Unit 2, Lesson 2
Circular Grid
Grade 8
Preparation
Lesson Narrative
This lesson formally defines the term dilation as a transformation in which each point on a figure moves along a line and changes its distance from a fixed point, called the center of dilation. The scale factor determines how far each point moves.
First, students are introduced to the circular grid as an effective tool for performing a dilation. By using the structure of the grid in the next activities, they find that each grid circle maps to a grid circle, line segments map to line segments, and the image of a polygon is a scaled copy of the polygon (MP7). In addition, students determine scale factors that are used and explain their reasoning (MP3).
- Create dilations of polygons using a circular grid given a scale factor and center of dilation.
- Explain (orally) how a dilation affects the size, side lengths and angles of polygons.
Let’s dilate figures on circular grids.
Required Preparation
Provide access to straightedges. For the digital version of the activity, acquire devices that can run the applet.
Provide access to straightedges. For the digital version of the activity, acquire devices that can run the applet.
Provide access to straightedges. For the digital version of the activity, acquire devices that can run the applet.
A dilation is a transformation that can reduce or enlarge a figure. Each point on the figure moves along a line closer to or farther from a fixed point. That fixed point is the center of the dilation. All of the original distances are multiplied by the same scale factor.
Triangle is a dilation of triangle . The center of dilation is . The scale factor is 3.
Every point of triangle is 3 times as far from as every corresponding point of triangle .