Filling and Wrapping: Three Dimensional Measurement
Surface Area and Volume of Polygonal Prisms and Cylinders: Understand surface area and volume of prisms and cylinders and how they are related.
- Describe prisms by using their vertices, faces, and edges
- Visualize three-dimensional shapes and the effects of slicing those shapes by planes
- Deepen understanding of volume and surface area of rectangular prisms
- Estimate and calculate surface area and volume of polygonal prisms by relating them to rectangular prisms
- Explore the relationships between the surface area and volume of prisms
- Relate surface area and volume for common figures, especially optimization of surface area for fixed volume
- Predict the effects of scaling dimensions on linear, area, and volume measures of cylinders and solid figures
- Investigate the relationship between volume and surface area of prisms and cylinders
- Use volume and surface area of prisms to develop formulas for volume and surface area of cylinders
- Discover that volumes of prisms and cylinders can be calculated as the product of the height and the area of the base
- Solve problems that involve questions about surface area and volume of solid figures
Area and Circumference of Circles: Understand the area and circumference of circles and how they are related.
- Relate area of a circle to covering a figure and circumference to surrounding a figure
- Estimate and calculate area and circumference of circles
- Explore the relationship between circle radius (and diameter) and area
- Investigate the connection of π to area calculation by estimating the number of ‘radius squares’ needed to cover a circle
- Investigate the relationship between area and circumference of a circle
- Solve problems that involve questions about area and circumference of circles
Volume of Spheres, Cones and Pyramids: Understand the relationship between the volume of cylinders to cones, spheres and pyramids.
- Relate volume of cylinders to volume of cones, spheres
- Estimate and calculate volume of spheres, cones and pyramids
- Relate volume of cones to volume of cylinders and volume of pyramids to volume of prisms
- Solve problems that involve questions about surface area and volume of spheres, cones and pyramids
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