Fifth Grade Mathematics
Unit 3
Whole Number Multiplication and Volume
Printable Parent Letter
During Unit 3, your children will recognize volume as an attribute of threedimensional space. They will understand that volume can be measured by finding the total number of samesize units of volume required to fill the space without gaps or overlaps. They will understand that a 1unit by 1unit by 1unit 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 threedimensional 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.

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 multidigit 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 wholenumber 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 wholenumber 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 wholenumber edge lengths in the context of solving real world and mathematical problems.
 Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real world problems.

Carroll County Public Schools Video Support
Open Array for Multiplication

Ways Parents Can Help

Explore volume by finding the volume of boxes you have in your home. Measure the box to find the length, height and width. Use multiplication to find the volume.

If you have cubes at your home, use them to build a variety of rectangular prisms with the same volume. For example with 12 cubes you could make a 2 x 3 x 2 rectangular prism or a 1 x 6 x 2 rectangular prism.

Connect the area model of multiplication to the standard algorithm

Some Support Sites

Key Vocabulary to Know 
measurement
attribute
volume
solid figure
right rectangular prism
unit
unit cube
gap
overlap
cubic units (cubic cm, cubic in, cubic ft)
nonstandard cubic units

edge lengths
height
area of base
standard algorithm
multiply
factor
product
associative property of multiplication
