ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
TIMELINE: 2nd Quarter
GRADE: 8
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
Academic
Vocabulary
1. In the real number
system, rational and
irrational numbers are in
one to one
correspondence to
points on the number
line
1. In the real number
system, rational and
irrational numbers are in
one to one
correspondence to
points on the number
line
1. In the real number
system, rational and
irrational numbers are in
one to one
correspondence to
points on the number
line
e. Use square root and cube root
symbols to represent solutions to
equations of the form x2 = p and x3
= p, where p is a positive rational
number. I
I will model square root and
cube to represent solutions
to equations of the form x2
= p and x3 = p, where p is a
positive rational number.
Appl
Holt, Rinehart, and Winston
P. 146-147, 240, 154, 380381
Square root
Cube Root
f. Evaluate square roots of small
perfect squares and cube roots of
small perfect cubes. I
I will assess square roots of
small perfect squares
Eval
Holt, Rinehart, and Winston
P. 146-147, 380-381
Evaluate
Perfect square
Perfect cube
Appl
Holt, Rinehart, and Winston
P. 112-114, 156
Whole number
Holt, Rinehart, and Winston
P. 156, 745, 780
Scientific
notation
I will evaluate cube roots of
small perfect cubes.
g. Use numbers expressed in the
form of a single digit times a whole
number power of 10 to estimate
very large or very small quantities,
and to express how many times as
much one is than the other. I
I will utilize numbers
expressed in the form of a
single digit times a whole
number power of 10 to
estimate very large
quantities to express how
many times as much one is
than the other.
I will use numbers
expressed in the form of a
single digit times a whole
number power of 10 to
estimate small quantities to
express how many times as
much one is than the other.
1. In the real number
system, rational and
irrational numbers are in
one to one
correspondence to
points on the number
h. Perform operations with numbers
expressed in scientific notation,
including problems where both
decimal and scientific notation are
used.
© Learning Keys, 800.927.0478, www.learningkeys.org
I will perform operations
with numbers expressed in
scientific notation, including
problems where decimals
are used.
Appl
Page 1
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
TIMELINE: 2nd Quarter
GRADE: 8
Evidence Outcome
line
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
Appl
p. 96-97
Academic
Vocabulary
I will explain operations with
numbers expressed in
scientific notation, including
problems where scientific
notation is used.
i. Use scientific notation and choose
units of appropriate size for
measurements of very large or very
small quantities. I
I will use scientific notation
for measurements of very
large quantities.
I will use scientific notation
for measurements of very
small quantities.
I will choose units of
appropriate size for
measurements of very large
small quantities.
I will choose units of
appropriate size for
measurements of very
small quantities.
2. Direct and indirect
measurement can be
used to describe and
make comparisons
2. Direct and indirect
measurement can be
used to describe and
make comparisons
ii. Interpret scientific notation that
has been generated by technology.
I
I will interpret scientific
notation that has been
generated by technology.
a. Explain a proof of the
Pythagorean Theorem and its
converse. I
I will explain a proof of the
Pythagorean Theorem and
its converse.
Comp
Holt, Rinehart, and Winston
p. 290-291
Pythagorean
Theorem
Converse
b. Apply the Pythagorean Theorem
to determine unknown side lengths
in right triangles in real-world and
mathematical problems in two and
three dimensions. I
I will apply the Pythagorean
Theorem to determine
unknown side lengths in
right triangles in real-world
problems in two
Appl
Holt, Rinehart, and Winston
p. 290-291, 234
Two
dimensions
Three
dimensions
© Learning Keys, 800.927.0478, www.learningkeys.org
p. 96-97
Page 2
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
TIMELINE: 2nd Quarter
GRADE: 8
Evidence Outcome
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
Academic
Vocabulary
Appl
Holt, Rinehart, and Winston
p. 290-291
Coordinate
System
dimensions.
I will apply the Pythagorean
Theorem to determine
unknown side lengths in
right triangles in real-world
problems in three
dimensions.
I will apply the Pythagorean
Theorem to determine
unknown side lengths in
right triangles in
mathematical problems in
two dimensions.
I will apply the Pythagorean
Theorem to determine
unknown side lengths in
right triangles in
mathematical problems in
three dimensions.
2. Direct and indirect
measurement can be
used to describe and
make comparisons
c. Apply the Pythagorean Theorem
to find the distance between two
points in a coordinate system. I
Use rational approximations of
irrational numbers to compare the
size of irrational numbers, locate
© Learning Keys, 800.927.0478, www.learningkeys.org
I will model the
Pythagorean Theorem to
find the distance between
two points in a coordinate
system.
I will use rational
approximations of irrational
numbers to compare the
size of irrational numbers,
Page 3
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
TIMELINE: 2nd Quarter
GRADE: 8
Evidence Outcome
Student-Friendly
Learning Objective
them approximately on a number
line diagram, and estimate the value
of expressions. (CCSS:8.NS.2)
S1B1
locate them approximately
on a number line diagram,
and estimate the value of
expressions.
Apply the properties of integer
exponents to generate equivalent
numerical expressions.
(CCSS:8.EE.1)
I will apply the properties of
integer exponents to
generate equivalent
numerical expressions.
Use properties of operatins to
generate equivalent expressions.
(CCSS:7.EE) S1B1
I will use properties of
operatins to generate
equivalent expressions.
Level of
Thinking
Resource Correlation
Academic
Vocabulary
Rational numbers
Irrational numbers
Line diagram
Expression
Numerical
Expressions
Equivalent
Expressions
_____________________________
Holt, Rinehart, and Winston
Order and find absolute value of
rational numbers. (CCSS:6.NS.7)
S1B2
i.
Interpret statements of
inequality as statements
about the relative
position of two numbers
on a number line
diagram.
(CCSS:6.NS.7a)
ii. Write, interpret, and explain
statements of order for
rational numbers in
real-world contexts.
(CCSS:6.NS.7b)
iii. Define the absolute value of
a rational number as its
© Learning Keys, 800.927.0478, www.learningkeys.org
Line diagram
I will order absolute value
of rational numbers.
I will find absolute value of
rational numbers.
APPL
Real-World
Contexts
Absolute Value
I will interpret statements of
inequality as statements
about the relative position
of two numbers on a
number line diagram.
I will write statements of
order for rational numbers
in real-world contexts.
I will interpret statements of
order for rational numbers
Page 4
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
TIMELINE: 2nd Quarter
GRADE: 8
Evidence Outcome
distance from 0 on the
numer line and interpret
absolute value as
magnitude for a positive
or negative quantity in a
real-world situation.
(CCSS: 6.NS.7c)
iv. Distinuguish comparisons of
absolute value from
statements about order.
(CCSS:6.NS.7d)
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
Academic
Vocabulary
APPL
Holt, Rinehart, and Winston
Squares
in real-world contexts.
I will explain statements of
order for rational numbers
in real-world contexts.
I will define the absolute
value of a rational number
as its distance from 0 on
the numer line and interpret
absolute value as
magnitude for a positive
quantity in a real-world
situation.
I will define the absolute
value of a rational number
as its distance from 0 on
the numer line and interpret
absolute value as
magnitude for a negative
quantity in a real-world
situation.
I will distinuguish
comparisons of absolute
value from statements
about order.
_____________________________
Apply concepts of squares, primes,
composites, factors, and multiples
to solve problems. S1B3
I will apply concepts of
squares to solve problems.
Primes
I will apply concepts of
primes to solve problems.
I will apply concepts of
composites to solve
© Learning Keys, 800.927.0478, www.learningkeys.org
Composites
Factors
Page 5
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
TIMELINE: 2nd Quarter
GRADE: 8
Evidence Outcome
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
problems.
Academic
Vocabulary
Multiples
I will apply concepts of
factors to solve problems.
I will apply concepts of
multiples to solve problems.
___________________________
Analyze proportional relationships
and use them to solve real-world
and mathematical problems.
(CCSS:7.RP) S1B4
_____________________________
Compute unit rates associated with
ratis of fractions, including ratios
lengths, areas and other quantities
measured in like or different units.
(CCSS:7.RP.1) S1B4
______________________
I will analyze proportional
relationships and use them
to solve real-world
problems.
I will analyze proportional
relationships and use them
to solve mathematical
problems.
______________________
I will compute unit rates
associated with ratios of
fractions, including ratios
lengths, areas and other
quantities measured in like
units.
_______
_____________________
ANAL
Holt, Rinehart, and Winston
APPL
Holt, Rinehart, and Winston
Proportional
Relationships
Unit Rates
Ratios
I will compute unit rates
associated with ratios of
fractions, including ratios
lengths, areas and other
quantities measured in
different units.
_____________________________
Use proportional relationships to
solve multistep ratio and percent
problems. (CCSS:7.RP.3) S1B4
© Learning Keys, 800.927.0478, www.learningkeys.org
I will use proportional
relationships to solve
multistep ratio and percent
problems.
APPL
Ratio
Holt, Rinehart, and Winston
Percents
Page 6
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
TIMELINE: 2nd Quarter
GRADE: 8
Evidence Outcome
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
Academic
Vocabulary
Apply properties of operations to
calculate with numbers in any form,
convert between forms as
appropriate, and assess the
reasonableness of answeres using
mental computation and estimation
strategies. (CCSS: 7.EE.3) S1B4
I will apply properties of
operations to calculate with
numbers in any form,
convert between forms as
appropriate, and assess the
reasonableness of
answeres using mental
computation and estimation
strategies.
APPL
Holt, Rinehart, and Winston
Properties of
Operations
I will solve problems
involving scale drawings of
geometric figures, including
computing actual lengths
and areas from a scale
drawing and reproducing a
scale drawing at a different
scale.
APPL
Holt, Rinehart, and Winston
Scale drawing
I will apply understanding of
addition and subtraction to
add and subtract rational
numbers including integers.
APPL
Holt, Rinehart, and Winston
Horizontal Number
Line
____________________________
Solve problems involving scale
drawings of geometric figures,
including computing actual lengths
and areas from a scale drawing and
reproducing a scale drawing at a
different scale. (CCSS:7.G.1)
S1B43
____________________________
Apply understanding of addition and
subtraction to add and subtract
rational numbers including integers.
(CCSS: 7.NS.1)
i.
Represent addition and
subtraction on a
horizontal or vertical
number line diagram.
(CCSS: 7.NS.1)
ii. Describe situatins in which
opposite quantities
combine to make 0.
(CCSS: 7.NS.1a)
iii. Demonstrate p + q as a
number located a a
distance |q| from p, in
the positive or negative
© Learning Keys, 800.927.0478, www.learningkeys.org
I will represent addition
and subtraction on a
horizontal number line
diagram.
Vertical Number
Line
Rational Numbers
I will represent addition and
subtraction on a vertical
number line diagram.
I will describe situatins in
which opposite quantities
Page 7
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
TIMELINE: 2nd Quarter
GRADE: 8
Evidence Outcome
iv.
v.
vi.
vii.
viii.
direction depending on
whether q is positive or
negative.
(CCSS:7.NS.1b)
Show that a number and its
opposite have a sum of
0 (are additive
inverses).
(CCSS:7.NS.1b)
Interpret sums of rational
numbers by describing
real-world contexts.
(CCSS: 7.NS.1C)
Demonstrate subtraction of
rational numbers as
adding the additive
inverse, p – q = p + (-q).
(CCSS: 7.NS.1c)
Show that the distance
between two rational
numbers on the number
line is the absolute
value of their difference,
and apply this principle
in real-world contexts.
(CCSS: 7.NS.1c)
Apply properties of
operations as strategies
to add and subtract
rational numbers.
(CCSS: 7.NS.1d)
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
Academic
Vocabulary
combine to make 0.
I will demonstrate p + q as
a number located a a
distance |q| from p, in the
positive or negative
direction depending on
whether q is positive.
I will demonstrate p + q as
a number located a a
distance |q| from p, in the
positive or negative
direction depending on
whether q is negative.
I will show that a number
and its opposite have a
sum of 0 (are additive
inverses).
I will interpret sums of
rational numbers by
describing real-world
contexts.
I will demonstrate
subtraction of rational
numbers as adding the
additive inverse
I will show that the distance
between two rational
numbers on the number
line is the absolute value of
their difference and apply
this principle in real-world
© Learning Keys, 800.927.0478, www.learningkeys.org
Page 8
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
TIMELINE: 2nd Quarter
GRADE: 8
Evidence Outcome
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
Academic
Vocabulary
contexts.
I will apply properties of
operations as strategies to
add rational numbers.
I will apply properties of
operations as strategies to
subtract rational numbers.
_____________________________
Apply and extend previous
understanding of multiplication and
division and of fractions to multiply
and divide rational numbers
including integers. (CCSS:7.NS.2)
S1B5
i.
Apply properties of
operatons to
multiplication of rational
numbers. (CCSS:
7.NS.2a)
ii. Interpret products of rational
numbers by describing
real-world contexts.
(CCSS:7.NS.2a)
iii. Apply properties of
operatons to divide
integers. (CCSS:
7.NS.2b)
iv. Apply properties of
operations as strategies
to multiply and divide
rational numbers.
(CCSS: 7.NS.2c)
v. Convert a rational number
to a decimal using long
© Learning Keys, 800.927.0478, www.learningkeys.org
I will apply previous
understanding of
multiplication and division
and of fractions to multiply
and divide rational numbers
including integers.
APPL
Holt, Rinehart, and Winston
Properties of
Operations
I will extend previous
understanding of
multiplication and division
and of fractions to multiply
and divide rational numbers
including integers
I will apply properties of
operatons to multiplication
of rational numbers.
I will interpret products of
rational numbers by
describing real-world
contexts.
I will apply properties of
operatons to divide integers
I will apply properties of
Page 9
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
TIMELINE: 2nd Quarter
GRADE: 8
Evidence Outcome
division. (CCSS:
7.NS.2d)
vi. Show that the decimal form
of a rational number
terminates in 0s or
eventually repeats.
(CCSS: 7.NS.2d)
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
APPL
Holt, Rinehart, and Winston
Academic
Vocabulary
operations as strategies to
multiply rational numbers.
I will apply properties of
operations as strategies to
divide rational numbers.
I will convert a rational
number to a decimal using
long division.
I will show that the decimal
form of a rational number
terminates in 0s or
eventually repeats.
____________________________
Apply properties of operations to
calculate with numbers in any form,
convert between forms as
appropriate, and assess the
reasonableness of answers using
mental computation and estimation
strategies. (CCSS:7.EE.3)
I will apply properties of
operations to calculate with
numbers in any form,
convert between forms as
appropriate, and assess the
reasonableness of answers
using mental computation
strategies.
I will apply properties of
operations to calculate with
numbers in any form,
convert between forms as
appropriate, and assess the
reasonableness of answers
using mental estimation
strategies.
© Learning Keys, 800.927.0478, www.learningkeys.org
10
Page
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
TIMELINE: 2nd Quarter
GRADE: 8
Evidence Outcome
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
Academic
Vocabulary
Solve real-world and mathematical
problems by graphing points in all
four quadrants of the coordinate
plane including the use of
coordinates and absolute value to
find distances between points with
the same first coordinate or the
same second coordinate. (CCSS:
6.NS.8) S4B4
I will solve real-world and
mathematical problems by
graphing points in all four
quadrants of the coordinate
plane including the use of
coordinates and absolute
value to find distances
between points with the
same first coordinate.
APPL
Holt, Rinehart, and Winston
Coordinate Plane
Absolute Value
I will solve real-world and
mathematical problems by
graphing points in all four
quadrants of the coordinate
plane including the use of
coordinates and absolute
value to find distances
between points with the
same second coordinate..
____________________________
Solve problems involving
measurement and estimation of
intervals of time, liquid, volumes,
and masses of objects. (CCSS:
3.MD) S5B1
I will solve problems
involving measurement of
intervals of time, liquid,
volumes, and masses of
objects.
I will solve problems
involving estimation of
intervals of time, liquid
volumes, and masses of
objects.
© Learning Keys, 800.927.0478, www.learningkeys.org
11
APPL
Time of objects
Liquid of objects
Volumes of objects
Masses of objects
Page
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
TIMELINE: 2nd Quarter
GRADE: 8
Evidence Outcome
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
Academic
Vocabulary
Use properties of supplementary,
complementary, vertical, and
adjacent angles in a multi-step
problem to write and solve simple
equations for an unknown angle in a
figure. (CCSS: 7.G.5)S5B1
I will use properties of
supplementary in a multistep problem to write
simple equations for an
unknown angle in a figure.
APPL
Holt, Rinehart, and Winston
Supplementary
angle
Complementary
angle
I will use properties of
complementary in a multistep problem to solve
simple equations for an
unknown angle in a figure.
Vertical angle
Adjacent angle
I will use properties of
vertical, and adjacent
angles in a multi-step
problem to write and solve
simple equations for an
unknown angle in a figure.
I will use properties of
adjacent angles in a multistep problem to write and
solve simple equations for
an unknown angle in a
figure.
____________________________
Solve real-world and mathematical
problems involving area, volume
and surface area of two- and threedimensional objects composed of
triangles, quadrilateral, polygons,
cubes, and right prisms, (CCSS:
7.G.6)S5B1
I will solve real-world
problems involving area,
volume and surface area of
two- and three- dimensional
objects composed of
triangles, quadrilateral,
polygons, cubes, and right
prisms.
APPL
Volume
Holt, Rinehart, and Winston
Surface Area
Triangle
Quadrilateral
Polygon
I will solve mathematical
© Learning Keys, 800.927.0478, www.learningkeys.org
12
Page
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
TIMELINE: 2nd Quarter
GRADE: 8
Evidence Outcome
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
problems involving area,
volume and surface area of
two- and three- dimensional
objects composed of
triangles, quadrilateral,
polygons, cubes, and right
prisms.
____________________________
Measure length indirectly. (CCSS:
1.MD) S5B2
_____________________________
Analyze proportional relationships
and use them to solve real-world
and mathematical problems (CCSS:
7.RP)S5B2
____________________________
Represent measurement quantities
using diagrams such as number line
diagrams that feature a
measurement scale.
(CCSS:4.MD.2) S5B3
____________________________
Solve problems involving scale
drawings of geometric figures,
including computing actual lengths
and areas from a scale drawing and
reproducing a scale drawing at a
different scale. (CCSS: 7.RP.1)
© Learning Keys, 800.927.0478, www.learningkeys.org
13
I will measure length
indirectly.
I will analyze proportional
relationships and use them
to solve real-world
problems.
I will analyze proportional
relationships and use them
to solve mathematical
problems.
I will represent
measurement quantities
using diagrams such as
number line diagrams that
feature a measurement
scale.
I will solve problems
involving scale drawings of
geometric figures, including
computing actual lengths
and areas from a scale
drawing and reproducing a
scale drawing at a different
Academic
Vocabulary
Cube
Right Prism
APPL
Holt, Rinehart, and Winston
ANAL
Holt, Rinehart, and Winston
Porportions
APPL
Measurement scale
Holt, Rinehart, and Winston
APPL
Area of scale
Holt, Rinehart, and Winston
Length of scale
Page
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
TIMELINE: 2nd Quarter
GRADE: 8
Evidence Outcome
____________________________
Compute unit rates associated with
ratios of fractions, including ratios of
lengths, areas, and other quantities
measured in like or different units.
© Learning Keys, 800.927.0478, www.learningkeys.org
14
Student-Friendly
Learning Objective
scale.
I will compute unit rates
associated with ratios of
fractions, including ratios of
lengths, areas, and other
quantities measured in like
or different units.
Level of
Thinking
Resource Correlation
Academic
Vocabulary
APPL
Holt, Rinehart, and Winston
Page