Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Seventh – Ratios and Proportions
Math Standard: 7.RP.1
Math Standard: 7.RP.2
Compute unit rates associated with ratios of fractions, Recognize and represent proportional relationships
including ratios of lengths, area and other quantities
between quantities.
measured in like or different units.
a. Decide whether two quantities are in a proportional
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: 7.RP.3
Use proportional relationships to solve multistep ratio
and percent problems.
relationship, e.g., by testing for equivalent ratios in a
table or graphing on a coordinate plane and observing
whether the graph is a straight line through the origin.
b. Identify the constant of proportionality (unit rate) in
tables, graphs, equations, diagrams, and verbal
descriptions of proportional relationships.
c. Represent proportional relationships by equations.
7.RP.1 Essential Skills and Concepts:
1. Calculate unit rates using ratios of fractions
(complex fractions)
write a ratio using fractions and label the units
solve unit rates using division
apply the multiplicative inverse to find the unit
rate
d. Explain what a point (x, y) on the graph of a
proportional relationship means in terms of the
situation, with special attention to the
points (0, 0) and (1, r) where r is the unit rate.
7.RP.2 Essential Skills and Concepts:
1. Determine if two quantities are proportional
use a table of proportional values to determine
the rate of change
graph coordinates from a table to show rate of
change
write a ratio from a table or a graph
2. Identify the constant of proportionality (unit rate)
explain how the ratios are equivalent
explain the proportional relationship between x
and y showing that as x increases, y increases
determine if the quantities are proportional if
they form a straight line
7.RP.3 Essential Skills and Concepts:
1. Use proportions to solve real world problems.
write a proportion with complex fractions from
a variety of word problems
solve the proportion using a variety of methods.
2. Solve percent problems in real world situations
solve tax problems
solve problems that include gratuity and
commission
solve problems that include mark-ups and
mark-downs
3. Solve percent of change
find the difference between the original and the
new value
set-up and solve a ratio of change out of
original
express the percent mark-up or mark-down as a
percent of change.
4. Solve percent of error problems
find the absolute value of the difference
between the result and the accepted value
divide by the accepted value
5. Solve interest problems
identify the missing component using the given
formula (interest, principal, rate, or time)
change rate from percent to a decimal
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Seventh – Ratios and Proportions
7.RP.1 Mathematical Language: ratio, unit rate,
7.RP.2 Mathematical Language: constant of
equivalent ratio, complex fractions, reciprocal,
proportionality, proportions, cross products,
multiplicative inverse
coefficient, ordered 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.
7.RP.3 Mathematical Language: percent of change
(increase/decrease), percent of error, interest, simple
interest, principal, markup, markdown, tax, gratuity,
tip, commission, accepted value, sales tax
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Seventh – The Number System
Math Standard: 7.NS.1
Math Standard: 7.NS.2
Apply and extend previous understandings of addition Apply and extend previous understandings of
and subtraction to add and subtract rational numbers; multiplication and division and of fractions to multiply
represent addition and subtraction on a horizontal or
and divide rational numbers.
vertical number line diagram.
a. Understand that multiplication is extended from
a. Describe situations in which opposite quantities
combine to make 0.
b. Understand p + q as the number located a distance
|q| from p, in the positive or negative direction
depending on whether q is positive or negative. Show
that a number and its opposite have a sum of 0 (are
additive inverses). Interpret sums of rational numbers
by describing real world contexts.
c. Understand subtraction of rational numbers as
adding the additive inverse, p – q = p + (–q). 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.
d. Apply properties of operations as strategies to add
and subtract rational numbers.
7.NS.1 Essential Skills and Concepts:
1. Interpret sums, differences, products and quotients
of rational numbers by describing real-world
contexts
model addition and subtraction of integers on a
number line (vertical and horizontal)
understand how to use absolute value of a
number
calculate the distance from zero on a number
line
model how to add, subtract, multiply and divide
negative rational numbers
identify the solution to a real world problem as
either positive or negative
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: 7.NS.3
Solve real-world and mathematical problems involving
the four operations with rational numbers.
(Computations with rational numbers extend the rules
for manipulating fractions to complex fractions.)
fractions to rational numbers by requiring that
operations continue to satisfy the properties of
operations, particularly the distributive property,
leading to products such as (–1)(–1) = 1 and the rules
for multiplying signed numbers. Interpret products of
rational numbers by describing real-world contexts.
b. Understand that integers can be divided, provided
that the divisor is not zero, and every quotient of
integers (with non-zero divisor) is a rational number. If
p and q are integers, then – (p/q) = (–p)/q = p/ (–q).
Interpret quotients of rational numbers by describing
real-world contexts.
c. Apply properties of operations as strategies to
multiply and divide rational numbers.
d. Convert a rational number to a decimal using long
division; know that the decimal form of a rational
number terminates in 0s or eventually
repeats.
7.NS.2 Essential Skills and Concepts:
1. Interpret sums, differences, products and quotients
of rational numbers by describing real-world
contexts
model addition and subtraction of integers on a
number line (vertical and horizontal)
understand how to use absolute value of a
number
calculate the distance from zero on a number
line
model how to add, subtract, multiply and divide
negative rational numbers
identify the solution to a real world problem as
either positive or negative
7.NS.3 Essential Skills and Concepts:
1. Use order of operations to write and solve
problems with all rational numbers
use the order of operations to solve problems
with rational numbers including complex
fractions
The academic vocabulary or content language
Essential MATH Skills Alignment – Math Standards
is listed under each standard. There are 30-40
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design: OASIS, LLC words in bold that should be taught to mastery.
Grade: Seventh – The Number System
2. Apply properties of operations
2. Apply properties of operations
show that a number and its opposite have a sum
show that a number and its opposite have a sum
of zero (additive inverse property)
of zero (additive inverse property)
apply the distributive property to rational
apply the distributive property to rational
numbers
numbers
recognize that a number cannot be divided by
recognize that a number cannot be divided by
zero
zero
3. Convert a rational number to a decimal
3. Convert a rational number to a decimal
divide the numerator by the denominator using
divide the numerator by the denominator using
long division
long division
determine if the decimal terminates or repeats
determine if the decimal terminates or repeats
Mathematical Language: complex fractions, order of
Mathematical Language: properties of operations
Mathematical Language: properties of operations
operations, integer
(associative, commutative, identity, distributive),
(associative, commutative, identity, distributive),
rational numbers, terminating decimals, repeating
decimals
rational numbers, terminating decimals, repeating
decimals
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Seventh – Expressions and Equations
Math Standard: 7.EE.1
Math Standard: 7.EE.2
Apply properties of operations as strategies to add,
Understand that rewriting an expression in different
subtract, factor, and expand linear expressions with
forms in a problem context can shed light on the
rational coefficients.
problem and how the quantities in it are related
7.EE.1 Essential Skills and Concepts:
1. Use properties of operations to write equivalent
expressions using rational numbers.
simplify expressions
factor expressions. ie. 5x + 10 = 5(x +2)
use properties to expand expressions
7.EE.2 Essential Skills and Concepts:
1. Rewrite expressions to better understand a real
world problem
show how different quantities are related by
rewriting the expression using variables
Mathematical Language: expression, factor, rational
number, term, constant, coefficient, variable
Mathematical Language: expression, quantity
Math Standard: 7.EE.4
Use variables to represent quantities in a real-world or
mathematical problem, and construct simple
equations and inequalities to solve problems by
reasoning about the quantities.
7.EE.4 Essential Skills and Concepts:
1. Write and solve multi-step equations from realworld word problems
identify the variable in a real world problem
identify the coefficient in a real world problem.
identify the constant in a real world problem
identify the operation need to solve the problem
use inverse operations to solve an equation
2. Write and solve multi-step inequalities from realworld word problems
identify the inequality symbol needed to solve
the problem
know that the inequality symbol changes
direction when multiplying or dividing by a
negative coefficient
graph the solution set of an inequality
a. Solve word problems leading to equations of the
form px + q = r and p(x + q) = r, where p, q, and r are
specific rational numbers. Solve equations of these
forms fluently. Compare an algebraic solution to an
arithmetic solution, identifying the sequence of the
operations used in each approach.
b. Solve word problems leading to inequalities of the
form px + q > r or px + q < r, where p, q, and r are
specific rational numbers. Graph the solution set of
the inequality and interpret it in the context of the
problem.
(see middle column for skills and concepts)
Mathematical Language: variable, coefficient,
constant, equation, inequality, inverse operations,
solution, solution set
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: 7.EE.3
Solve multi-step real-life and mathematical problems
posed with positive and negative rational numbers in
any form (whole numbers, fractions, and decimals),
using tools strategically. 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.
7.EE.3 Essential Skills and Concepts:
1. Use tools and strategies to solve multi-step real-life
world problems.
convert between fractions, decimals and
percents
use estimation and mental computation
strategies
Mathematical Language: estimation, convert,
properties of operations (associative, commutative,
identity, distributive
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Seventh – Geometry
Math Standard: 7.G.1
Math Standard: 7.G.2
Solve problems involving scale drawings of geometric
Draw (freehand, with ruler and protractor, and with
figures, including computing actual lengths and areas
technology) geometric shapes with given conditions.
from a scale drawing and reproducing a scale drawing
Focus on constructing triangles from three measures
at a different scale.
of angles or sides, noticing when the conditions
determine a unique triangle, more than one triangle,
or no triangle.
7.G.1 Essential Skills and Concepts:
7.G.2 Essential Skills and Concepts:
1. Solve problems involving scale drawings of
1. Draw geometric figures given parameters
geometric figures
draw the geometric shape by freehand
identify the scale factor of two given figures
draw the geometric shape with ruler and
draw a geometric figure to scale
protractor
calculate area of a scale drawing
draw the geometric shape with technology
find missing lengths of a scale drawing
2. Determine if three given lengths create a triangle
investigate the changing in dimensions as it
recognize the sum of two smaller sides must be
relates to scale factor
larger than the third side.
Mathematical Language: scale factor, scale drawing,
Mathematical Language: obtuse, acute, isosceles,
scale, scale model, dimensions
equilateral, scalene, right (triangle classification)
Math Standard: 7.G.4
Know the formulas for the area and circumference of a
circle and use them to solve problems; give an
informal derivation of the relationship between the
circumference and area of a circle.
7.G.4 Essential Skills and Concepts:
1. Explain the relationship between the parts of a
circle to generate the formulas for circumference
and area
examine the relationship between the radius and
the diameter and their role in calculating the
circumference of a circle
explain how Pi is derived from the ratio of the
circumference to the diameter
examine the relationship between the radius, the
diameter, and Pi and their role in calculating the
area of a circle
examine and explain the relationship between
the area and circumference of a circle
2. Use the formula for circumference and area of
circles to solve problems.
solve mathematical and real-life problems using
knowledge of the formula for circumference
and area of circle (see middle column for language)
Math Standard: 7.G.5
Use facts about supplementary, complementary,
vertical, and adjacent angles in a multi-step problem
to write and solve simple equations for an unknown
angle in a figure.
7.G.5 Essential Skills and Concepts:
1. Write equations using facts about supplementary,
complimentary, vertical and adjacent angles to
solve for an unknown angle in a figure
use knowledge of angles to write and solve
equations for the unknown angle in a figure
7.G.4 Mathematical Language: radius, diameter, Pi,
circumference, area of a circle, arc, center, chord
7.G.5 Mathematical Language: supplementary
angles, complimentary angles, vertical angles,
adjacent angles, central angle
7.G.6 Mathematical Language: area, volume, surface
area, polygon, composite shapes
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: 7.G.3
Describe the two-dimensional figures that result from
slicing three- dimensional figures, as in plane sections
of right rectangular prisms and right rectangular
pyramids.
7.G.3 Essential Skills and Concepts:
1. Identify cross-sectional views of right rectangular
prisms and pyramids.
recognize that cuts made parallel will take the
shape of the base.
recognize that cuts made perpendicular will take
the shape of the lateral face
recognize that cuts made at an angle will produce
a parallelogram
Mathematical Language: cross-section, parallel,
perpendicular, face, lateral face, base, parallelogram,
right rectangular prism, right rectangular pyramid
Math Standard: 7.G.6
Solve real-world and mathematical problems involving
area, volume and surface area of two- and threedimensional objects composed of triangles,
quadrilaterals, polygons, cubes, and right prisms.
7.G.6 Essential Skills and Concepts:
1. Solve real world problems involving area of twodimensional figures.
find the area using the formula for triangles,
quadrilaterals, and polygons.
find the unknown side length when given the
area
2. Solve real world problems involving volume of
three-dimensional figures
find the volume using the formula for cubes and
right rectangular prisms and triangular prisms
find the unknown side length when given the
volume
3. Solve real world problems involving surface area of
three-dimensional figures
add the faces/base(s) of a three-dimensional
figure to calculate surface area
find the unknown side length of a cube when
given the surface area(see middle column for lang.)
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Seventh – Statistics & Probability
Math Standard: 7.SP.1
Math Standard: 7.SP.2
Understand that statistics can be used to gain
Use data from a random sample to draw inferences
information about a population by examining a sample about a population with an unknown characteristic of
of the population; generalizations about a population
interest. Generate multiple samples (or simulated
from a sample are valid only if the sample is
samples) of the same size to gauge the variation in
representative of that population. Understand that
estimates or predictions.
random sampling tends to produce representative
For example, estimate the mean word length in a book
samples and support valid inferences
by randomly sampling words from the book; predict
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: 7.SP.3
Informally assess the degree of visual overlap of two
numerical data distributions with similar variabilities,
measuring the difference between the centers by
expressing it as a multiple of a measure of variability.
the winner of a school election based on randomly
sampled survey data.
7.SP.1 Essential Skills and Concepts:
1. Identify how statistics can be used to gain
information about a population.
explain why it is difficult to gather statistics on an
entire population
understand that a sample is only valid if it is
representative of a population
describe the characteristics of random sampling
use a random sample to draw inferences about a
population
Gauge how far off the estimate or prediction might be
7.SP.2 Essential Skills and Concepts:
1. Create a random sample from a population
identify the population
collect data from multiple random samples
(collected or simulated)
compare data collected from random samples
use collected data to make a prediction about
the population
Mathematical Language: population, random
sample, statistics, survey, inference
Mathematical Language: population, random
sample, simulated sample, prediction
Math Standard: 7.SP.4
Use measures of center and measures of variability for
numerical data from random samples to draw
informal comparative inferences
about two populations.
Math Standard: 7.SP.5
Understand that the probability of a chance event is a
number between 0 and 1 that expresses the likelihood
of the event occurring. Larger numbers indicate
greater likelihood. A probability near 0 indicates an
unlikely event, a probability around . indicates an
event that is neither unlikely nor likely, and a
probability near 1 indicates a likely event.
7.SP.5 Essential Skills and Concepts:
1. Determine the likelihood of an event occurring
understand and define the concept of theoretical
probability
know that all probabilities are between 0 and 1
and are written as a fraction
understand that the closer the fraction is to 1 the
greater the probability of the event will occur
7.SP.4 Essential Skills and Concepts:
1. analyze two sets of data by comparing the
measures of center and variability
draw comparative inferences using two sets of
data
7.SP.3 Essential Skills and Concepts:
1. Calculate and compare measures of central
tendency and variability for two sets of data
calculate and compare the mean and Mean
Absolute Deviation (M.A.D.) for two sets of data
calculate and compare the median and
interquartile range for two sets of data
Mathematical Language: measures of center (central
tendency), variability, Mean Absolute Deviation,
interquartile range
Math Standard: 7.SP.6
Approximate the probability of a chance event by
collecting data on the chance process that produces it
and observing its long-run relative frequency, and
predict the approximate relative frequency given the
probability.
7.SP.6 Essential Skills and Concepts:
1. Explore the relationship between theoretical and
experimental probability.
conduct experiments with various numbers of
trials
record the relative frequency (number of
successful events) when conducting an
experiment
recognize that as the number of trials increase,
the experimental probability approaches the
theoretical probability
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Seventh – Statistics & Probability
7.SP.4 Mathematical Language: measures of center
7.SP.5 Mathematical Language: probability,
(central tendency), measures of variability,
theoretical probability
comparative inferences
Math Standard: 7.SP.7
Develop a probability model and use it to find
probabilities of events. Compare probabilities from a
model to observed frequencies; if the agreement is
not good, explain possible sources of the discrepancy.
a. Develop a uniform probability model by assigning
equal probability to all outcomes, and use the model
to determine probabilities of events.
b. Develop a probability model (which may not be
uniform) by observing frequencies in data generated
from a chance process.
Math Standard: 7.SP.8
Find probabilities of compound events using organized
lists, tables, tree diagrams, and simulation.
a. Understand that, just as with simple events, the
probability of a compound event is the fraction of
outcomes in the sample space for which the
compound event occurs.
b. Represent for compound events using methods
such as organized lists, tables and tree diagrams. For
an event described in everyday language (e.g., “rolling
double sixes”), identify the outcomes in the sample
space which compose the event.
c. Design and use a simulation to generate frequencies
for compound events.
7.SP.7 Essential Skills and Concepts:
1. Determine the likelihood of an event occurring in a
real-world application
use probability model to predict outcomes
and the probability an event will happen
Mathematical Language: probability, theoretical
probability, experimental probability, outcomes,
events, sample size
For example, use random digits as a simulation tool to
approximate the answer to the question: If 40% of
donors have type A blood, what is the probability that
it will take at least 4 donors to find one with type A
blood?
7.SP.8 Essential Skills and Concepts:
1. Determine probability of compound events
define compound events as either independent
or dependent
calculate compound events
use organized lists, tables, tree diagrams, and
simulations to determine the probability of
compound events
Mathematical Language: probability, theoretical
probability, experimental probability, relative
frequency, outcomes, events, sample size, tree
diagrams, compound events, organized lists,
simulations
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.
7.SP.6 Mathematical Language: probability,
theoretical probability, experimental probability,
relative
frequency, outcomes, events, sample size