Lesson 3

Creating Cross Sections by Dilating

Lesson Narrative

In this lesson, students build on their work with dilations in earlier units. Students create dilations of a rectangle and suspend them to resemble cross sections of a pyramid. They learn that given a pyramid’s base, its cross sections are dilations of the base with scale factors between 0 and 1.

These activities help build the spatial visualization skills and familiarity with cross sections they will need to derive volume formulas later in the unit. For example, students will later use dilations and cross sections to conclude that pyramids of the same height and with bases of equal area have equal volumes, regardless of the particular shapes of the bases.

Through articulating things they notice and things they wonder about dilations, students attend to precision in the language they use to describe what they see (MP6).

Learning Goals

Teacher Facing

• Comprehend that a pyramid’s cross sections can be thought of as dilations of its base using scale factors from 0 to 1.

Student Facing

• Let’s create cross sections by doing dilations.

Required Preparation

Be prepared to display an applet for all to see in the synthesis of the activity Pyramid Mobile.

Student Facing

• I know that a pyramid’s cross sections are dilations of its base with scale factors ranging from 0 to 1.

Building On