Lesson 13

How Much Will Fit?

Lesson Narrative

The purpose of this lesson is to remind students of the tangible meaning of volume: that it’s the amount of space contained in a three-dimensional figure. Students estimate the amount of stuff different containers hold, recalling units of measurement commonly used for volume, like fluid ounces, cups, liters, gallons, cubic feet, and cubic centimeters (also known as milliliters). They revisit the names of figures learned prior to this unit: cylinders, cones, rectangular prisms, and spheres, and see some physical containers that can be modeled with these. It is important for students to make these connections between physical and mathematical objects so that, later on, real-world objects can be modeled with idealized figures.

Students also learn a method for quickly drawing a cylinder. Later in the unit, they also learn quick methods for sketching a cone and a sphere. This skill was included both because it is a handy thinking tool to have access to in problem solving and also because it helps students better understand the meaning of terms like radius and height as they apply to these mathematical objects.

Learning Goals

Teacher Facing

  • Draw a cylinder and label its height and radius, describe (in writing) the shape of the “base” of the figure.
  • Estimate the volumes of various containers using different units of measure, and explain (orally) the reasoning.

Student Facing

Let’s reason about the volume of different shapes.

Required Preparation

Consider bringing in containers, dried rice, and measuring tools for the What’s Your Estimate activity. It is also recommended that you have various-sized solid objects for students to pass around during the Do You Know These Figures activity.  

Learning Targets

Student Facing

  • I know that volume is the amount of space contained inside a three-dimensional figure.
  • I recognize the 3D shapes cylinder, cone, rectangular prism, and sphere.

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.
  • cone

    A cone is a three-dimensional figure like a pyramid, but the base is a circle.

  • 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.

  • cylinder

    A cylinder is a three-dimensional figure like a prism, but with bases that are circles.

  • 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
  • sphere

    A sphere is a three-dimensional figure in which all cross-sections in every direction are circles.

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