# 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 Preparation

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

### Student Facing

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