Grade 5
Math Unit 4
Title
Suggested Time Frame
Time Frame – 4th Six Weeks
Suggested Duration: 20 days
Guiding Questions
Unit 4 – Geometry and Measurement
CISD Safety Net Standards: 5.4H
Big Ideas/Enduring Understandings
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Area and Perimeter related to Volume
Use Graphic Organizers to sort 2D figures
Solve problems by calculating conversions
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How is tiling used to find accurate measurements?
What is the starting point when measuring?
How can you convert units of measurement within the same
system?
Vertical Alignment
*TEKS one level below*
*TEKS one level below*
TEA MATH VERTICAL ALIGNMENT—K-6th Grade
Sample Assessment Question
Coming soon!
CISD Math Grade 5 Unit 4
Updated November 30, 2016
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Grade 5
Math Unit 4
The resources included here provide teaching examples and/or meaningful learning experiences to address the District Curriculum. In order to address the TEKS to the proper
depth and complexity, teachers are encouraged to use resources to the degree that they are congruent with the TEKS and research-based best practices. Teaching using only the
suggested resources does not guarantee student mastery of all standards. Teachers must use professional judgment to select among these and/or other resources to teach the
district curriculum. Some resources are protected by copyright. A username and password is required to view the copyrighted material. District Specificity/Examples TEKS
clarifying examples are a product of the Austin Area Math Supervisors TEKS Clarifying Documents.
Ongoing TEKS
MAT.5.01 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The
student is expected to:
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
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Focus is on application
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Students should assess which tool to apply rather than
trying only one or all
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Students should evaluate the effectiveness of
representations to ensure they are communicating
mathematical ideas clearly
Students are expected to use appropriate mathematical
vocabulary and phrasing when communicating ideas
Students are expected to form conjectures based on
patterns or sets of examples and non-examples
(B) use a problem-solving model that incorporates analyzing given information, formulating a
plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
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(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
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(G) display, explain, and justify mathematical ideas and arguments using precise mathematical
language in written or oral communication
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CISD Math Grade 5 Unit 4
Updated November 30, 2016
Precise mathematical language is expected.
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Grade 5
Math Unit 4
Knowledge and Skills with
Student Expectations
District Specificity/ Examples
Vocabulary
Resources
Resources listed and categorized to
indicate suggested uses. Any
additional resources must be aligned
with the TEKS.
Geometry and Measurement --- 20 days
5.04 Algebraic reasoning. The
student applies mathematical
process standards to develop
concepts of expressions and
equations. The student is
expected to:
5.04C generate a numerical
pattern when given a rule in
the form y = ax or y = x + a and
graph
5.04C
Students should be able to transfer information from an equation,
table, or graph to a different representation.
Example:
Use the rule y = x + 3 or to write a sequence of numbers. Starting
with a 0, students write 0, 3, 6, 9, 12, . . .
Use the rule y = x + 6 to write a sequence of numbers. Starting with
0, students write 0, 6, 12, 18, 24, . . .
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Use the rule y = 3x to write a sequence of numbers. Starting with 0,
students write 0, 3, 6, 9, 18, . . .
Use the rule y = 6x to write a sequence of numbers. Starting with 0,
students write 0, 6, 12, 18, 24 . . .
Graph the ordered pairs that represent y = 2x
Ordered pairs
(0, 0)
(3, 6)
(6, 12)
(9, 18)
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CISD Math Grade 5 Unit 4
Updated November 30, 2016
Additive Pattern
Graph
In-put/Out-out
Table
Multiplicative
Pattern
Rule
X – axis
Y – axis
Area of the base
Cube
Formula
V=lxwxh
V = s x s x s (cube)
V = Bh
Height
Length
Rectangular Prism
Volume
Width
Area
Base
Expression/Equati
on
Perimeter
Text Resources
HMH Go Math:
Modules 9 & 10
Web Resources:
Region 11 Livebinder
NCTM lluminations
Khan Academy
Literature
Mystery Math: A First Book of
Algebra – David A. Adler
Algebra & Geometry: Anything
But Square! – Dan Green
Counting on Frank – Rod
Clement
Page 3 of 10
5.04G use concrete objects
and pictorial models to
develop the formulas for the
volume of a rectangular prism,
including the special form for a
cube (V = l x w x h, V = s x s x s,
and V = Bh)
5.04G
The concept of volume should be extended from area with the idea
that students are building an area (bottom of a rectangular prism or
cube) with a layer of unit cubes, then adding layers of unit cubes on
top of the bottom layer.
Measure volumes by counting unit cubes, in order to help develop
volume formulas, using cubic cm, cubic in., cubic ft., and improvised
units
Grade 5
Math Unit 4
The Great Pyramid of Giza:
Measuring Length, Area, Volume
and Angles – Janey Levy
Is a Blue Whale the Biggest Thing
There is? – Robert E. Wells
Millions to Measure – David M.
Schwartz
Volume – Chris Woodford
Perimeter, Area, and Volume: A
Monster Book of Dimensions –
David A. Adler
Sir Cumference and the Isle of
Immeter – Cindy Neuschwander
Spaghetti and Meatballs for All!:
A Mathematical Story – Marilyn
Burns
(3 x 2) represented by first layer
(3 x 2) x 5 represented by number of 3 x 2 layers
(3 x 2) + (3 x 2) + (3 x 2) + (3 x 2)+ (3 x2) = 6 + 6 + 6 + 6 + 6 + 6 = 30
6 representing the size/area of one layer
CISD Math Grade 5 Unit 4
Updated November 30, 2016
Page 4 of 10
Grade 5
Math Unit 4
Students can then learn the formulas V= l · w · h or V=B · h or
V=s · s · s for right rectangular prisms and cubes as efficient methods
for computing volume, maintaining the connection between these
methods and their previous work with computing the number of unit
cubes that pack a right rectangular prism or cube.
CISD Math Grade 5 Unit 4
Updated November 30, 2016
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*CISD Safety Net*
5.04H represent and solve
problems related to perimeter
and/or area and related to
volume
5.04H
Grade 5
Math Unit 4
Mr. Rutherford is covering the miniature golf course with an artificial
grass. How many 1-foot squares of carpet will he need to cover the
entire course?
Example:
A rectangular garden has as an area of 80 square feet. It is 5 feet
wide. How long is the garden?
Example:
A plan for a house includes rectangular room with an area of 60
square meters and a perimeter of 32 meters. What are the length
and the width of the room?
*Note: Perimeter problems involving rectangles often give only one
length and one width, thus remembering the basic formula can help
to prevent the usual error of adding only one length and one width.
CISD Math Grade 5 Unit 4
Updated November 30, 2016
Page 6 of 10
5.05 Geometry and
measurement. The student
applies mathematical process
standards to classify twodimensional figures by
attributes and properties. The
student is expected to
5.05A classify two-dimensional
figures in a hierarchy of sets
and subsets using graphic
organizers based on their
attributes and properties
5.05A
Students should have experience discussing the properties of shapes.
A sample of questions that might be posed to students include:
A parallelogram has 4 sides with both sets of opposite sides parallel.
What types of quadrilaterals are parallelograms?
Regular polygons have all of their sides and angles congruent. Name
or draw some regular polygons.
All rectangles have 4 right angles. Squares have 4 right angles so they
are also rectangles. True or False?
*Note: The concept of congruence may be part of classroom
conversation, but does not appear until middle school.
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CISD Math Grade 5 Unit 4
Updated November 30, 2016
Grade 5
Math Unit 4
Angles
Attribute
Figure
Geometric
Property
Parallel lines
Perpendicular
lines
Polygon
quadrilateral
parallelogram
rectangle
rhombus
square
trapezoid
triangle
circle
hexagon
pentagon
octagon
Shape
Sides
TwoDimensional
Vertex
Vertices
Sets
Subsets
Text Resources
HMH Go Math:
Module 11
Web Resources
Region 11 Livebinder
NCTM lluminations
Khan Academy
Literature
The Greedy Triangle – Marilyn
Burns
If You Were a Quadrilateral –
Bonnie Coulter Leech
Shape Up!:Fun with Triangles
and Other Polygons – David A.
Adler
Page 7 of 10
5.06 Geometry and
measurement. The student
applies mathematical process
standards to understand,
recognize, and quantify
volume. The student is
expected to:
5.06A recognize a cube with
side length of one unit as a unit
cube having one cubic unit of
volume and the volume of a
three-dimensional figure as the
number of unit cubes (n cubic
units) needed to fill it with no
gaps or overlaps if possible
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5.06A
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.
As students develop their understanding volume they understand
that a 1-unit by 1-unit by 1-unit cube is the standard unit for
measuring volume. This cube has a length of 1 unit, a width of 1 unit
and a height of 1 unit and is called a cubic unit. This cubic unit is
written with an exponent of 3 (e.g., in3, m3). Students connect this
notation to their understanding of powers of 10 in our place value
system.
5.06B determine the volume of
a rectangular prism with whole
number side lengths in
problems related to the
number of layers times the
number of unit cubes in the
area of the base
CISD Math Grade 5 Unit 4
Updated November 30, 2016
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Grade 5
Math Unit 4
Cubic Units
Side Length
Threedimensional
Unit Cube
Volume
Area of the
base
Number of
layers
Number of
sides
Rectangular
Prism
Unit Cubes
Volume
Text Resources
HMH Go Math:
Module 12
Web Resources
Region 11 Livebinder
NCTM lluminations
Khan Academy
Literature
Mummy Math: An Adventure in
Geometry – Cindy Neuschwander
Perimeter, Area and Volume: A
Monster Book of Dimensions –
David A. Adler
5.06B
The concept of volume should be extended from area with the idea
that students are covering an area (bottom of a rectangular prism or
cube) with a layer of unit cubes, then adding layers of unit cubes on
top of the bottom layer
Page 8 of 10
Grade 5
Math Unit 4
(3 x 2) represented by first layer
(3 x 2) x 5 represented by number of 3 x 2 layers
(3 x 2) + (3 x 2) + (3 x 2) + (3 x 2)+ (3 x2) = 6 + 6 + 6 + 6 + 6 + 6 = 30
6 representing the size/area of one layer
5.07 Geometry and
measurement. The student
applies mathematical process
standards to select
appropriate units, strategies,
and tools to solve problems
involving measurement. The
student is expected to
5.07A solve problems by
calculating conversions within
a measurement system,
customary or metric
CISD Math Grade 5 Unit 4
Updated November 30, 2016
Students can then learn the formulas V= l x w x h or V=B x h or V=s x
s x s for right rectangular prisms and cubes as efficient methods for
computing volume, maintaining the connection between these
methods and their previous work with computing the number of unit
cubes that pack a right rectangular prism or cube.
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5.07A
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Know relative sizes of measurement units within one system
of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec.
Within a single system of measurement, express
measurements in a larger unit in terms of a smaller unit.
Record measurement equivalents in a two-column table.
For example, know that 1 ft is 12 times as long as 1 in.
Express the length of a 4 ft snake as 48 in.
Generate a conversion table for feet and inches listing the
number pairs (1, 12), (2, 24),(3, 36), …
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Conversions
Customary
Measurement
System
Metric
Text Resources
HMH Go Math
Module 13
Web Resources
Region 11 Livebinder
NCTM lluminations
Khan Academy
Page 9 of 10
Grade 5
Math Unit 4
Literature
Beanstalk: The Measure of A
Giant – Ann McCallum
Counting on Frank – Rod
Clement
How Big is a Foot? - Rolf Myller
How Tall, How Short, How
Faraway? – David A. Adler
Is a Blue Whale The Biggest
Thing There is? – Robert E. Wells
Jim and the Beanstalk –
Raymond Briggs
Millions to Measure – David M.
Schwartz
Room for Ripley – Stuart J.
Murphy
Twelve Snails to One Lizard: A
Tale of Mischief and
Measurement – Susan Hightower
CISD Math Grade 5 Unit 4
Updated November 30, 2016
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