Classroom Resource

Rotation and Dilation

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

In this video from KCPT, watch an animated demonstration of rotating and dilating a triangle on the coordinate plane. In the accompanying classroom activity, students watch the video; draw rotations and dilations of a triangle; and identify center of rotation, angle of rotation, and scale factors in classmates drawings. To get the most from the lesson, students should be comfortable graphing points on the coordinate plane and reproducing a drawing of a geometric shape at a different scale. Prior exposure to rotation and dilation is helpful.

Content Standards

Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.16
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

Unpacked Content

Vocabulary

Dissection arguments
Cavalieri's Principle
Cylinder
Pyramid
Cone
Ratio
Circumference
Parallelogram
Limits
Conjecture
Cross-section

Knowledge

Students know:

Techniques to find the area and perimeter of parallelograms.
Techniques to find the area of circles or polygons.

Skills

Students are able to:

Accurately decompose circles, cylinders, pyramids, and cones into other geometric shapes.
Explain and justify how the formulas for circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone may be created from the use of other geometric shapes.

Understanding

Students understand that:

Geometric shapes may be decomposed into other shapes which may be useful in creating formulas.
Geometric shapes may be divided into an infinite number of smaller geometric shapes, and the combination of those shapes maintain the area and volume of the original shape.

Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.26
Verify experimentally the properties of dilations given by a center and a scale factor.

Unpacked Content

Vocabulary

Dilations
Center
Scale factor

Knowledge

Students know:

Methods for finding the length of line segments (both in a coordinate plane and through measurement).
Dilations may be performed on polygons by drawing lines through the center of dilation and each vertex of the polygon then marking off a line segment changed from the original by the scale factor.

Skills

Students are able to:

Accurately create a new image from a center of dilation, a scale factor, and an image.
Accurately find the length of line segments and ratios of line segments.
Communicate with logical reasoning a conjecture of generalization from experimental results.

Understanding

Students understand that:

A dilation uses a center and line segments through vertex points to create an image which is similar to the original image but in a ratio specified by the scale factor.
The ratio of the line segment formed from the center of dilation to a vertex in the new image and the corresponding vertex in the original image is equal to the scale factor.

Interdisciplinary Connection(s)

Link to Resource

https://aptv.pbslearningmedia.org/resource/mkcpt-math-g-rotationdilation/rotati…

Content Type / Source

CR Resource Type

Audio/Video

Resource Provider

PBS

Accessibility

License

License Type

PD

Comments or Notes

This resource contains a rotations and dilations activity sheet and problem cards.

Approved Date

2022-09-13

Curated by

Design by Adaptive Theme