Volume Unit 4
Formative Assessment
Volume Unit 4
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Formative Assessment
NAME: ______________________________________
1. The rectangular prism shown below has a length of 6 inches, a width of
4 inches, a height of 10 inches. What is the measure of its volume?
Draw below what one unit of volume measure looks like.
Mathematical Concepts
Unit Overview
Materials and Preparation
Academic Vocabulary
Instruction
Rectangular (Square) Prism
Rectangular Prism
Rectangular Prism with Fractional Measure
Developing a Formula
Cavaleri’s Principle for Oblique Prisms
Triangular Prism
Extension to Volume of Cylinder
Formative Assessment
Formative Assessment Record
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16!
Volume Unit 4
Formative Assessment
Volume Unit 4
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2. The rectangular prism shown below has a length of 5 inches, a width of
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4 inches and a height of 2 ! inches. What is the measure of its
volume?
Mathematical Concepts
Unit Overview
Materials and Preparation
Academic Vocabulary
Instruction
Rectangular (Square) Prism
Rectangular Prism
Rectangular Prism with Fractional Measure
Developing a Formula
Cavaleri’s Principle for Oblique Prisms
Triangular Prism
Extension to Volume of Cylinder
Formative Assessment
Formative Assessment Record
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17!
Volume Unit 4
Formative Assessment
Volume Unit 4
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3. The bases of the prism shown below each have a length of 10 inches
and a width of 4 inches. The height of the prism is 10 inches. What
is the measure of its volume? Explain why.
Mathematical Concepts
Unit Overview
Materials and Preparation
Academic Vocabulary
Instruction
Rectangular (Square) Prism
Rectangular Prism
Rectangular Prism with Fractional Measure
Developing a Formula
Cavaleri’s Principle for Oblique Prisms
Triangular Prism
Extension to Volume of Cylinder
Formative Assessment
Formative Assessment Record
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18!
Volume Unit 4
Formative Assessment
Volume Unit 4
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4. Each side of a hexagonal prism has a length of 7 ! !". The apothem
(the distance from the center of the hexagon to one of its sides) is
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6 ! !". The area of the base is 292 ! !"! . The height of the prism
is 10 cm. What is the measure of its volume? Show all work.
Mathematical Concepts
Unit Overview
Materials and Preparation
Academic Vocabulary
Instruction
Rectangular (Square) Prism
Rectangular Prism
Rectangular Prism with Fractional Measure
Developing a Formula
Cavaleri’s Principle for Oblique Prisms
Triangular Prism
Extension to Volume of Cylinder
Formative Assessment
Formative Assessment Record
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19!
Volume Unit 4
Formative Assessment
Volume Unit 4
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5. The area of a cylinder’s base is 25!!" and the measure of its volume is
500!!"! . How tall is the cylinder?
Mathematical Concepts
Unit Overview
Materials and Preparation
Academic Vocabulary
Instruction
Rectangular (Square) Prism
Rectangular Prism
Rectangular Prism with Fractional Measure
Developing a Formula
Cavaleri’s Principle for Oblique Prisms
Triangular Prism
Extension to Volume of Cylinder
Formative Assessment
Formative Assessment Record
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20!
Volume Unit 4
Formative Assessment Record
Volume Unit 4
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NAME_______________________________________
Indicate the levels of mastery demonstrated by circling those for which there is clear evidence:
Item
Level
Description
Circle highest level of performance
ToMV 4
Item 1
Volume rectangular
prism,
6!×!4!×!10
Find and compare volumes
of right rectangular prisms
by employing partial
structuring strategies
240 cubic inches, or 240 in3 with diagram of
a cubic inch, not a square inch or inch.
ToMV 3c
Find and compare volumes
of right rectangular prisms
by counting unit cubes (no
hidden cubes).
240 but lack of indication of unit
ToMV 5
Item 2
Volume rectangular
prism,
1
5!×!4!×!2
4
Find and compare volumes
of right rectangular prisms
(including some with
fractional dimensions)
using units with partial
structuring strategies.
Volume of oblique
rectangular prism,
6!×!4!×!10
Find and compare volumes
of right rectangular prisms
using partial structuring
strategies
Explain and use
Cavalieri’s principle to
find the volume of
different non-right prisms
and cylinders.
Formative Assessment Record continued on next page:
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A response that indicates use of whole
numbers only, such as 40.
240 in3 with an explanation that refers to
slicing, layering, or otherwise invoking the
idea that sliding the slice or layer does not
affect its volume. May include idea of
translation parallel to base.
ToMV 4
Find and compare volumes
of right rectangular prisms
using partial structuring
strategies.
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20!×!2! + 20!×
ToMV 4
ToMV 6d
Item 3
Either the product 45in3 with diagram of a
cubic inch or a product strategy, such as
!
21!
Treats oblique cylinder as a right cylinder so
finds a volume of 240 in3 but does not
justify.
Notes
Volume Unit 4
Formative Assessment Record
Volume Unit 4
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Item 4
ToMV 6c
Volume of hexagonal
prism with fractional
dimension
Find and compare volume
of a variety of prisms.
Item 5
ToM 6b
Find height of a
cylinder given its area
and volume measures.
!
Find and compare volumes
of right cylinders using
sweeping of area through
height.
22!
1
!"#$!×!!"#$ℎ!! = 292 !"!
2
Note if student multiplies all dimensions,
which indicates a lack of understanding of
generating volume by sweeping area through
a length.
Thinks of volume as product of area and
height, and so 500 in3 /25 in2
Volume Unit 4
Net of Prism
Volume Unit 4
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23!