Lesson 13

Decomposing Bases for Area

Lesson Narrative

In this lesson, students continue working with the volume of right prisms. They encounter prisms where the base is composed of triangles and rectangles, and decompose the base to calculate the area. They also work with shapes such as heart-shaped boxes or house-shaped figures where they have to identify the base in order to see the shape as a prism and calculate its volume (MP1). When students look for the prism structure in a shape to solve a problem, they are engaging in MP7.

Learning Goals

Teacher Facing

  • Critique (orally) different methods for decomposing and calculating the area of a prism’s base.
  • Explain (orally and in writing) how to decompose and calculate the area of a prism’s base, and then use it to calculate the prism’s volume.

Student Facing

Let’s look at how some people use volume.

Learning Targets

Student Facing

  • I can calculate the the volume of a prism with a complicated base by decomposing the base into quadrilaterals or triangles.

CCSS Standards


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.
  • cross section

    A cross section is the new face you see when you slice through a three-dimensional figure.

    For example, if you slice a rectangular pyramid parallel to the base, you get a smaller rectangle as the cross section.

  • 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
  • volume

    Volume is the number of cubic units that fill a three-dimensional region, without any gaps or overlaps.

    For example, the volume of this rectangular prism is 60 units3, because it is composed of 3 layers that are each 20 units3.

    Two images. First, a prism made of cubes stacked 5 wide, 4 deep, 3 tall. Second, each of the layers of the prism is separated to show 3 prisms 5 wide, 4 deep, 1 tall.

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