Unit 6 - Filling and Wrapping

By the end of this unit, students are expected to:

Surface Area and Volume of Polygonal Prisms and Cylinders:

• 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:

• 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:

• 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

Helping At Home

When your child encounters a new problem, it is a good idea to ask questions such as:

• What are the shapes and properties of the figures in the problem?

• Which measures of a figure are involved—length, surface area, or volume?

• What measurement strategies or formulas might help in using given information to find unknown measurements?

Filling and Wrapping - Explanation of Concepts for Those Helping at Home - Connected Mathematics 3 Resource