## 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