Formative Instructional and Assessment Tasks
Volume Argument
5.MD.5-Task 2
Domain
Cluster
Standard(s)
Materials
Task
Measurement and Data
Geometric measurement: understand concepts of volume and relate volume to
multiplication and to addition.
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 x w x h and V = b x 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.
Paper and pencil
Bennett and Seth are having an argument about the formula for finding the volume of a
rectangular prism. Bennett says that to find volume you have to know the length, height,
and width of the figure. Seth says that you only need to know the base and height of the
figure.
Which student do you agree with? Why? Write an expression that shows each boy’s
formula for finding volume.
Draw a rectangular prism and label it with dimensions. How would Bennett find the
volume of this prism? How would Seth find its volume?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FIFTH GRADE
Formative Instructional and Assessment Tasks
Level I
Limited Performance
 Student is unable to explain
why either boy’s strategy is
correct.
 Student needs assistance to
calculate the volume of the
drawn.
1.
2.
3.
4.
5.
6.
7.
8.
Rubric
Level II
Not Yet Proficient
 Student chooses one boy’s
strategy and explains why it is
correct, but does not recognize
that both volumes are
equivalent.
 Student writes an expression
for the selected strategy but not
both.
 Student uses the selected
strategy (but not both
formulas) to find the volume of
the prism they draw.
Level III
Proficient in Performance
 Student recognizes that both
boys are correct.
 Student explains that length
times width is the same thing
as the area of the base, and this
is why Seth’s formula is
equivalent to Bennett’s.
 Student writes both
expressions: A = l x w x h and
A=bxh
 Student draws a rectangular
prism and calculates its
volume using both formulas
(Bennett’s and Seth’s).
Standards for Mathematical Practice
Makes sense and perseveres in solving problems.
Reasons abstractly and quantitatively.
Constructs viable arguments and critiques the reasoning of others.
Models with mathematics.
Uses appropriate tools strategically.
Attends to precision.
Looks for and makes use of structure.
Looks for and expresses regularity in repeated reasoning.
NC DEPARTMENT OF PUBLIC INSTRUCTION
FIFTH GRADE
Formative Instructional and Assessment Tasks
Volume Argument
Bennett and Seth are having an argument about the formula for finding the volume
of a rectangular prism. Bennett says that to find volume you have to know the
length, height, and width of the figure. Seth says that you only need to know the
base and height of the figure.
Which student do you agree with? Why? Write an expression that shows each
boy’s formula for finding volume.
Draw a rectangular prism and label it with dimensions. How would Bennett find
the volume of this prism? How would Seth find its volume?
NC DEPARTMENT OF PUBLIC INSTRUCTION
FIFTH GRADE