Fifth Grade Mathematics – Unit 3
Dear Parents,
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.
Whole number Multiplication/volume
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 nonoverlapping parts, applying this technique to solve real
world problems.
.
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.
Background information and examples
for Parents
open array model for multiplication
http://video.carrollk12.org/view/WELCHOPENARR
AYWITHMULT
Key Vocabulary
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