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Grade 5 Mathematics, Quarter 2, Unit 2.2
Volume
Overview
Number of instructional days:
10
(1 day = 60 minutes)
Content to be learned
Mathematical practices to be integrated

Understand the concepts of volume and relate
to multiplication and addition.
Make sense of problems and persevere in solving
them.

Understand and use unit cubes to measure
volume.

Explain the meaning of the problem.

Recognize and apply the formulas for volume.

Consider similar problems to gain insight into
its solution.

Recognize volume is additive (add the volumes
of two nonoverlapping right rectangular
prisms).

Check their answers to problems using
different methods.

Solve real-word problems using volume.

Fluently multiply multidigit whole numbers
using the standard algorithm.

Apply the formulas V = b x h and V = l x w x h.
Reason abstractly and quantitatively.

Make sense of quantities in situations.

Consider the units involved.

Flow between contextual and noncontextual
situations during problem solving.

How would you apply the formula to find the
volume of a right rectangular prism?

How would you show that volume is additive?

How would you show the process of
multiplying multidigit whole numbers using the
standard algorithm?
Essential questions

What is volume?

What are the attributes of a cube?

How do you find volume using unit cubes?

What is the formula for finding volume of a
right rectangular prism?
Warwick Public Schools, in collaboration with
the Charles A. Dana Center at the University of Texas at Austin
C-21
Grade 5 Mathematics, Quarter 2, Unit 2.2
Volume (10 days)
Written Curriculum
Common Core State Standards for Mathematical Content
Measurement and Data
5.MD
Geometric measurement: understand concepts of volume and relate volume to multiplication and
to addition.
5.MD.3
Recognize volume as an attribute of solid figures and understand concepts of volume
measurement.
a.
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.
b.
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.
5.MD.4
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised
units.
5.MD.5
Relate volume to the operations of multiplication and addition and solve real world and
mathematical problems involving volume.
a.
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.
b.
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.
c.
Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the non-overlapping parts,
applying this technique to solve real world problems.
Number and Operations in Base Ten
5.NBT
Perform operations with multi-digit whole numbers and with decimals to hundredths.
5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.
Warwick Public Schools, in collaboration with
the Charles A. Dana Center at the University of Texas at Austin
C-22
Grade 5 Mathematics, Quarter 2, Unit 2.2
Volume (10 days)
Common Core Standards for Mathematical Practice
1
Make sense of problems and persevere in solving them.
Mathematically proficient students start by explaining to themselves the meaning of a problem and
looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They
make conjectures about the form and meaning of the solution and plan a solution pathway rather than
simply jumping into a solution attempt. They consider analogous problems, and try special cases and
simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate
their progress and change course if necessary. Older students might, depending on the context of the
problem, transform algebraic expressions or change the viewing window on their graphing calculator to
get the information they need. Mathematically proficient students can explain correspondences between
equations, verbal descriptions, tables, and graphs or draw diagrams of important features and
relationships, graph data, and search for regularity or trends. Younger students might rely on using
concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students
check their answers to problems using a different method, and they continually ask themselves, “Does
this make sense?” They can understand the approaches of others to solving complex problems and
identify correspondences between different approaches.
2
Reason abstractly and quantitatively.
Mathematically proficient students make sense of quantities and their relationships in problem situations.
They bring two complementary abilities to bear on problems involving quantitative relationships: the
ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the
representing symbols as if they have a life of their own, without necessarily attending to their referents—
and the ability to contextualize, to pause as needed during the manipulation process in order to probe into
the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent
representation of the problem at hand; considering the units involved; attending to the meaning of
quantities, not just how to compute them; and knowing and flexibly using different properties of
operations and objects.
Clarifying the Standards
Prior Learning
In fourth grade, students learned to apply the formulas for area and perimeter for rectangles in real-world
and mathematical problems. They described, analyzed, and classified two-dimensional shapes.
Current Learning
Students recognize volume as an attribute of three-dimensional space. They understand that a 1-unit by
1-unit by 1-unit cube is the standard unit for measuring volume. Students measure necessary attributes of
shapes in order to determine volumes to solve real-world and mathematical problems. They recognize that
the volume of two smaller right rectangular prisms can be added to find the total volume of a larger
figure. Right rectangular prisms and rectangular prisms are used interchangeably now, but later a
distinction will be made between prisms and right prisms.
Future Learning
In sixth grade, students reason about right rectangular prisms with fractional side lengths and prepare to
work on scale drawings and constructions in grade 7.
Warwick Public Schools, in collaboration with
the Charles A. Dana Center at the University of Texas at Austin
C-23
Grade 5 Mathematics, Quarter 2, Unit 2.2
Volume (10 days)
Additional Findings
Students recognize volume as an attribute of three-dimensional space. They understand that they can
quantify volume by finding the total number of same-sized units of volume that they need to fill the space
without gaps or overlaps. (Curriculum Focal Points, NCTM, p. 17)
Warwick Public Schools, in collaboration with
the Charles A. Dana Center at the University of Texas at Austin
C-24