Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design: OASIS, LLC
Grade: Eighth – Number System
Math Standard: 8.NS.1
Math Standard: 8.NS.2
Know that numbers that are not rational are called
Use rational approximations of irrational numbers to
irrational. Understand informally that every number
compare the size of irrational numbers, locate them
has a decimal expansion; for rational numbers show
approximately on a number line diagram, and
that the decimal expansion repeats eventually, and
estimate the value of expressions (e.g., π2). For
convert a decimal expansion which repeats eventually example, by truncating the decimal expansion of √2,
into a rational number.
show that √2 is between 1 and 2, then between 1.4
and 1.5, and explain how to continue on to get better
approximations
8.NS.1 Essential Skills and Concepts:
8.NS.2 Essential Skills and Concepts:
1. Classify a number as rational or irrational
1. Determine the approximate location of an
identify a rational number as any number that
irrational number on a number line
can be written as a fraction, terminating
find the approximate location between
decimal, or repeating decimal
consecutive integers on a number line
identify a rational number as any real number
2. Compare and order rational and irrational numbers
that cannot be written in fraction form (noncompare rational and irrational numbers using
terminating, non-repeating decimal)
greater than and less than symbols
demonstrate that fractions that terminate will
order rational/irrational numbers in ascending
have denominators including only prime factors
and descending order
of 2 and/or 5
3. Approximate the value of an irrational number
2. Solve an equation to determine an equivalent
recognize/calculate perfect squares
fraction
approximate an irrational number using the two
convert repeating decimals into their fraction
perfect squares between which it falls
equivalent using patterns or algebraic reasoning
investigate repeating patterns that occur when
fractions have a denominator of 9, 99, or 11
Mathematical Language: irrational number, rational,
repeating decimal, terminating decimal, integer, real
number, whole number, natural number, truncate
Mathematical Language: approximate, radicals,
perfect square, perfect cubes, cube root, square root,
radicand, estimate; least to greatest; greatest to least.
ascending, and descending
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Eighth – Expressions and Equations
Math Standard: 8.EE.1
Math Standard: 8.EE.2
Know and apply the properties of integer exponents to Use square root and cube root symbols to represent
generate equivalent numerical expressions. For
solutions to equations of the form x2 = p and x3 = p,
where p is a positive rational number. Evaluate square
example, 32 × 3–5 = 3–3 = 1/33 = 1/27.
roots of small perfect squares and cube roots of small
perfect cubes. Know that Q2 is irrational
8.EE.1 Essential Skills and Concepts:
1. Apply the properties of integer exponents
explain the laws of integer exponents
2 Generate equivalent numerical expressions.
show how to generate equivalent numerical
expressions using the laws of integer exponents
8.EE.2 Essential Skills and Concepts:
1. Understand that non-perfect squares and nonperfect cubes are irrational.
recognize that non-perfect squares and nonperfect cubes are irrational
Mathematical Language: Laws of Exponents
Mathematical Language: inverse operations, square
root, cube root, perfect squares, perfect cubes,
principal square root.
Math Standard: 8.EE.4
Perform operations with numbers expressed in
scientific notation, including problems where both
decimal and scientific notation are used. Use scientific
notation and choose units of appropriate size for
measurements of very large or very small quantities
(e.g., use millimeters per year for seafloor spreading).
Interpret scientific notation that has been generated
by technology.
Math Standard: 8.EE.5
Graph proportional relationships, interpreting the unit
rate as the slope of the graph. Compare two different
proportional relationships represented in different
ways.
For example, compare a distance-time graph to a
distance-time equation to determine which of two
moving objects has greater speed.
OASIS, LLC
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
Math Standard: 8.EE.3
Use numbers expressed in the form of a single digit
times an integer power of 10 to estimate very large or
very small quantities, and to express how many times
as much one is than the other. For example, estimate
the population of the United States as 3 × 108 and the
population of the world as 7 × 109, and determine
that the world population is more than 20 times
larger.
8.EE.3 Essential Skills and Concepts:
1. Use scientific notation to estimate very large or
small quantities
write numbers in scientific notation
compare and interpret scientific notation
quantities
2. Recognize how many times larger one quantity is to
the other
understand if the exponent increases by one, its
value increases 10 times
understand if the exponent decreases by one, its
value decreases 10 times
Mathematical Language: scientific notation,
standard notation, powers, exponents
Math Standard: 8.EE.6
Use similar triangles to explain why the slope m is the
same between any two distinct points on a nonvertical line in the coordinate plane; derive the
equation y = mx for a line through the origin and the
equation y = mx + b for a line intercepting the vertical
axis at b.
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Eighth – Expressions and Equations
8.EE.4 Essential Skills and Concepts:
8.EE.5 Essential Skills and Concepts:
1. Interpret scientific notation that has been
1. Graph proportional relationships
generated by technology.
create a graph using proportions and show their
demonstrate multiplying and dividing numbers in
relationship
scientific notations.
2. Interpret the unit rate as the slope of the graph
2 Perform multiplications and divisions of numbers
show the unit rate of the graph
written in scientific notation.
3. Compare 2 different proportional relationships in
use laws of exponents to multiply or divide
different ways
numbers written in scientific notation
give an equation of a proportional relationship;
3. Add and subtract with scientific notation
draw a graph of the relationship
be able to subtract large numbers then translate
answer to scientific notation
750,000,000 - 500,000,000 = 250,000,000 2.5 x 108
4. Choose appropriate units of measurement of very
large or very small quantities
apply the appropriate unit of measurement for
the given situation.
Example 7:
3 x 108 is equivalent to 300 million, which represents a
large quantity.
Therefore, this value will affect the unit chosen
Mathematical Language: inverse operations, square
Mathematical Language: decimal notation,
magnitude
root, cube root, perfect squares, perfect cubes,
principal square root.
Math Standard: 8.EE.7
Solve linear equations in one variable.
a. Give examples of linear equations in one variable
with one solution, infinitely many solutions, or no
solutions. Show which of these possibilities
is the case by successively transforming the given
equation into simpler forms, until an equivalent
equation of the form x = a, a = a, or a = b
results (where a and b are different numbers).
Math Standard: 8.EE.8
Analyze and solve pairs of simultaneous linear
equations.
a. Understand that solutions to a system of two linear
equations in two variables correspond to points of
intersection of their graphs, because points of
intersection satisfy both equations simultaneously.
.
b. Solve linear equations with rational number
coefficients, including equations whose solutions
require expanding expressions using the distributive
property and collecting like terms.
b. Solve systems of two linear equations in two
variables algebraically, and estimate solutions by
graphing the equations. Solve simple cases by
inspection. For example, 3x + 2y = 5 and 3x + 2y = 6
have no solution because 3x + 2y cannot
simultaneously be 5 and 6.
c. Solve real-world and mathematical problems leading to
two linear equations in two variables. For example, given
coordinates for two pairs of
points, determine whether the line through the first pair
of points intersects the line through the second pair.
c. Solve real-world and mathematical problems
leading to two linear equations in two variables. For
example, given coordinates for two pairs of points,
determine whether the line through the first pair of
points intersects the line through the second pair.
OASIS, LLC
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
8.EE.6 Essential Skills and Concepts:
1. Identify similar triangles
identify corresponding part of similar triangles
2. Determine slope between any two points on a nonvertical line
find slope by calculating the simplified ratio of
vertical height to the horizontal length. (rise /
run)
3. Derive the equation y = mx for a line through the
origin and the equation y = mx + b for a line
intercepting the vertical axis at b
recognize that m represents the slope of the line
recognize that b represents the y intercept of
the line
use logical sequencing to determine the steps
necessary for writing a linear equation in slopeintercept form
Mathematical Language: similar figures, slopeintercept form of the equation
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design: OASIS, LLC
Grade: Eighth – Expressions and Equations
8.EE.7 Essential Skills and Concepts:
8.EE.8 Essential Skills and Concepts:
1. Solve one-variable equations
1. Solve real world/mathematical problems
solve a one-step equation with the variable on
with 2 linear equations. (System of Equations)
the left of the equal sign and with the variable on
graph the 2 linear equations, knowing that their
the right side of the equal sign
intersection (ordered pair) satisfies both
equations
solve two–step equations with the variable on
recognize that parallel lines have no solution, but
either side of the equal sign.
have the same slope and different y-intercepts
2 Solve linear equations using the distributive
recognize lines that are the same will have an
property
infinite number of solutions, but have the same
explain/demonstrate how the distributive
slope and y-intercept
property works
use substitution in order to solve the system of
3. Solve linear equations using combining like terms
equations
explain how to combine like terms on the same
side of the equal sign.
4. Solve simple equations with the variables on both
sides of the equal sign.
recognize that the variables are on both sides of
the equal sign.
demonstrate how to combine like terms when
the variables and numbers are on both sides of
the equal sign
5. Write equations from verbal descriptions and solve
translate the verbal description of a one step
equation into a written equation with a variable,
and then solve the equation
translate the verbal description of a two-step
equation into a written equation with a variable,
and then solve the equation
translate the variable description of a multi-step
equation into a written equation with a variable;
then solve the equation
Mathematical Language: decimal notation,
magnitude
Mathematical Language None specific
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Eighth – Functions
Math Standard: 8.F.1
Math Standard: 8.F.2
Understand that a function is a rule that assigns to
Compare properties of two functions each
each input exactly one output. The graph of a function represented in a different way (algebraically,
is the set of ordered pairs consisting of an input and
graphically, numerically in tables, or by verbal
the corresponding output.
descriptions). For example, given a linear function
(Function notation is not required in Grade 8.)
represented by a table of values and a linear function
represented by an algebraic expression, determine
which function has the greater rate of change.
8.F.1 Essential Skills and Concepts:
1. Identify a function by looking at a table, graph, or
equation
explain that there is only one x- value for each yvalue
use the vertical line test to identify if a graph is a
function
recognize that any non-vertical line is a function
understand that function is represented by an
equation written in slope intercept form
Example: Students recognize equations such as y = x or
y = xˆ2 + 3x + 4 as functions; whereas, equations such
as xˆ2 + yˆ2 = 25 are not functions
8.F.2 Essential Skills and Concepts:
1. Compare functions from different representations
(table, graph or equation) by determining which
function has a greater rate of change
use the slope formula to calculate the rate of
change when given a table of values
write the algebraic rule for a function when
given a written expression.
Mathematical Language: functions, y-value, x-value,
vertical line test, input, output, rate of
change, linear function, non-linear function
Mathematical Language: rate of change
OASIS, LLC
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
Math Standard: 8.F.3
Interpret the equation y = mx + b as defining a linear
function, whose graph is a straight line; give examples
of functions that are not linear.
For example, the function A = s2 giving the area of a
square as a function of its side length is not linear
because its graph contains the points (1,1), (2,4) and
(3,9), which are not on a straight
8.F.3 Essential Skills and Concepts:
1. Categorize functions as linear or non-linear
use the graph of y= mx + b to define a linear
function
determine a linear or nonlinear function in a
table by looking for a pattern in the outputs and
determining a consistency in the slopes.
recognize that points on a straight line will have
the same rate of change (slope) and be linear
Mathematical Language: non-linear
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design: OASIS, LLC
Grade: Eighth – Functions
Math Standard: 8.F.4
Math Standard: 8.F.5
Construct a function to model a linear relationship
Describe qualitatively the functional relationship
between two quantities. Determine the rate of change between two quantities by analyzing a graph (e.g.,
and initial value of the function from a description of a where the function is increasing or decreasing, linear
relationship or from two (x, y) values, including
or nonlinear). Sketch a graph that exhibits the
reading these from a table or from a graph. Interpret
qualitative features of a function that has been
the rate of change and initial value of a linear function described verbally
in terms of the situation it models, and in terms of its
graph or a table of values.
Essential Skills and Concepts:
Essential Skills and Concepts:
1a. Identify the rate of change (slope) and initial value 1. Analyze a graph of two quantities.
(y-intercept) from tables, graphs, and equations
explain the relationship between the two
1b Construct a function to model a linear
quantities of the graph
relationship between 2 quantities
2. Sketch the graph of a function from a verbal
1c. Interpret the rate of change and initial value of a
description
Linear function.
create a graph by interpreting a verbal
use 2 values from the table for the slope
description
formula to find the rate of change
3. Provide a verbal description of a function graph
use the slope and a point to find the initial
look at a graph and provide a verbal/written
value
description
find 2 coordinates on the graph, then either
use the slope formula or a method of counting
(rise over run) to determine the slope.
visually see where the line of the graph crosses
the y-axis and use that as the Initial value
use substitution for Y= mx + b to write the
function
use the slope and multiply it by the x-value
take the Y-value and substitute it for Y
solve for b to get the y-intercept
write the function using the rate of change and
initial value
2. Identify the rate of change (slope) and initial value
(y-intercept) from a verbal description to write a
function (linear equation)
write an expression from a verbal description
interpret the rate of change in the verbal
description
interpret the y-intercept in the verbal
description
Mathematical Language: rate of change, initial value,
slope formula, y-intercept
Mathematical Language: None specific
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Eighth – Geometry
Math Standard: 8.G.1
Math Standard: 8.G.2
Verify experimentally the properties of rotations,
Understand that a two-dimensional figure is
reflections, and translations:
congruent to another if the second can be obtained
from the first by a sequence of rotations, reflections,
a. Lines are taken to lines, and line segments to line
and translations; given two congruent figures,
segments of the same length.
describe a sequence that exhibits the congruence
b. Angles are taken to angles of the same measure.
between them.
c. Parallel lines are taken to parallel lines.
8.G.1 Essential Skills and Concepts:
1. Verify the properties of rotations, reflections, and
translations
identify the pre-image and image of different
figures
apply the properties of rotations, reflections,
and translations to lines.
apply the properties of rotations, reflections,
and translations to line segments
apply the properties of rotations, reflections,
and translations to angles.
apply the properties of rotations, reflections,
and translations to sets of parallel lines
use different tools (compasses, protractors,
rulers or technology) to explore how figures are
created from rotations, reflections, and
translations
8.G.2 Essential Skills and Concepts:
1. Understand that a two-dimensional figure is
congruent to another after applying a sequence of
rigid transformations
identify congruent figures
identify examples of rigid transformations
2. Understand that a two-dimensional figure is
congruent to another after applying a sequence of
rigid transformations
recognize that corresponding parts of congruent
figure are equal (congruent).
3. Identify a sequence of transformations between
two congruent figures.
determine the rigid transformation produced
from its preimage
recognize the symbol for congruency
write statements of congruency
recognize rigid transformations
Mathematical Language: pre-image, image,
reflection, rotation, line of reflection, rigid
transformation, center of rotation, clock-wise,
counter-clock-wise, transformation dilation, scale
factor, exterior angles, consecutive interior angles,
alternate interior angles, alternate exterior angles,
vertical angles, adjacent angles, supplementary angles,
complimentary angles, corresponding angles,
transversal, angle-angle criterion, deductive
reasoning, betweenness.
Mathematical Language: congruence
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The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
Math Standard: 8.G.3
Describe the effect of dilations, translations, rotations,
and reflections on two-dimensional figures using
coordinates
8.G.3 Essential Skills and Concepts:
1. Describe the effect of dilations, translations,
rotations, and reflections on two-dimensional
figures using coordinates
identify resulting coordinates after a
transformation
recognize dilations are a non-rigid
transformation
understand dilations can be enlargements or
reductions
demonstrate that a scale factor greater that one
produces an enlargement
demonstrate that a scale factor less that one
produces a reduction.
Mathematical Language: dilation, non-rigid
transformation, scale factor, enlargement, reduction
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Eighth – Geometry
Math Standard: 8.G.4
Math Standard: 8.G.5
Understand that a two-dimensional figure is similar to Use informal arguments to establish facts about the
another if the second can be obtained from the first by angle sum and exterior angle of triangles, about the
a sequence of rotations, reflections, translations, and
angles created when parallel lines are cut by a
dilations; given two similar two- dimensional figures,
transversal, and the angle-angle criterion for similarity
describe a sequence that exhibits the similarity
of triangles. For example, arrange three copies of the
between them.
same triangle so that the sum of the three angles
appears to form a line, and give an argument in terms
of transversals why this is so.
8.G.4 Essential Skills and Concepts:
8.G.5 Essential Skills and Concepts:
1. Understand that a two-dimensional figure is similar 1. Formulate facts about the interior and exterior
to another after applying a sequence of
angles of a triangle.
transformations
explore relationships existing between angle
identify congruent figures
sums and exterior angle sums of triangles
know that similar figures have congruent angles
2. Formulate facts about angles created from parallel
and proportional sides
lines cut by a transversal
understand that similar figures are produced by
recognize vertical angles, corresponding angles,
dilations
adjacent angles, alternate interior angles and
2. Describe a sequence that exhibits the similarity
alternate exterior angles
between two figures
3. Understand the angle-angle criterion for similarity
identify the scale factor applied to similar figures
of triangles
recognize that two triangles with two congruent
angles are similar
recognize two triangles with two congruent
angles, and sides of different lengths are similar
deduce that comparing the ratio of the sides of
the triangle will produce a scale factor
Mathematical Language: similarity, similar figures
Mathematical Language: transversal, deductive
reasoning, vertical angles. corresponding angles,
adjacent angles, alternate interior angles, alternate
exterior angles, supplementary angles
OASIS, LLC
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
Math Standard: 8.G.6
Using models, students explain the Pythagorean
Theorem, understanding that the sum of the squares
of the legs is equal to the square of the hypotenuse in
a right triangle. Students also understand that given
three side lengths with this relationship forms a right
triangle
8.G.6 Essential Skills and Concepts:
1. Determine the unknown side length in a right
triangle
find the missing side of a right triangle
2. Apply the Pythagorean Theorem to real-world
mathematical problems.
apply the Pythagorean Theorem to real-world
problems
Mathematical Language: PythagoreanTtheorem,
hypotenuse, ceg, Converse of Pythagorean Theorem
(Pythagorean Triples)
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Eighth – Geometry
Math Standard: 8.G.7
Math Standard: 8.G.8
Apply the Pythagorean Theorem to determine
Apply the Pythagorean Theorem to find the distance
unknown side lengths in right triangles in real-world
between two points in a coordinate system.
and mathematical problems in two and
three dimensions.
OASIS, LLC
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
Math Standard: 8.G.9
Know the formulas for the volumes of cones,
cylinders, and spheres and use them to solve realworld and mathematical problems.
8.G.7 Essential Skills and Concepts:
1. Determine the unknown side length in a right
triangle
find the missing side of a right triangle
2. Apply the Pythagorean Theorem to real-world
Mathematical problems.
apply the Pythagorean Theorem to real-world
problems
8.G.8 Essential Skills and Concepts:
1. Apply the Pythagorean Theorem to find the
distance between two points on a coordinate plane
construct a right triangle using two points
determine the lengths of the legs of a right
triangle by counting the vertical and horizontal
distance of the legs
use the lengths of the legs to calculate the
hypotenuse
understand that the line segment between the
two points is the length of the hypotenuse
8.G.9 Essential Skills and Concepts:
1. Know the formulas for the volume of cones,
cylinders and spheres.
know the area formula for circles
be able to explain the concept of volume
know the basic properties of cylinders, cones
and spheres
apply the formulas to find the volume of
cylinders, cones and spheres.
2. Apply the formulas to solve real-world problems
understand the relationship between the
volume of a cylinder and a cone by using the
appropriate formulas
understand the relationship between the
volume of a cylinder and spheres by using the
appropriate formulas
apply volume formulas to solve real-world
problems
Mathematical Language: right triangle
Mathematical Language: peaks, gaps, clusters, dot
plots (line plots), box plots, histograms, quartiles,
interquartile range
Mathematical Language: cylinder, cone, sphere,
volume
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Sixth – Statistics & Probability
Math Standard: 8.SP.1
Math Standard: 8.SP.2
Construct and interpret scatter plots for bivariate
Know that straight lines are widely used to model
measurement data to investigate patterns of
relationships between two quantitative variables. For
association between two quantities. Describe
scatter plots that suggest a linear association,
patterns such as clustering, outliers, positive or
informally fit a straight line, and informally assess the
negative association, linear association, and nonlinear
model fit by judging the closeness of the data points to
association.
the line.
8.SP.1 Essential Skills and Concepts:
8.SP.2 Essential Skills and Concepts:
1. Construct a scatter plot for bivariate data to
1. Model relationships between two quantitative
investigate patterns between two quantities
variables using scatter plots
draw a scatter plot representing two quantities
create a scatter plot using the data points
2. Interpret a scatter plot for bivariate data to
2. know that a scatter plot suggest a linear association
investigate patterns between two quantities
draw a line that comes closest to most of the
recognize a positive, negative and no association
data points, known as a line of best fit.
(correlations)
recognize clustering and outliers
Mathematical Language: scatter plot, bivariate,
outliers, clustering
Math Standard: 8.SP.4
Understand that patterns of association can also be
seen in bivariate categorical data by displaying
frequencies and relative frequencies in a two-way
table. Construct and interpret a two-way table
summarizing data on two categorical variables
collected from the same subjects. Use relative
frequencies calculated for rows or columns to describe
possible association between the two variables. For
example, collect data from students in your class on
whether or not they have a curfew on school nights
and whether or not they have assigned chores at
home. Is there evidence that those who have a curfew
also tend to have chores?
8.SP.4 Essential Skills and Concepts:
1. Display bivariate data in a two way table.
construct a two way table
draw conclusions by comparing the data
Mathematical Language: relative frequencies, twoway table, bivariate, clustering
Mathematical Language: line of best fit
OASIS, LLC
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
Math Standard: 8.SP.3
Use the equation of a linear model to solve problems
in the context of bivariate measurement data,
interpreting the slope and intercept.
8.SP.3 Essential Skills and Concepts:
1. Use an equation of a linear model to solve
problems
Mathematical Language: linear model, association