Unit 1, Lesson 13
Polyhedra
Grade 6
Preparation
Lesson Narrative
In this lesson, students learn about polyhedra and their nets. They also study prisms and pyramids as types of polyhedra with certain defining features.
Students begin by identifying the defining characteristics of polyhedra. They learn or review terminology, such as "faces," "edges," and "vertices," as they develop a working definition of "polyhedra."
Next, students explore the defining characteristics of prisms and pyramids. They consider the polygons that constitute the faces of a given prism or pyramid and how to arrange them into nets that can be assembled into the given polyhedron.
As students analyze polyhedra, prisms, and pyramids for defining characteristics and use their observations to distinguish these figures, they practice looking for and making use of structure (MP7). In communicating the geometric attributes that they see, students practice attending to precision (MP6).
An optional activity is included to give students an opportunity to assemble a net into a polyhedron and identify the number of vertices, edges, and faces.
A note about polygons and polyhedra:
Here are some important aspects of polygons:
- They are made out of line segments called edges.
- Edges meet at a vertex.
- The edges meet only at vertices.
- Polygons always enclose a two-dimensional region.
Here is an analogous way to characterize polyhedra:
- They are made out of filled-in polygons called faces.
- Faces meet at an edge.
- The faces meet only at edges.
- Polyhedra always enclose a three-dimensional region.
Students do not need to memorize a formal definition of a polyhedron, but recognizing its defining characteristics can help students make sense of nets and surface area.
In today’s activities, students are introduced to the idea of math norms as expectations that help everyone in the room feel safe, comfortable, and productive doing math together. Students then consider what norms would connect and support the math actions that the class recorded so far in the Math Community Chart.
- Compare and contrast (orally and in writing) features of prisms and pyramids.
- Comprehend and use the words “face”, “edge”, “vertex”, and “base” to describe polyhedra (in spoken and written language).
- Understand that the word “net” refers to a two-dimensional figure that can be assembled into a polyhedron, and create a net for a given polyhedron.
Let’s investigate polyhedra.
Required Materials
Activity 2
Required Preparation
Assemble collections of geometric figures that each contains at least 2 familiar polyhedra, 2 unfamiliar polyhedra, and 2 non-polyhedra. Prepare one collection for each group of 3–4 students. If pre-made polyhedra are unavailable, assemble some from the nets in the blackline master.
Print and pre-cut the nets and polygons in the blackline master. Prepare 1 set per group of 3–4 students, along with tape to join the polygons into a net.
Print the nets from the same blackline master as the one used for the Warm-up. For each student, prepare 2 copies of one net and tape or glue to assemble the net.
A base is a specific face of a prism or pyramid.
A prism has 2 identical bases that are parallel. A pyramid has 1 base.
A prism or pyramid is named for the shape of its base.
A net is a two-dimensional figure that can be folded to make a three-dimensional figure.
Here is a net for a cube.