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Big Ideas:
Volume of rectangular prisms 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 rectangular prism can be calculated by using the formulas 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. Students will determine the volume of rectangular prisms with fractional edge lengths either by modeling using cubes designated as '1/2-inch' cubes or by using a formula. They will reason that the formulas V=Bh and V = lwh are alternate strategies for finding the volume of a rectangular prism, possibly more efficient than modeling with fractional unit cubes. This lesson connects to finding volume of more complex figures in 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