During Unit 3, your children will recognize volume as an attribute of three-dimensional space. They will understand that volume can be measured by finding the total number of same-size units of volume required to fill the space without gaps or overlaps. They will understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. Your children will select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. They will decompose three-dimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes. Your children will measure necessary attributes of shapes in order to determine volumes to solve real world and mathematical problems.
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Students need to:
- Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
- A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
- A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
- Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
- Multiply multi-digit whole numbers using the standard algorithm.
- Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
- Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
- Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
- Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.