## Study the Solids

In this interactive geometry investigation, students explore geometric solids and their properties. Specifically, students count the number of faces, edges, and corners (vertices) in various solids.

Students will need the Geometric Solids Tool for this lesson.

Geometric Solids Tool |

As students are exploring the various geometric solids, begin a class discussion which includes the following points.

Students should note the following characteristics:

- Each solid has flat sides called
**faces**. - Each solid has
**edges**to connect the faces. - Each solid has
**corners**that connect the edges.*(Note that the activity sheet refers to corners as "vertices", so you may wish to familiarize students with this vocabulary.)*

If you have these shapes in your classroom, have students find the shapes that match those in this computer activity.

This lesson is designed to help students focus on the properties of each shape. The tools allow them to color the faces, edges, or corners (vertices) easily by holding the shift key while clicking the mouse on the paint palette and then on a face. (The edges are always white and the corners black.)

Distribute the Exploring Geometric Solids Activity Sheet to the students.

Exploring Geometric Solids Activity Sheet |

*Teacher Note:* For today's lesson, students will only
complete the table on the activity sheet. Save the three questions
below the table for tomorrow's lesson.

As students complete the activity sheet, guide them as needed. For example, when asking "How many sides does each face have?", guide the student to click the given face, and color the sides. When determining the number of faces, it may be helpful to color the faces and count as they color. (It's interesting to observe students doing this: some color all faces the same color, while others color the faces different colors.)

After determining the number of faces, students are asked to count the number of edges and vertices (corners) in the solid. Before actually counting the number of edges, students may wish to "guess" the number.

For example, working with the dodecahedron, a student may say each face has five sides — a pentagon. She counts 12 faces. In guessing the number of edges, she may estimate 60 and give as her reason, "5 sides × 12 faces = 60 edges." Counting the edges with the result of 30 provided an opportunity to have her take a second look at the dodecahedron and find out why. (Each edge is shared by two faces.)

Taking advantage of opportunities such as these enriches student understanding.

**Assessments**

Collect the students' activity sheets to assess student understanding. Answers to the activity sheet are available.

**Questions for Students**

- When you guessed the number of edges in a particular solid, were you correct? Did this affect how you guessed and counted the number of edges in the other solids?

[Student responses may vary. Note that students should use their incorrect guesses to inform future predictions.]

### Looking for Patterns

### Construct a Solid

### Making A Shape Jacket

### Learning Objectives

Students will:

- Analyze characteristics and properties of three-dimensional geometric shapes
- Count the number of faces, edges, and corners (vertices) in various geometric solids

### Common Core State Standards – Practice

- CCSS.Math.Practice.MP1

Make sense of problems and persevere in solving them.

- CCSS.Math.Practice.MP4

Model with mathematics.

- CCSS.Math.Practice.MP5

Use appropriate tools strategically.

- CCSS.Math.Practice.MP7

Look for and make use of structure.