Geometry : Unit #12 - The Third Dimension : Lesson #1

Introduction to the Third Dimension

Objective: SWBAT identify the shapes of cross-sections of three-dimensional objects.
Standards: HSG-GMD.B.4 MP3 MP4
Subject(s): Math
60 minutes
1 Do Now - 7 minutes

As students walk in the room, I hand them a page with an excerpt from the book Flatland by Edwin Abbott (Part I, Section 1: "Of the Nature of Flatland"). We read the passage out loud using the "popcorn" method. One student begins to read and then chooses the next student. While the students are reading, I hand them a penny. A. Square, the narrator of Flatland, uses a penny to describe how the "Flatlanders" see their world. I have the students view the penny as described in the passage. This activity helps students prepare for the activity they will complete later in the lesson. 

Prior to this activity, I show the students the 2007 film version of  Flatland in order to give context for the unit on the 3rd dimension.

2 Mini-Lesson - 10 minutes

At the beginning of the Mini-Lesson, students are shown pictures of various solids. I call on students to identify the solids. We discuss prisms and and then identify which of the solids are prisms. 

In the activity, students use play dough to investigate the shapes of cross sections of solids. Before they start, I model the activity using a cylinder. I show the students how to mold their clay into a cylinder and how to use a ruler to make various slices. Then the students repeat what I did to show they understand the task.

3 Activity - 23 minutes

In the activity, students work in pairs to create models of solids in order to identify the cross-sections of the solids (G.GMD.4, MP4). Students use clay or play dough to form the shapes and a ruler to make slices. They record their results in a chart

When students slice their shapes, it is helpful to have one student hold the shape while the other makes the slice. They may also have to reform their slice a bit depending on the type of clay used. 

One way of enacting the activity is to assign each pair a different shape to investigate. At the end of the activity, students present their results, while the other students draw representations of the cross-sections on their charts. 

4 Summary - 5 minutes

At the end of the lesson, students are shown examples of cross-sections and asked to identify the solids which have those cross-sections (G.GMD.4). Students discuss their answers with a partner. We then have a class discussion. There are multiple answers for the second set of cross-sections. I call on different students to give their answers and justify their responses (MP3).