MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 5
Unit 9
Unit
Description
Unit 9
Volume and Data
Suggested Length: 2-3 weeks
Big Idea(s)
Enduring Understanding
•
Develop understanding of volume
What
enduring
understandin
gs are
essential for
application
to new
situations
within or
beyond this
content?
Enduring Skills Rubric measures competency of the following skills:

Recognizes volume as an attribute of solid figures and understands
volume is measured using cubic units and can be found by packing a
solid figure with unit cubes and counting them. Represents the
volume of a solid figure as “n” cubic units
Solves real-world and mathematical problems by applying the
formulas for volume and/or relating volume to the operations of
multiplication and addition
Solves real-world and mathematical problems by recognizing volume
is additive by finding the volume of solid figures of two nonoverlapping parts
Defines volume using any cubic unit

How do we measure capacity?

How can I display a set of data?



Essential
Question(s)
What
questions will
provoke and
sustain
student
engagement
while
focusing
learning?
Standards
Which
standards
provide
endurance
beyond the
course,
leverage
across
multiple
disciplines,
and
readiness for
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them. Students
make sense that cubic units represent 3-dimensional objects and
have length, height, and width.
2. Reason abstractly and quantitatively. Students demonstrate abstract
reasoning to create a display of square and cubic units in order to
compare/contrast the measures of area and volume.
3. Construct viable arguments and critique the reasoning of others.
Students construct and critique arguments regarding their knowledge
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 5
Unit 9
the next
level?
4.
5.
6.
7.
8.
about volume and reasonableness of their calculations.
Model with mathematics. Students use snap cubes to build cubes and
rectangular prisms in order to generalize a formula for the volume of
rectangular prisms.
Use appropriate tools strategically. Students select and use tools such
as tables, cubes, and other manipulatives to represent situations
involving the relationship between volume and area.
Attend to precision. Students attend to the precision when comparing
and contrasting the prisms made using the same amount of cubes.
Look for and make use of structure. Students recognize volume as an
attribute of solid figures and understand concepts of volume
measurement. Students use their understanding of the mathematical
structure of area and apply that knowledge to volume.
Look for and express regularity in repeated reasoning. Students relate
new experiences to experiences with similar contexts when studying a
solid figure that can be packed without gaps or overlaps using n unit
cubes is said to have a volume of n cubic units.
Standards for Mathematical Content
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 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 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-
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 5
Unit 9
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 non-overlapping right rectangular prisms by
adding the volumes of the non-overlapping parts, applying this
technique to solve real world problems.
Supporting
Standard(s
)
Which
related
standards will
be
incorporated
to support
and enhance
the enduring
standards?
5.MD.2
Make a line plot to display a data set of measurements in
fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this
grade to solve problems involving information presented in line plots.
For example, given different measurements of liquid in identical
beakers, find the amount of liquid each beaker would contain if the
total amount in all the beakers were redistributed equally.
5.NF.1 Add and subtract fractions with unlike denominators (including mixed
numbers) by replacing given fractions with equivalent fractions in
such a way as to produce an equivalent sum or difference of
fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12
= 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
5.NF.3
Interpret a fraction as division of the numerator by the
denominator (a/b = a ÷ b). Solve word problems involving division of
whole numbers leading to answers in the form of fractions or mixed
numbers, e.g., by using visual fraction models or equations to
represent the problem. For example, interpret 3/4 as the result of
dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that
when 3 wholes are shared equally among 4 people each person has
a share of size 3/4. If 9 people want to share a 50-pound sack of rice
equally by weight, how many pounds of rice should each person
get? Between what two whole numbers does your answer lie?
5.NF.4 Apply and extend previous understandings of multiplication to
multiply a fraction or whole number by a fraction.
a.
Interpret the product (a/b) × q as a parts of a partition of q into b
equal parts; equivalently, as the result of a sequence of operations a
× q ÷ b. For example, use a visual fraction model to show (2/3) × 4 =
8/3, and create a story context for this equation. Do the same with
(2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 5
Unit 9
Instruction
al
Outcomes
I am learning to…
 Create a line plot to display a data set of measurements in fractions
of a unit (1/2, 1/4, 1/8)
What must
 Solve problems involving information presented in line plots which use
students learn
fractions of a unit (1/2, 1/4, 1/8) by adding, subtracting, multiplying,
and be able
and dividing fractions
to by the end
 Recognize a unit cube has 1 cubic unit of volume and is used to
of the unit to
measure volume of three-dimensional shapes.
demonstrate

Recognize any solid figure packed without gaps or overlaps and filled
mastery?
with (n) “unit cubes” indicates the total cubic units or volume
Measure volume by counting unit cubes, cubic cm, cubic in., cubic
ft., and improvised units.
 Multiply the three dimensions in any order to calculate volume
(commutative and associative properties)
 Develop a formula for volume of a rectangle prism by comparing
volume when filled with cubes to volume by multiplying the height by
the area of the base, or when multiplying the edge lengths (l x w x h)
 Use additive volume to calculate volume of complex rectangular
prisms
Vocabular
y
What
vocabulary
must students
know to
understand
and
communicat
e effectively
about this
content?
Essential Vocabulary
cube
cubic units (cubic centimeter, cubic foot, cubic inch, etc.)
Data
Formula
line plot
number line
redistributed
right rectangular prism
unit cube
volume
Supporting Vocabulary
Area
at least
at most
base
mean (average)
median
mode
maximum/greatest
minimum/least
range
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 5
Unit 9
Resources
& Activities
What
resources
could we use
to best teach
this unit?
Stepping Stones (www.origoeducation.com)
5.MD.3
o Module 3: Lesson 8
5.MD.4
o Module 3: Lesson 8
5.MD.5
o Module 3: Lessons 7- 12
Origo Fundamentals Online Interactive Activities
www.origoeducation.com Log in to SLATE, then choose “channels” on the
left side of dashboard. Choose “Fundamentals” then search titles for the
following activity:
o “Perfect Pairs”
Engage NY
(https://www.engageny.org/resource/grade-5-mathematics)
5.MD.3
o Module 5: Topics A, B
5.MD.4
o Module 5: Topic A
5.MD.5
o Module 5: Topic B
Howard County Website
(https://grade5commoncoremath.wikispaces.hcpss.org/home)
K-5 Math Teaching Resources
(http://www.k-5mathteachingresources.com/)
5.MD.3
o http://www.k-5mathteachingresources.com/support-files/build-acubic-meter.pdf
o http://www.k-5mathteachingresources.com/supportfiles/exploring-volume.pdf
o http://www.k-5mathteachingresources.com/support-files/openbox-templates.pdf
o http://www.k-5mathteachingresources.com/support-files/buildingrectangular-prisms.pdf
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 5
Unit 9
5.MD.4
o http://www.k-5mathteachingresources.com/support-files/3dstructures.pdf
o http://www.k-5mathteachingresources.com/support-files/roll-arectangular-prism.pdf
o http://www.k-5mathteachingresources.com/support-files/four-openboxes.pdf
5.MD.5
o http://www.k-5mathteachingresources.com/support-files/whats-thevolume.pdf
o http://www.k-5mathteachingresources.com/support-files/orderingrectangular-prisms.pdf
o http://www.k-5mathteachingresources.com/support-files/designinga-toy-box.pdf
o http://www.k-5mathteachingresources.com/support-files/create-a3d-sculpture.pdf
o http://www.k-5mathteachingresources.com/support-files/comparingbuildings.pdf
o http://www.k-5mathteachingresources.com/support-files/find-thevolume.pdf
o http://www.k-5mathteachingresources.com/support-files/joesbuildings.pdf
Common Core Sheets
 http://www.commoncoresheets.com/SortedByGrade.php?Sorted=5
md2
 http://www.commoncoresheets.com/SortedByGrade.php?Sorted=5
md4
Teaching Volume Unit (TPT $6):
 https://www.teacherspayteachers.com/Product/Teaching-VolumeUnit-Common-Core-Aligned-5th-Grade-317137
Common Core Assessment Pack-Common Core Grade 5 (TPT $12.50):
 https://www.teacherspayteachers.com/Product/Common-CoreAssessment-Pack-Math-Grade-5-411127
Mastering the Grade 5 K-PREP in Mathematics (American Book Company
2013)
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 5
Unit 9
Illustrative Mathematics
o https://www.illustrativemathematics.org/content-standards/5
Illuminations
o http://illuminations.nctm.org/Search.aspx?view=search&cc=2014_202
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Remember there are other sources in your school that may not be listed
on this common resources list due to variation in each individual
school. Examples of other great resources your school may have access
to include: Everyday Math Games, Investigations, Everyday Partner
Games, AVMR file folders, Ongoing Assessment Project, etc.
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