## Study the Solids

3-5
1

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.

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.

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.

Assessment Option

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

Extension

Move on to the next lesson, Looking for Patterns.

Question 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.]

### Getting to Know the Solids

3-5
Students are introduced to some of the basic polyhedra. Students explore the shapes of the faces of these solids.

### Looking for Patterns

3-5
Students discover Euler's Formula, a way of calculating the number of faces, edges, and vertices of geometric solids.

### Construct a Solid

3-5
Students construct physical models of geometric solids.

### Making A Shape Jacket

3-5
Students identify which geometric solids can be made from given nets. Students also create nets for common geometric solids.

### 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.

### NCTM Standards and Expectations

• Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes.

### 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.