Math

# Teaching Solid Figures: Vertices, Edges and More

In Teaching Flat Plane Shapes and Solid Shapes, we explore different attributes for flat and solid shapes. This lesson extends those concepts by having students identify and count specific attributes of solid shapes, such as vertices or edges. It is designed for students in Grades K–1 but can be extended or simplified to adjust for your students’ readiness.

• Key Standard: Identify and analyze three-dimensional shapes, using mathematical language to describe their similarities, differences, parts, and other attributes. (Common Core: K.G.B.4; Florida BEST: MA.1.GR.1.1)
• Objective: In this lesson, students will explore the parts that make up solid figures.

## Lesson: Identify and Analyze Solid Figures

Materials: One rectangular prism, cube, sphere, cone, cylinder, and pyramid for each group of students.

Preparation: Distribute solid figures to groups of students.

Prerequisite Skills and Background: Students should be able to recognize and name solid figures.

• Say: A face is a flat surface of a solid object. Show students the idea by holding up a solid object such as a rectangular prism and asking if anyone can identify a face of the object.
• Ask: Which solid figures have faces that are polygons? (rectangular prism, cube, and pyramid)
• Say: Put the other solid figures aside for now.
• Ask: Which solid figure has faces that are rectangles? (rectangular prism)
• Say: Count the number of faces a rectangular prism has. Mark each face as you count. To mark the faces temporarily, use stickers or sticky notes. Copy the table below as students are working so that all students can see it.

Teacher Tips:

• For your materials, if possible, use real world examples that relate to your students’ interests. For example, if some of your students play a sport that uses a spherical ball, you could make them a group and use that ball.
• Because so much of this lesson relies on examining and analyzing physical objects, it works well for students who are visually impaired. In place of the table below, explain what information you are looking for and have students describe the same information for each of the solid figures.
 Solid Figure Number of Faces Number of Edges Number of Vertices Rectangular Prism
• Ask: How many faces does a rectangular prism have? (6)
Record 6 on the table.
• Say: The line segment where two faces meet is an edge. Hold up a solid figure and show students an example of an edge. Count the number of edges a rectangular prism has. Mark each edge as you count. Similar to faces, use a marker, stickers, or sticky notes.
• Ask: How many edges does a rectangular prism have? (12) Record 12 on the table.
• Say: The point where edges meet is a vertex. Count the number of vertices a rectangular prism has. Mark each vertex as you count.
• Ask: How many vertices does a rectangular prism have? (8) Record 8 on the table.
• Have students find the number of faces, edges, and vertices of a cube and a pyramid. Record the answers in the table.

Teacher Tip: For students not yet ready for the mathematical vocabulary used here, you can use side instead of edge and corner instead of vertex.

 Solid Figure Number of Faces Number of Edges Number of Vertices Rectangular Prism 6 12 8 Cube 6 12 8 Pyramid 5 8 5
• Ask: Why do you think that a rectangular prism and a cube have the same number of faces, edges, and vertices? Lead students to realize that the faces of a rectangular prism and a cube are all rectangles, but in the case of the cube, the rectangles are squares. A cube is a special type of rectangular prism.

## Faces, Edges, and Vertices for Curved Surfaces

• Say: Take out your solid figures that have curved surfaces. Look at the sphere.
• Ask: Does a sphere have any edges or vertices? (no) Why not?
This is not a simple question and requires thinking critically about what an edge or vertex is. For example, many real-world objects that we call spheres, such as soccer balls, are in fact complex solid shapes with many edges and vertices. Consider using think-pair-share, where students independently think through their reasoning, share it with a partner, and then you facilitate a discussion around how a sphere has no faces, so it can’t have any edges, and because it has no edges, it can’t have any vertices.
• Say: Look at the cone.
• Ask: Does a cone have any edges? (no) Why not? Again, consider using think-pair-share. Avoid telling students that they are right or wrong. Instead, lead them to see that a cone only has one face, and you need more than one face to form an edge.
• Ask: Does a cone have any vertices? Lead students to see that a cone has no edges (at least no straight ones!), but the point where the surface of the cone ends is called the vertex of the cone.
• Say: Look at the cylinder.
• Ask: Does a cylinder have any edges or vertices? (no) Why not? Although a cylinder has two faces, the faces don’t meet, so there are no edges or vertices.

## Wrap-Up and Assessment Hints

To assess students’ understanding, you could introduce a new solid shape, such as a triangular prism, and have students fill out another row of the chart.

To explore more attributes of regular solid figures, ask questions such as the following:

• Which solid figures have opposite faces that are parallel? (rectangular prism, cube, cylinder)
• Which solid figures have opposite faces that are congruent? (rectangular prism, cube, cylinder, pyramid)
• Which solid figure has all congruent faces? (cube)

Through questioning strategies such as these, you will be able to judge your students’ understanding of solid figures. For students who are ready, you can ask questions that stretch into higher grade standards and promote a deeper understanding of solid figures:

• What would the cross-section of a solid look like? How would it change depending on what angle you use?
• How could you figure out how much liquid it would take to fill up the shape?

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