Lesson 15

More Nets, More Surface Area

Lesson Narrative

This lesson further develops students’ ability to visualize the relationship between nets and polyhedra and their capacity to reason about surface area.

Previously, students started with nets and visualized the polyhedra that could be assembled from the nets. Here they go in the other direction—from polyhedra to nets. They practice mentally unfolding three-dimensional shapes, drawing two-dimensional nets, and using them to calculate surface area. Students also have a chance to compare and contrast surface area and volume as measures of two distinct attributes of a three-dimensional figure.

Learning Goals

Teacher Facing

  • Draw and assemble a net for the prism or pyramid shown in a given drawing.
  • Interpret (using words and other representations) two-dimensional representations of prisms and pyramids.
  • Use a net without gridlines to calculate the surface area of a prism or pyramid and explain (in writing) the solution method.

Student Facing

Let’s draw nets and find the surface area of polyhedra.

Required Preparation

Copy and cut the blackline master for the Building Prisms and Pyramids activity. Make one copy for every 9 students, so that each student gets one drawing of a polyhedron. Consider assignments of polyhedra in advance.

Learning Targets

Student Facing

  • I can calculate the surface area of prisms and pyramids.
  • I can draw the nets of prisms and pyramids.

CCSS Standards

Building On

Addressing

Glossary Entries

  • base (of a prism or pyramid)

    The word base can also refer to a face of a polyhedron.

    A prism has two identical bases that are parallel. A pyramid has one base.

    A prism or pyramid is named for the shape of its base.

    Two figures, a pentagonal prism and a hexagonal pyramid.
  • face

    Each flat side of a polyhedron is called a face. For example, a cube has 6 faces, and they are all squares.

  • net

    A net is a two-dimensional figure that can be folded to make a polyhedron.

    Here is a net for a cube.

    Six squares arranged with 4 in a row, 1 above the second square in the row, and one below the second square in the row.
  • polyhedron

    A polyhedron is a closed, three-dimensional shape with flat sides. When we have more than one polyhedron, we call them polyhedra.

    Here are some drawings of polyhedra.

    3 polyhedra, from left to right shapes resemble a house, drum, and star.
  • prism

    A prism is a type of polyhedron that has two bases that are identical copies of each other. The bases are connected by rectangles or parallelograms.

    Here are some drawings of prisms.

    A triangular prism, a pentagonal prism, and a rectangular prism.
  • pyramid

    A pyramid is a type of polyhedron that has one base. All the other faces are triangles, and they all meet at a single vertex.

    Here are some drawings of pyramids.

    a rectangular pyramid, a hexagonal pyramid, a heptagonal pyramid
  • surface area

    The surface area of a polyhedron is the number of square units that covers all the faces of the polyhedron, without any gaps or overlaps.

    For example, if the faces of a cube each have an area of 9 cm2, then the surface area of the cube is \(6 \boldcdot 9\), or 54 cm2.