ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
TIMELINE: 3rd Quarter
GRADE: 5TH
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
Academic
Vocabulary
Concepts and skills
students master: 4. The
concepts of
multiplication and
division can be applied
to multiply and divide
fractions
c. 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. In general,
(a/b) × (c/d) = ac/bd. I
We will explain and
illustrate the process and
procedures of multiplying
and dividing whole numbers
by fractions.
Analysis
e.g. (2/3) x (4/5) = 8/15;
(2/3) x 4 = 8/3
Interpret, product,
factor, equivalent,
variable, verify,
sequence
Concepts and skills
students master: 4. The
concepts of
multiplication and
division can be applied
to multiply and divide
fractions
d. Find the area of a rectangle with
fractional side lengths by tiling it
with unit squares of the
appropriate unit fraction side
lengths, and show that the area
is the same as would be found
by multiplying the side lengths.
i. Multiply fractional side lengths
to find areas of rectangles,
and represent fraction
products as rectangular areas.
I
e. Interpret multiplication as
scaling (resizing).
i. Compare the size of a product
to the size of one factor on
the basis of the size of the
other factor, without
performing the indicated
multiplication. I
exchange.smarttech.com –
area by B. Bands
Area, formula,
length, width, unit
squares, multiplying,
rectangles, products,
equivalent, multiply,
illustrate, fractional,
tiling
exchange.smarttech.com –
multiplication of fractions
Interpret,
multiplication, scale,
compare, product,
factor, equivalence,
predict, infer, identity
element
(multiplication
property of 1)
Concepts and skills
students master: 4. The
concepts of
multiplication and
division can be applied
to multiply and divide
fractions
Concepts and skills
students master: 4. The
concepts of
multiplication and
ii. Apply the principle of fraction
equivalence a/b = (n × a)/(n ×
b) to the effect of multiplying
a/b by 1. I
f. Solve real world problems
involving multiplication of
fractions & mixed numbers. I
© Learning Keys, 800.927.0478, www.learningkeys.org
We will demonstrate with
tiles how to find the area of
rectangles, using fractional
side lengths.
Appl
Comp
Appl
We will demonstrate the
multiplication of fractions to
include mixed numbers.
Appl
exchange.smarttech.com –
Equivalents by T. Mitchell,
Fractions by Trident Media
Works
Chapter 8 unit 12 and 13
Scott Foresman-Addison
Wesley Mathematics
Multiply, product,
fractions, mixed
numbers, each,
improper fraction,
Page 1
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
Evidence Outcome
division can be applied
to multiply and divide
fractions
Concepts and skills
students master: 4. The
concepts of
multiplication and
division can be applied
to multiply and divide
fractions
Concepts and skills
students master: 4. The
concepts of
multiplication and
division can be applied
to multiply and divide
fractions
Concepts and skills
students master: 4. The
concepts of
multiplication and
division can be applied
to multiply and divide
fractions
Concepts and skills
students master: 2.
Geometric figures can
be described by their
attributes and specific
locations in the plane
TIMELINE: 3rd Quarter
GRADE: 5TH
g. Interpret division of a unit
fraction by a non-zero whole
number, and compute such
quotients. I
h. Interpret division of a whole
number by a unit fraction, &
compute such quotients. I
Solve real world problems
involving division of unit
fractions by non-zero whole
numbers and division of whole
numbers by unit fractions. I
a. Graph points on the coordinate
plane to solve real-world and
mathematical problems. I
Concepts and skills
b. Represent real world and
© Learning Keys, 800.927.0478, www.learningkeys.org
Student-Friendly
Learning Objective
We will solve real world
problems involving the
multiplication of fractions
and mixed numbers.
We will interpret the division
of a unit fraction by a nonzero whole number.
We will determine the
quotients of a unit fraction
by a non-zero whole
number.
We will interpret the division
of a whole number by a unit
fraction.
We will compute the
quotients of division of a
whole number by a unit
fraction.
We will solve real world
problems involving division
of unit fractions by non-zero
whole numbers and the
division of whole numbers
by unit fractions.
Level of
Thinking
Resource Correlation
Academic
Vocabulary
¾ x 1 2/3
simplify, reduce,
lowest terms, GCF
Appl
(1/3) ÷ 4 = 1/12 because
(1/12) x 4 = 1/3
Inverse, quotient,
whole number,
quotients, compute,
unit fraction
Comp
4 ÷ (1/5) = 20 because 20 x
(1/5) =4
Whole number,
divide, quotients,
compatible numbers,
find, compute, unit
fraction
Appl
e.g.; How much chocolate
will each person get if 3
people share ½ lb. of
chocolate equally? How
many 1/3-cup servings are
in 2 cups of raisins?
Unit fraction,
division, quotient,
multiply, inverse,
compatible numbers
We will use coordinate
planes to solve real world
mathematical problems.
Comp
We will represent real world
Appl
Coordinate plane,
ordered pair, xvalue, y-value,
origin, solve, plot
exchange.smarttech.com
Quadrant,
Page 2
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
Evidence Outcome
students master: 2.
Geometric figures can
be described by their
attributes and specific
locations in the plane
Concepts and skills
students master:
2. Geometric figures can
be described by their
attributes and specific
locations in the plane
TIMELINE: 3rd Quarter
GRADE: 5TH
mathematical problems by
graphing points in the first
quadrant of the coordinate
plane, and interpret coordinate
values of points in the context of
the situation. C
c.
Classify two-dimensional figures
into categories based on their
properties.
i. Explain that attributes
belonging to a category of
two-dimensional figures
also belong to all
subcategories of that
category. I
ii.
Classify two-dimensional
figures in a hierarchy based
on properties. I
Concepts and skills
a. Generate two numerical
patterns using given rules. C
students master: 1.
Number patterns are
based on operations and
relationships
Concepts and skills
b. Identify apparent relationships
students master: 1.
between corresponding terms.
C
Number patterns are
based on operations and
relationships
Concepts and skills
c. Form ordered pairs consisting
students master: 1.
of corresponding terms from the
Number patterns are
two patterns, and graph the
© Learning Keys, 800.927.0478, www.learningkeys.org
Student-Friendly
Learning Objective
Level of
Thinking
and mathematical problems
by graphing points in the
first quadrant of the
coordinate plane.
Resource Correlation
Academic
Vocabulary
area, volume, coordinates
coordinate plant,
coordinate value, x
and y-values,
determine, illustrate
We will interpret coordinate
values of points in the
context of a given situation.
We will explain that
attributes belonging to a
category of twodimensional figures also
belong to all subcategories
of that category.
We will classify twodimensionals figures based
on properties
Comp
e.g.; all rectangles have
four right angles and
squares are rectangles, so
all squares have four right
angles.
Comp
We will create two
numerical patterns using
given rules.
Comp
We will identify the
numerical pattern between
corresponding terms and
state the rule.
Analysis
We will form ordered pairs
consisting of corresponding
terms from the two
Appl
Example: edges,
congruence, number of
sides, vertices
Example: In and out
machine; table of values
two-dimensional,
properties,
attributes,
categorize,
parallelogram,
quadralaterals,
rectangles, squares,
rhombus, polygons,
angles, obtuse,
acute, right, parallel,
perpendicular,
vertices,
congruence,scalene,
isosceles, equilateral
Create, numerical
patterns, explain
Corresponding,
relationships,
distinguish, identify
Exchange.smarttech.com
Area, volume, coordinates
ordered pairs,
patterns, graph,
coordinate plane, x
Page 3
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
Evidence Outcome
based on operations and
relationships
Concepts and skills
students master: 1.
Number patterns are
based on operations and
relationships
Concepts and skills
students master:
1. Number patterns are
based on operations and
relationships
Concepts and skills
students master:
1. Number patterns are
based on operations and
relationships
TIMELINE: 3rd Quarter
GRADE: 5TH
ordered pairs on a coordinate
plane. I
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
patterns, and graph the
ordered pairs on a
coordinate plane.
Academic
Vocabulary
axis, y axis,
horizontal,
vertical,negative
numbers, positive
numbers, origin, x
and y values
Relationships,
corresponding,
patterns, discuss
d. Explain informally relationships
between corresponding terms in
the patterns. C
We will give examples of
relationships between
corresponding terms in
patterns.
Comp
e. Use patterns to solve problems
including those involving saving
and checking accounts I
We will use patterns to
solve problems including
those involving saving and
checking accounts.
Analysis
Patterns, saving
account, checking
account,
relationships, solve
f.
We will explain, extend, and
use patterns and
relationships in solving
problems, including those
involving saving and
checking accounts such as
understanding that
spending more means
saving less.
We will convert
measurement units within a
given measurement
system.
Analysis
Patterns,
relationships, saving
and checking
accounts,
summarize, utilize,
compare, contrast,
Explain, extend, and use
patterns and relationships in
solving problems, including
those involving saving and
checking accounts such as
understanding that spending
more means saving less I
Concepts and skills
d. Convert like measurement units
students master:
within a given measurement
1. The decimal number
system.
system describes place
i. Convert among different-sized
value patterns and
standard measurement units
relationships that are
within a given measurement
repeated in large and
system.
small numbers and
ii. Use measurement
forms the foundation for
conversions in solving multiefficient algorithms.
step, real world problems.
Concepts and skills
a. Model and justify the formula
students master: 1.
for volume of rectangular
© Learning Keys, 800.927.0478, www.learningkeys.org
e.g. converting inches to
feet or cups to gallons.
We will use measurement
conversions in solving
multi-step, real world
problems.
We will measure the
exchange.smarttech.com area, volume, coordinates
Volume, rectangular
prisms, construct,
Page 4
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
Properties of
multiplication and
addition provide the
foundation for volume an
attribute of solids.
Concepts and skills
students master: 1.
Properties of
multiplication and
addition provide the
foundation for volume,
an attribute of solids.
TIMELINE: 3rd Quarter
GRADE: 5TH
Evidence Outcome
i.
prisms.
Model the volume of a right
rectangular prism with wholenumber side lengths by
packing it with unit cubes. I
ii.
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. I
iii.
Represent threefold wholenumber products as volumes
to represent the associative
property of multiplication. I
b. Find volume of rectangular
prisms using a variety of
methods and use these
techniques to solve real world
and mathematical problems.
i. Measure volumes by counting
unit cubes, using cubic cm,
cubic in, cubic ft, and
improvised units. I
ii.
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. I
iii.
Use the additive nature of
© Learning Keys, 800.927.0478, www.learningkeys.org
Student-Friendly
Learning Objective
volume of a right
rectangular prism with
whole-number side lengths
by packing it with unit
cubes.
We will illustrate 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.
We will recognize threefold
whole-number products as
volumes to represent the
associative property of
multiplication.
We will calculate volumes
by counting unit cubes,
using cubic cm, cubic in.,
cubic ft. and improvised
units.
We will 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.
We will use the additive
Level of
Thinking
Resource Correlation
utilize, determine,
equivalent, height,
base, assosciative
property, length,
associative property
Eval
Comp
Academic
Vocabulary
exchange.smarttech.com
area, volume, coordinates –
circumference, volume,
surface by Ehudgins
Comp
Exchange.smarttech.com
Gardening with Science
and Math by David O’Neil
Appl
Volume, measure,
cubic units, apply,
formula, edge
lengths, rectangular
prisms, solid, width,
height, base, cubes
Appl
Appl
Page 5
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
Evidence Outcome
volume to find volumes of
solid figures composed of two
non-overlapping right
rectangular prisms by adding
the volumes of the nonoverlapping parts. I
Concepts and skills
students master: 1.
Visual displays are used
to interpret data
TIMELINE: 3rd Quarter
GRADE: 5TH
a. Represent and interpret data.
i. Make a line plot to display a
data set of measurements
in fractions of a unit (1/2,
1/4, 1/8). M
Use operations on fractions for
this grade to solve problems
involving information presented
in line plots. M
© Learning Keys, 800.927.0478, www.learningkeys.org
Student-Friendly
Learning Objective
Level of
Thinking
nature of volume to find
volumes of solid figures
composed of two nonoverlapping right
rectangular prisms.
We will create a line plot to
display a data set of
measurements in fractions
of a unit (1/2, ¼, 1/8).
Resource Correlation
Academic
Vocabulary
Example: the different els of
a house or building;
Quonset with another
shape attached.
Appl
Appl
e.g.; give 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
Data, demonstrate,
line plot, display,
illustrate, organize
Page 6