Lesson 3

Dilations with no Grid

Lesson Narrative

In the previous lesson, students applied dilations on a circular grid. The circular grid provides two levels of scaffolding:

  • The radial lines give rays from the center of the grid which help find the dilated image of points on those rays.
  • The circles provide a way to measure the distance of points from the center of dilation.

In this lesson, students apply dilations to points with no grid. In order to perform a dilation, three pieces of information are still needed: a center of dilation, a scale factor, and a point which is dilated. Students practice identifying centers, scale factors, and images of dilation. They also use dilations to make perspective drawings. 

Performing dilations without a grid engages students in MP1 as they think about the meaning of dilation in terms of the given information (center, scale factor, point being dilated).

Learning Goals

Teacher Facing

  • Create a dilation of a figure given a scale factor and center of dilation.
  • Explain (orally) the effect of the scale factor on the size of the image of a polygon and its distance from the center of dilation.
  • Identify the center, scale factor, and image of a dilation without a circular grid.

Student Facing

Let’s dilate figures not on grids.

Required Materials

Required Preparation

Ensure that rulers, index cards, and colored pencils are available in the geometry toolkits.

Learning Targets

Student Facing

  • I can apply a dilation to a polygon using a ruler.

CCSS Standards


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