Big Ideas:
Volume of cubes can be determined by building models, using unit cubes with fraction edge lengths when appropriate.
Decomposing and rearranging provide a geometric way of both seeing that a measurement formula is the right one and seeing why it is the right one.
Formulas for finding volume use variables for which measurements can be substituted.
Volume of a cube can be calculated by using the formula V = s^3, V = lwh, and V = Bh.
This lesson builds on students' work with volume of rectangular prisms with whole number edge lengths, as well as fraction and mixed number multiplication and exponents. Using cubes designated as '1/2-inch' cubes, students will use a series of clues to model and then determine the volume of cubes with various, including fractional edge lengths. They will reason about why the formulas V=Bh, V = lwh, and V=s^3 are alternate strategies for finding the volume of a cube, possibly more efficient than modeling with fractional unit cubes. This lesson connects to finding volume of more complex figures in 6th, 7th, and 8th grade.
Vocabulary: 3-dimensional figure, base of 3-dimensional figure, cube, cubed, cubic units, edge, edge length, exponent, face, height, volume
Special Materials:
1 set (ideally about 1,000) cubes, such as centimeter cubes or unit cubes from Base Ten Blocks