Volume of Figures and the Puzzle Maker


Lisa Castaneda, Math Teacher

School / Organization, City and State / Province
Shoreline, WA

Grade Level
6 or 7

Common Core Standards Met

  • 6th: Solve real-world and mathematical problems involving area, surface area, and volume
  • 6.G.4. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. ~Note: the surface area elements appear in a later lesson. ~ Apply these techniques in the context of solving real-world and mathematical problems
  • 7th: Draw, construct, and describe geometrical figures and describe the relationships between them
  • 7.G.2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions
  • 7.G.3. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids

Time Needed
Two class periods.


  • How is volume different than surface area? How does changing the dimensions of a rectangular prism impact the volume?
  • Students will be able to define volume and explain how it is different than area
  • Students will be able to calculate the volume of various rectangular prisms
  • Students will be able to make changes to a figure to derive a specific volume

In this lesson students explore the concept of volume by manipulating the dimensions of the test chamber in the Puzzle maker. They gain practice working with the formula for rectangular prisms, explore changing the dimensions of the room and their effects on volume as well as differences in volume and surface area. More complex figures are introduced as students manipulate the dimensions into rooms that are not perfect rectangular prisms and are then faced with finding the volume of more irregular shapes.


  • Volume – the number of cubic units needed to fill a 3-D figure
  • Surface area – the sum of the area of the bases and lateral faces of a 3-D figure

Teacher Materials Needed

  • If possible, a computer that will allow you to project the Puzzle Maker for class discussion purposes
  • Some sort of demonstration rectangular prism or cube (such as a Rubik’s cube) to illustrate volume

Student Materials Needed

  • The Puzzle Maker
  • Paper and pencil

Lesson Plan
Download Volume of Figures and the Puzzle Maker