6.GM.4.1 Predict, describe, and apply translations (slides), reflections (flips), and rotations (turns) to a twodimensional figure.
In a Nutshell
A translation of a twodimensional 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 twodimensional 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 yaxis). A twodimensional figure can also be rotated or “turned” clockwise or counterclockwise. The description of a rotation of a twodimensional 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 twodimensional figure provides an opportunity to check the accuracy of the result.
Student Actions

Teacher Actions


Develop the ability to make predictions and draw conclusions about the results of a given translation, reflection, or rotation for twodimensional 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 twodimensional 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 twodimensional figure changes position when it is translated, reflected, or rotated. For example, the task could be performing transformations using a twodimensional shape cut out of cardstock.
 Pose purposeful questions to assess students’ understanding of how translations, reflections, and rotations transform twodimensional figures. For example, what transformations or sequences of transformations can be used to map the preimage to its image in the coordinate plane below?

Key Understandings

Misconceptions


Translations slide a twodimensional figure left or right and up or down.

Reflections create a mirror image of the original twodimensional figure by flipping the figure across a given line.

Rotations turn a twodimensional figure clockwise or counterclockwise.

The transformation of a twodimensional figure can be described using different transformations or a combination of transformations.


Think the terms translation, reflection, and rotation are interchangeable.
 Forget that twodimensional 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
6th Grade Introduction
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