Shapes and Space: Thinking Three-Dimensionally
Students explore three-dimensional figures through investigations into cross
sections, volume, and optimization. Students first use centimeter cubes to
explore surface area and volume of rectangular solids and other figures that
can be built from cubes. They then explore prisms and cylinders and develop
surface area and volume formulas for each. Lastly, they work with pyramids
and cones and again develop surface area and volume formulas as well as creating
nets for different solids.
NCTM standard: Geometry
- Analyze characteristics and properties of two- and three-dimensional geometric
shapes and develop mathematical arguments about geometric relationships
- Use visualization, spatial reasoning, and geometric modeling to solve
problems
NCTM standard: Measurement
- Understand measurable attributes of objects and the units, systems, and
processes of measurement
- Apply appropriate techniques, tools, and formulas to determine measurements
Primary Mathematical Goals
- Draw nets and cross sections to see the connection between two- and three-dimensional
figures
- Develop and use formulas for the surface areas of geometric solids
- Make three-dimensional models
- Develop and use formulas for the volumes of geometric solids
- Understand and compare units of surface area and volume
