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.
Watch as the National Museum of Mathematics uses an image of a visitor to create a "Human Tree" using dilations. This video focuses on how similar figures can create dilations and how exponents can be used in an equation to express the proportional relationship in fractals. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers.
In this animated Math Shorts video from the Utah Education Network, learn about rotation, which describes how a geometric shape turns around a point, called the center of rotation. When a geometric shape rotates on a coordinate plane, it stays exactly the same distance from the center of rotation. In the accompanying classroom activity, students are given two rotations from a handout and work in pairs to try to determine whether one figure is a rotation of the other figure around the given point. If the figure is a rotation, the student pair must add one more rotation to the grid. If the figure is not a rotation, the student pair must add one accurate rotation to the grid. This resource is part of the Math at the Core: Middle School Collection.
In Module 2, Topic A students revisit what scale drawings are and discover two systematic methods of how to create them using dilations. The comparison of the two methods yields the Triangle Side Splitter Theorem and the Dilation Theorem.
Module 2, Topic B is an in-depth study of the properties of dilations. Though students applied dilations in Topic A, their use in the ratio and parallel methods was to establish relationships that were consequences of applying a dilation, not directly about the dilation itself. In Topic B, students explore observed properties of dilations (Grade 8 Module 3) and reason why these properties are true. This reasoning is possible because of what students have studied regarding scale drawings and the triangle side-splitter and dilation theorems. With these theorems, it is possible to establish why dilations map segments to segments, lines to lines, etc. Some of the arguments involve an examination of several sub-cases; it is in these instances of thorough examination that students must truly make sense of problems and persevere in solving them (MP.1).
In Lesson 6, students revisit the study of rigid motions and contrast the behavior of the rigid motions to that of a dilation. Students confirm why the properties of dilations are true in Lessons 7–9. Students repeatedly encounter G.SRT.A.1a and b in these lessons and build arguments with the help of the ratio and parallel methods (G.SRT.B.4). In Lesson 10, students study how dilations can be used to divide a segment into equal divisions. Finally, in Lesson 11, students observe how the images of dilations of a given figure by the same scale factor are related, as well as the effect of a composition of dilations on the scale factor of the composition.
