• Think the terms translation, reflection, and rotation are interchangeable.

• Forget that two-dimensional figures may be reflected across any line including diagonal lines like the line y=x, not just across horizontal or vertical axis.
• Think the terms clockwise and counterclockwise are interchangeable.

• Not be able to see the difference between counterclockwise/clockwise rotations and reflections across vertical /horizontal lines.

OKMath Framework Introduction