MA19.MM.12 | ALEX

Mathematics (2019) Grade(s): 09-12 - Mathematical Modeling

MA19.MM.12

Use technology and other tools to explore the results of simple transformations using three- dimensional coordinates, including translations in the x, y, and/or z directions; rotations of $90^{\circ}$, $180^{\circ}$, or $270^{\circ}$ about the x, y, and z axes; reflections over the xy, yz, and xy planes; and dilations from the origin.

COS Examples
Example: Given the coordinates of the corners of a room in a house, find the coordinates of the same room facing a different direction.

Unpacked Content

Knowledge

Students know:

how to translate points in the two dimensional coordinate plane and can extend this knowledge to three dimensions.
how to rotate points 90, 180 or 270 degrees in the two dimensional coordinate plane and can extend this knowledge to the three dimensional coordinate system.
how to reflect two dimensional objects over the x- or y-axis and can extend this knowledge to the three dimensional coordinate system.

Skills

Students are able to:

extend their knowledge of transformations in the two dimensional coordinate plane to the three dimensional coordinate system.

Understanding

Students understand that: transformations can be performed in the three dimensional coordinate systems and the transformations are similar to those in the two dimensional coordinate plane.

Vocabulary

Transformation
Translation
Rotation
Three Dimensional Coordinates