Volume and Surface Area
(taken from “Big Ideas by Dr. Small”):
- The area of an object is a two-dimensional attribute. Area can be a single measure of a 2-D shape on an object or a combined measure of a 3-D shape, like surface area.
- The capacity of an object tells how much it will hold.
- The volume of a 3-D object tells how much material it takes to build the object.
- The mass of an object tells how heavy it is.
STUDENT LEARNING GOALS:
GOAL #1: I can calculate the surface area of right prisms.
- VIDEO: Nets of Polyhedra (Source: Khan Academy)
- VIDEO: Surface Area of a Box (Source: Khan Academy)
- VIDEO: Surface Area of a Rectangular Prism (Source: Khan Academy)
- VIDEO: Surface Area of a Triangular Prism (Source: Khan Academy)
- PRACTICE: Nets of Polyhedra (Source: Khan Academy)
- PRACTICE: Calculating Surface Area (Source: MathFrog)
- QUIZ: Nets of Prisms and Cylinders (Source: Nelson Education)
- QUIZ: Surface Area of a Rectangular Prism (Source: Nelson Education)
- QUIZ: Determining the Surface Area of Prisms (Source: Nelson Education)
- INTERACTIVE: Nets of Prisms (Source: Learner.org)
- INTERACTIVE: Exploring Nets, Surface Area and Volume (Source: LearnAlberta.ca)
GOAL #2: I can determine the volume of right prisms.
- Determine, through investigation using a variety of tools (e.g., nets, concrete materials, dynamic geometry software, Polydrons), the surface area of right prisms;
- Solve problems that involve the surface area and volume of right prisms and that require conversion between metric measures of capacity and volume (i.e., millilitres and cubic centimetres).
- Determine the relationships among units and measurable attributes, including … the volume of a right prism;
- Sketch different polygonal prisms that share the same volume;
- Determine, through investigation using a variety of tools and strategies (e.g., decomposing right prisms; stacking congruent layers of concrete materials to form a right prism), the relationship between the height, the area of the base, and the volume of right prisms with simple polygonal bases (e.g., parallelograms, trapezoids), and generalize to develop the formula (i.e., Volume = area of base x height);