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Grade 7
Mathematics CCRS Standards and Alabama COS
Evidence of Student
Attainment
Teacher
Vocabulary
CCRS Standard
Standard ID
1. Compute unit rates
associated with ratios
of fractions, including
ratios of lengths, areas
and other quantities
measured in like or
different units.
Example: If a person
walks 1/2 mile in each
1/ hour, compute the
4
unit rate as the
complex fraction 1/2/1/4
miles per hour,
equivalently 2 miles per
hour.
Ratios &
Proportional
Relationships
Analyze
proportional
relationships
and use them to
solve real-world
and
mathematical
problems.
7.RP.1
Unit rate
Students:
Given ratios of fraction to
fractions in contextual
Ratio
situations,
2. Recognize and
represent proportional
relationships between
quantities.
Ratios &
Proportional
Relationships
Analyze
proportional
relationships
and use them to
solve real-world
and
mathematical
problems.
7.RP.2
Students:
Justify relationships
as proportional and
identify the constant of
proportionality using
graphs, tables,
equivalent ratios, and
equations,
a. Decide whether two
quantities are in a
proportional
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.
Franklin County Schools
Given the graph of a
proportional relationship
in a contextual situation,
(i.e. buying CDs of equal
price),
Skills
Understanding
Resources
Students know:
Students are able to: Students
understand that:
Techniques for
producing ratios
equivalent to
given ratios,
including finding
unit rates.
Determine
Unit rates are Click below to
equivalent ratios
access all ALEX
(including unit rates) used to clearly
for ratios consisting of communicate rates resources aligned
to this standard.
fractions.
in contextual
situations and allow
for clearer
 ALEX
comparisons.
Resources
Unit rate
Students know:
Students are able to: Students
understand that:
Proportional
relationships
Characteristics
of graphs, tables,
and equations that
define
proportional
situations,
Produce graphs,
tables, and the
related equations,
Calculate the equivalent
unit rate and justify the
unit rate within the given
context.
Explain the
relationships between
representations of
proportions and extend
that relationship into a
rule (equation).
Knowledge
Relationships
between graphs,
tables, and
equations in
proportional
situations,
The role of
unit rate in a
graph of a
proportional
relationship.
The constant of
proportionality (unit
rate) in a
Communicate the relationship
relationships between communicates the
rate of change for Click below to
graphs, tables, and
equations in order to one variable with access all ALEX
justify relationships as respect to the
resources aligned
other, regardless of to this standard.
proportional.
how the
proportional
 ALEX
relationship is
Resources
represented.
Grade 7
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
c. Represent
proportional
relationships by
equations.
Example: If total cost t
is proportional to the
number n of items
purchased at a constant
price p, the relationship
between the total cost
and the number of
items can be expressed
as t = pn.
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources
Explain the
association between the
unit rate and any point
on the line, (i.e. "If I paid
$3/CD, then point (5, 15)
means that I can buy 5
CDs for $15").
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.
3. Use proportional
relationships to solve
multistep ratio and
percent problems.
Examples: Sample
problems may involve
simple interest, tax,
markups and
markdowns, gratuities
and commissions, fees,
percent increase and
decrease, percent error.
Ratios &
Proportional
Relationships
Analyze
proportional
relationships
and use them to
solve real-world
and
mathematical
problems.
7.RP.3
Franklin County Schools
Students:
Given multi-step
problems involving
contexts with ratios and
percents,
Solve and justify
solutions using a variety
of representations and
solution paths.
Students know:
Students are able to: Students
understand that:
Techniques for
representing
mathematical
contexts that
include percents
and ratios,
Strategically
choose and apply
representations that
aid in solutions of
percent and ratio
problems,
Techniques for Solve and
producing ratios
interpret the
equivalent to
solutions.
given ratios,
including finding
unit rates.
Patterns and
relationships in
mathematical
contexts can be
represented in a
variety of ways in
order to solve
problems, including
that a variety of
representations of
ratio and percent
can be used to
solve and interpret
mathematical
contexts.
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Grade 7
CCRS Standard
4. Apply and extend
previous
understandings of
addition and
subtraction to add and
subtract rational
numbers; represent
addition and
subtraction on a
horizontal or vertical
number line diagram.
Mathematics CCRS Standards and Alabama COS
Standard ID
The Number
System
Apply and
extend previous
understandings
of operations
with fractions to
add, subtract,
multiply, and
divide rational
numbers.
7.NS.1
a. Describe situations in
which opposite
quantities combine to
make 0.
Example: A hydrogen
atom has 0 charge
because its two
constituents are
oppositely charged.
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
Franklin County Schools
Evidence of Student
Attainment
Students:
Teacher
Vocabulary
Absolute value
Describe situations
Rational number
that illustrate the additive
inverse property as
Additive inverse
adding opposites to equal
zero.
Properties of
operations (Table 3)
Given contextual or
mathematical problems
involving both positive
and negative rational
numbers,
Find and justify sums
and differences of
rational numbers through
connections to a variety
of representations
(including distance on a
number line) used for
addition and subtraction
of whole numbers and
fractions.
Knowledge
Skills
Understanding
Students know:
Students are able to: Students
understand that:
Strategies for
modeling addition
and subtraction of
rational numbers
(e.g. two-color
chips and charge
models for
integers, distance
on a number line),
Strategically
choose and apply
appropriate
representations for
operations and
rational numbers in
contexts in order to
solve problems,
Characteristics
of addition and
subtraction
problems (Table
1).
Use logical
reasoning to
communicate and
interpret solutions
and solution paths for
problems involving
rational numbers.
Resources
Finding sums
and differences of
rational numbers
(negative and
positive) involves
determining
direction and
distance on the
number line,
Visual and
concrete models
help make sense of
abstract
mathematical
representations of
numbers and
computations.
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access all ALEX
resources aligned
to this standard.
a.
ALEX
Resources
Grade 7
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources
= 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.
5. Apply and extend
previous
understandings of
multiplication and
division and of fractions
to multiply and divide
rational numbers.
The Number
System
Apply and
extend previous
understandings
of operations
with fractions to
add, subtract,
multiply, and
a. Understand that
divide rational
multiplication is
extended from fractions numbers.
to rational numbers by 7.NS.2
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
Franklin County Schools
Students:
Rational number Students know:
Students are able to: Students
understand that:
Find and justify
Properties of
products and quotients of operations
rational numbers
(positive and negative)
through connections to a
variety of representations
and properties of
operations (including
multiplicative identity and
inverse) used for
multiplication and
division of whole
numbers and fractions,
Techniques for
accurately
performing
multiplication and
division of whole
numbers and
fractions,
Use long division to
convert a rational
number to a decimal and
explain why it must end
in a zero or repeat.
Characteristics
Use logical
of multiplication
and division
reasoning to
problems.
communicate and
interpret solutions
and solution paths,
Accurately
perform multiplication
and division of whole
numbers and
fractions,
Strategically
choose and apply
The properties appropriate
of operations
representations for
(Table 3) and their operations with
appropriate
rational numbers in
application,
contexts in order to
solve problems,
Use the division
algorithm to convert
fractions to decimals
(terminating and
Strategies for
finding products
and quotients of
rational numbers
(negative and
positive) follow
logically from
patterns
established with
operations on
whole numbers and
fractions,
The use of the
standard algorithm
for division helps
makes sense of
when the decimal
form of a fraction
repeats or
terminates.
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ALEX
Resources
Grade 7
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
integers can be divided,
provided that the
divisor is not zero, and
every quotient of
integers (with nonzero
divisor) is a rational
number. If p and q are
integers, then –(p/q) =
(–p)/ = p/
q
(–q). Interpret
quotients of rational
numbers by describing
real-world contexts.
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources
repeating).
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.
6. Solve real-world and
mathematical problems
involving the four
operations with rational
numbers. 1
(1computations with
rational numbers
extend the rules for
manipulating fractions
to complex fractions.)
The Number
System
Apply and
extend previous
understandings
of operations
with fractions to
add, subtract,
multiply, and
divide rational
numbers.
7.NS.3
Franklin County Schools
Complex fraction Students know:
Students:
Students are able to:
Given a variety of word
problems involving all
Characteristics Interpret
four operations on
of multiplication, mathematical
rational numbers,
division, addition, contexts (involving
involving a variety of
and subtraction
addition, subtraction,
complexities, (e.g.. mixed
contexts,
multiplication, and
numbers, complex
division of rational
fractions, location of the
Techniques for numbers) and
unknown, etc.),
performing all four represent quantities
and operations
operations on
Explain and justify
rational numbers. physically, pictorially,
solutions using a variety
or symbolically,
of representations
Students
understand that:
Finding sums,
differences,
products, and
quotients of
rational numbers
(negative and
positive) follow
logically from
patterns
established with
operations on
Click below to
access all ALEX
resources aligned
to this standard.

ALEX
Resources
Grade 7
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources
Strategically use a whole numbers and
variety of
fractions.
representations to
solve addition,
subtraction,
multiplication, and
division word
problems,
including equations.
Explain
connections between
physical/pictorial
representations of
mathematical
contexts and related
equations.
7. Apply properties of
operations as strategies
to add, subtract, factor,
and expand linear
expressions with
rational coefficients.
Expressions &
Equations
Use properties
of operations to
generate
equivalent
expressions.
7.EE.1
Students:
Given contextual or
mathematical problems
which may be modeled
by linear algebraic
expressions with rational
coefficients,
Properties of
operations
Rational
coefficients
Students know:
Students are able to: The students
understand that:
The properties
of operations
(Table 3) and their
appropriate
application.
Accurately add,
subtract, factor, and
expand linear
algebraic expressions
with rational
coefficients.
Use properties of the
operations (Table 3) to
produce combined and
re-written forms of the
expressions that are
useful in resolving the
problem.
8. Understand that
rewriting an expression
in different forms in a
problem context can
shed light on the
problem, and how the
quantities in it are
related.
Example: a + 0.05a =
Expressions &
Equations
Use properties
of operations to
generate
equivalent
expressions.
7.EE.2
Franklin County Schools
The distributive
property, factoring,
and combining like
terms,are used to
justify the
equivalence of
alternate forms of
expressions for use
in problem solving
situations.
Students:
Students know:
Students are able to: Students
understand that:
Explain how
combining or
decomposing parts of
algebraic expressions can
reveal different aspects
of the expression and be
useful in interpreting a
The properties
of operations
(Table 3) and their
appropriate
application.
Accurately add,
subtract, factor, and
expand linear
algebraic expressions
with rational
coefficients.
Rewriting
expressions in
multiple equivalent
forms allows for
thinking about
problems in
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Click below to
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resources aligned
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Resources
Grade 7
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
1.05a means that
“increase by 5%” is the
same as “multiply by
1.05.”
9. Solve multistep reallife 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.
Examples: If a woman
making $25 an hour
gets a 10% raise, she
will make an additional
1/
10 of her salary an
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
problem. (e.g., When
determining the number
of tiles needed for a
border around a square
pool of side n, the
expression 4n + 4 shows
counting 4 sides and
then 4 corners. The
expression 4(n+1) shows
counting four sides which
each include one corner.
The expression 4(n+2) 4 shows counting the
outer border then
subtracting the corners
as they have been
counted twice).
Expressions &
Equations
Solve real-life
and
mathematical
problems using
numerical and
algebraic
expressions and
equations.
7.EE.3
Franklin County Schools
Students:
Given contextual
problems involving any
combination of numbers
from the rational
numbers,
Model the problem
with mathematical
symbols, expressions,
and equations that aid in
solving the problem,
Select strategies that
are useful, choose the
appropriate form of
computation, reach a
solution, and defend the
solution in terms of the
original context
(including mental
computation and
estimation strategies).
Understanding
Resources
different ways,
Different but
equivalent forms of
mathematical
expressions reveal
important features
of the situation and
aid in problem
identification and
solving.
Students know:
Students are able to: Students
understand that:
Techniques for
estimation, mental
computation, and
their appropriate
application,
Translate verbal
There are
forms of a problem
into mathematical
multiple ways to
symbols, expressions, solve problems,
and equations,
The properties
of operations and
equality (Tables 3
and 4), and their
appropriate
application.
Accurately use
the properties of
operations and
equality to aid in
solving the equation,
Accurately
compute with positive
and negative rational
numbers with and
without technology,
Use estimation
and mental
computation
Strategically
using properties of
operations and
equality allows
solutions to
problems to be
defended,
Checking the
reasonableness of
answers leads to
self correcting of
errors,
Problem solving
takes effort, time,
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Grade 7
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
hour, or $2.50, for a
new salary of $27.50. If
you want to place a
towel bar 9 3/4 inches
long in the center of a
door that is 27 1/2
inches wide, you will
need to place the bar
about 9 inches from
each edge; this
estimate can be used
as a check on the exact
computation.
10. 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.
Expressions &
Equations
Solve real-life
and
mathematical
problems using
numerical and
algebraic
expressions and
equations.
a. Solve word problems 7.EE.4
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.
Example: The perimeter
Franklin County Schools
Skills
Understanding
Resources
strategies to reach
and perseverance.
solutions and to judge
reasonableness of
answers found
through paper/pencil
or technology
computation.
Students:
Given a real world or
mathematical situation,
Define the variables
and constants in the
situation,
Relate them to one
another,
Write equations
describing the
relationship,
Solve the equation
(linear situations) using
properties of the
operations and equality.
Given a contextual
situation involving a
linear inequality,
Variable
Students know:
Students are able to: Students
understand that:
The properties
of operations,
equality and
inequality (Tables
3, 4 and 5), and
their appropriate
application,
Accurately use
Real world
the properties of
operations, equality, problems can be
and inequality (Tables interpreted,
3, 4 and 5) to
modeled, and
produce equivalent
solved using
forms of an algebraic equations and
expression, equation, inequalities,
Techniques for or inequality to aid in
solving the equations Solving an
solving linear
or inequality,
equations and
equation or
inequalities,
inequality means
Graph inequalities finding all values of
the variable that
Techniques for and identify the
makes the
solving problems solution set on the
graph.
statement true,
arithmetically
(e.g., systematic
guess, check, and
revise) noting
problem structure
by examining
smaller numbers
or a simpler
In solving an
equation the
properties of
operations and
equality must be
used to maintain
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Grade 7
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
of a rectangle is 54 cm.
Its length is 6 cm. What
is its width?
Teacher
Vocabulary
Knowledge
Skills
problem, or
looking for a
pattern and
generalizing.
Model the situation
with an inequality,
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.
Example: As a
salesperson, you are
paid $50 per week plus
$3 per sale. This week
you want your pay to
be at least $100. Write
an inequality for the
number of sales you
need to make, and
describe the solutions.
11. 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.
Evidence of Student
Attainment
Problems may
be frequently
solved
arithmetically, or
modeled and solved
algebraically, and
that the structure
of mathematics
may be used to
demonstrate that
these strategies
can and do lead to
the same result.
Graph the solution
set of the inequality,
Interpret and defend
the solution in the
context of the original
problem.
Students:
Given contextual or
mathematical problems
involving scale drawings
of geometric figures,
Solve, then
communicate and justify
solution paths for
computing actual lengths
and areas.
Given a scale drawing,
Students will
Franklin County Schools
Resources
the equality
through successive
manipulations until
the solution is
revealed,
Solve the inequality,
Geometry
Draw construct,
and describe
geometrical
figures and
describe the
relationships
between them.
7.G.1
Understanding
Scale drawing
Students know:
Students are able to: Students
understand that:
Strategies for
computing actual
lengths from scale
drawings,
Select and
A scale drawing
strategically apply
methods to accurately represents a real
compute actual
object with
lengths and areas
accurate
from scale drawings, measurements
where each of the
Choose and apply measurements has
appropriate tools in been increased or
order to reproduce a decreased by the
same factor,
scale drawing at a
Strategies for
computing area,
Units for
measuring length
and area,
The
interpretation of
different scale.
In scale
drawings of
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Grade 7
CCRS Standard
12. Draw (freehand,
with ruler and
protractor, and with
technology) geometric
shapes with given
conditions. Focus on
constructing triangles
from three measures of
angles or sides, noticing
when the conditions
determine a unique
triangle, more than one
triangle, or no triangle.
Mathematics CCRS Standards and Alabama COS
Standard ID
Geometry
Draw construct,
and describe
geometrical
figures and
describe the
relationships
between them.
7.G.2
Evidence of Student
Attainment
Teacher
Vocabulary
Franklin County Schools
Understanding
scale/ratio
notation.
Students:
Given sets of conditions
for geometric shapes,
Students know:
Students are able to: Students
understand that:
Techniques for
using rulers,
protractors, and
technology to
create geometric
shapes,
Compose and
decompose geometric Shapes are
figures,
categorized based
on the
Draw (freehand, characteristics of
their attributes
with a ruler and
protractor, or using [angle size, side
length, side
technology)
relationships,
geometric shapes
from given conditions, (parallel or
perpendicular)].
Draw (freehand, with
a ruler and protractor,
and with technology) the
corresponding shapes.
Descriptive
language for
attributes of
triangles, (e.g.
side opposite an
angle, side
adjacent to an
angle, etc.).
Given three measures (a
combination of side
lengths and angle
measures) of a triangle,
Geometry
Draw construct,
and describe
geometrical
figures and
describe the
relationships
between them.
7.G.3
Skills
reproduce the drawing at
a different scale.
Use observations
from the drawing,
reasoning, and
mathematical language,
to justify whether the
conditions determine a
unique figure, more than
one figure, or no figure.
13. Describe the twodimensional figures that
result from slicing
three-dimensional
figures, as in plane
sections of right
rectangular prisms and
right rectangular
pyramids.
Knowledge
Students:
Given a 3-D figure, (e.g.
right rectangular prism,
right rectangular
pyramid, cone, etc.),
Describe the plane
(2-D) section that results
Resources
geometric figures
lengths change by
the scale factor
while areas change
by the square of
the scale factor.
Use logical
reasoning and
mathematical
language to justify
whether given
conditions will
produce a unique
figure, more than one
figure, or no figure
(with special
emphasis on
triangles).
Slicing
Students know:
Plane section
Strategies for Model and
visualizing and
visualize 3-D figures,
modeling
geometric figures, Describe the
geometric attributes
Strategies for of the plane section
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Students are able to: Students
understand that:
Modeling,
composing, and
decomposing
geometric figures
aids in visualizing,
ALEX
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ALEX
Resources
Grade 7
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
Teacher
Vocabulary
from slicing the 3-D
figure.
Knowledge
Skills
Understanding
Resources
composing and
resulting from the
investigating, and
decomposing
"slicing" of a 3-D
describing
geometric shapes, shape, such as a right geometric
rectangular prism or problems.
right rectangular
Descriptive
pyramid.
language for
attributes of 2-D
and 3-D figures.
14. 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.
Geometry
Solve real-world
and
mathematical
problems
involving angle
measure, area,
surface area,
and volume.
7.G.4
Students:
Area
Students know:
Students are able to: Students
understand that:
Describe the
relationship between the
formulas for area and
circumference of a circle
and derive an equation
relating the two
formulas.
Circumference
Strategies for
representing
contexts involving
area and
circumference of
circular regions,
Discriminate
between contexts
asking for
circumference and
those asking for area
measurements,
Strategies
including standard
formulas (A = πr2,
C = 2πr or C =
πd) for computing
the area and
circumference of
circular regions.
Strategically
choose and apply
appropriate methods
for representing and
calculating area and
circumference of
circular regions,
Given real world and
mathematical problems
involving area and
circumference of circular
regions,

Franklin County Schools
Use a variety of
representations
including
models,
drawings, and
equations based
on area and
circumference
formulas to find
and justify
solutions and
solution paths.
Circumference
is measured in
length units and is
the distance around
a circle,
The area of a
plane figure is
measured by the
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size squares that
resources aligned
exactly cover the
to this standard.
interior space of
the figure, and
 ALEX
Use properties of when counting
Resources
these squares is
operation and
difficult such as in a
equality to relate
variables in formulas, circle, formulas
allow for more
(i.e., area and
accurate calculation
circumference of a
of the area,
circle).
The length of
the radius of a
circle is related to
both the area and
circumference of
that region.
Grade 7
CCRS Standard
15. Use facts about
supplementary,
complementary,
vertical, and adjacent
angles in a multistep
problem to write and
solve simple equations
for an unknown angle
in a figure.
16. Solve real-world
and mathematical
problems involving
area, volume and
surface area of twoand three-dimensional
objects composed of
triangles, quadrilaterals,
polygons, cubes, and
right prisms.
Mathematics CCRS Standards and Alabama COS
Standard ID
Geometry
Solve real-world
and
mathematical
problems
involving angle
measure, area,
surface area,
and volume.
7.G.5
Geometry
Solve real-world
and
mathematical
problems
involving angle
measure, area,
surface area,
and volume.
7.G.6
Evidence of Student
Attainment
Students:
Given multi-step
problems involving angle
measures,
Use knowledge of
supplementary,
complementary, vertical,
and adjacent angles to
create and solve
equations for unkown
angles, and justify
solutions and solution
paths.
Teacher
Vocabulary
Supplementary
angles
Complementary
angles
Vertical angles
Adjacent angles
Area
Students:
Given real world and
mathematical problems
Volume
involving area, volume,
and surface area
Surface area
(problems include figures
composed of triangles,
quadrilaterals, polygons,
cubes, and right prisms),
Use a variety of
strategies to solve
problems, and justify
solutions and solution
paths.
Knowledge
Understanding
Students know:
Students are able to: Students
understand that:
Defining
characteristics of,
relationships
among, and
situations that
produce,
supplementary,
complementary,
vertical, and
adjacent angles.
Visually represent
Angle measure
verbal contexts
involving angles,
is additive,
Strategically
choose and apply
appropriate methods
for representing and
calculating angle
measures,
Angles created
by two intersecting
lines have
relationships that
can be used to
solve problems.
Strategies for
visually
representing
contexts involving
angle measures.
Use logical
reasoning to apply
knowledge of
supplementary,
complementary,
vertical, and adjacent
angles to create
equations and solve
multi-step problems.
Students know:
Students are able to: Students
understand that:
Measureable
attributes of
objects,
specifically area,
volume, and
surface area,
Model the surface
area of a 3-D shape Formulas
as a 2-D net,
represent
generalizations of
relationships
Strategically
among
choose and apply
measurements of
methods for
geometric objects
determining area,
volume, and surface that can be used to
solve problems,
area of geometric
Strategies for
representing the
surface area of a
3-D shape as a 2- shapes composed of
Area and
D net,
triangles,
quadrilaterals,
volume are
Strategies for polygons, cubes and additive,
determining area right prisms,
of polygons and
Franklin County Schools
Skills
Surface area of
Resources
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Resources
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a.
ALEX
Resources
Grade 7
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
volume of right
prisms.
Skills
Accurately
compute area and
surface area of
polygons,
Accurately
compute volume of
right prisms.
17. Understand that
statistics can be used to
gain information about
a population by
examining a sample of
the population;
generalizations about a
population from a
sample are valid only if
the sample is
representative of that
population. Understand
that random sampling
tends to produce
representative samples
and support valid
inferences.
Statistics &
Probability
Use random
sampling to
draw inferences
about a
population.
7.SP.1
Representative
Students:
Given data collected on a samples
sample from a
population,
Population
Make, explain and
justify inferences about
the population, if any,
that could be made from
the sample data.
Random
sampling
Inferences
Given a statistical
question about a
population,
Describe and justify a
data collection process
that would result in
representative data from
which inferences about
the population can be
drawn,
Explain and justify
their reasoning
concerning data
Franklin County Schools
Sample
Understanding
a shape composed
of right prisms is
represented by the
sum of the areas of
the faces of the
object,
Models can
represent
measurable
attributes of
objects and help to
solve problems.
Students know:
Students are able to: Students
understand that:
Methods of
determining
mean, median,
interquartile
range, and mean
absolute deviation
(from 6th grade),
Determine if a
sampling procedure Statistics can
allows for inferences be used to gain
to be made about the information about a
population from
population by
which the sample was examining a sample
drawn,
of the population,
Use logical
reasoning and
statistical
mathematical
language to explain
and justify examples
of inferences, if any,
The
that can be drawn
relationship
between a sample about a population
and the population based on the analysis
of the data and the
that the sample
was drawn from. data collection
process,
Characteristics
of random
sampling and
representative
samples,
Draw valid
conclusions from
generated statistical
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about a population resources aligned
from a sample are to this standard.
valid only if the
sample is
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representative of
Resources
that population,
Random
sampling tends to
produce
representative
samples and
support valid
inferences.
Grade 7
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
collection processes that
do not allow
generalizations, (i.e.,
non-representative
samples) from the
sample to the population.
18. Use data from a
random sample to draw
inferences about a
population with an
unknown characteristic
of interest. Generate
multiple samples (or
simulated samples) of
the same size to gauge
the variation in
estimates or
predictions.
Example: Estimate the
mean word length in a
book by randomly
sampling words from
the book; predict the
winner of a school
election based on
randomly sampled
survey data. Gauge
how far off the estimate
or prediction might be.
Statistics &
Probability
Use random
sampling to
draw inferences
about a
population.
7.SP.2
Students:
Given data from a
random sample,
Skills
Understanding
Resources
models.
Generate
multiple samples
Simulated
Analyze the data and samples
explain inferences about
the population that can
Inferences
be drawn from the
sample data.
Population
Students know:
Students are able to: Students
understand that:
Strategies for
generating
random samples,
Use statistical
vocabulary to explain
inferences about a
population when
analyzing data from
random samples,
Methods of
determining
mean, median,
Ask statistical
interquartile
range, and mean questions about
absolute deviation populations,
(from 6th grade),
Statistics can
be used to gain
information about a
population by
examining a sample
of the population,
Generalizations
about a population
from a sample are
Generate multiple valid only if the
Characteristics random samples from sample is
of random
populations in order representative of
sampling and
to gauge the variation that population,
representative
in estimates,
Random sampling
samples,
Use variation in tends to produce
representative
The
sample data to
relationship
explain possible error samples and
support valid
between a sample in estimates and
inferences.
and the population predictions.
Given a population,
Ask statistical
questions and generate
multiple samples (or
simulated samples) of
the same size to gauge
the variation in estimates
or predictions.
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Resources
that the sample
was drawn from.
19. Informally assess
the degree of visual
overlap of two
numerical data
distributions with
Statistics &
Probability
Draw informal
comparative
inferences about
Franklin County Schools
Students:
Given two sets of data
with similar variabilities,
Numerical data
distributions
Variability
Informally assess and
Students know:
Students are able to: Students
understand that:
Methods of
determining
mean, median,
Calculate the
mean, median,
interquartile range,
A set of data
collected to answer
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Grade 7
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
similar variabilities,
two populations.
measuring the
7.SP.3
difference between the
centers by expressing it
as a multiple of a
measure of variability.
Example: The mean
height of players on the
basketball team is 10
cm greater than the
mean height of players
on the soccer team,
about twice the
variability (mean
absolute deviation) on
either team; on a dot
plot, the separation
between the two
distributions of heights
is noticeable.
Evidence of Student
Attainment
describe the degree of
visual overlap of the
distributions by
comparing visual
representations of data
sets, (e.g., line plots,
coordinate plane graphs)
and statistical measures
of center and variability.
Teacher
Vocabulary
Measures of
center
Measures of
variability
Mean absolute
deviation
Knowledge
Skills
interquartile
and mean absolute
range, and mean deviation,
absolute deviation
(from 6th grade), Organize data in
ways that aid in
Methods for
identifying significant
visually
features of the data,
representing data, (e.g. putting data in
(e.g., line plots,
order to find the
coordinate
median, displaying in
graphs),
a graph to see overall
shape),
Understanding
a statistical
question has a
distribution which
can be described by
its center, spread,
and overall shape,
Resources

ALEX
Resources
Using different
representations and
descriptors of a
data set can be
useful in seeing
important features
Characteristics
of the situation
and definitions of Describe the
mean, median,
distribution of a set of being investigated,
interquartile
data by referring to
range, and mean measures of center, Statistical
absolute deviation. spread, and shape,
measures of center
and variability that
describe data sets
Effectively
can be used to
communicate a
compare data sets
comparison of data
and answer
sets using visual
representations, (e.g., questions.
line plots, coordinate
graphs) and statistical
measures, (e.g.,
mean, variability).
20. Use measures of
center and measures of
variability for numerical
data from random
samples to draw
informal comparative
inferences about two
populations.
Example: Decide
whether the words in a
chapter of a seventhgrade science book are
Statistics &
Probability
Draw informal
comparative
inferences about
two populations.
7.SP.4
Franklin County Schools
Students:
Numerical data
distributions
Generate statistical
questions that compare
two populations,
Methods of
Random samples determining
mean, median,
interquartile
Informal
range, and mean
comparative
absolute deviation
inferences
(from 6th grade),
Collect and organize
data from random
samples to address the
questions,
Describe the sample
Students know:
Methods for
visually
Students are able to: Students
understand that:
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A set of data
collected to answer resources aligned
to this standard.
a statistical
question has a
distribution which
 ALEX
Resources
Organize data in can be described by
its center, spread,
ways that aid in
identifying significant and overall shape,
features of the data,
Calculate the
mean, median,
interquartile range,
and mean absolute
deviation,
Grade 7
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
generally longer than
the words in a chapter
of a fourth-grade
science book.
Evidence of Student
Attainment
Teacher
Vocabulary
distributions using
measures of center and
variability,
Justify answers to
the questions by drawing
informal comparative
inferences about the two
populations from the
data sets and their
descriptive statistics.
21. 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 1/2
indicates an event that
is neither unlikely nor
likely, and a probability
near 1 indicates a likely
event.
Statistics &
Probability
Investigate
chance
processes and
develop, use,
and evaluate
probability
models.
7.SP.5
Franklin County Schools
Probability
Students:
Given a variety of chance
events,
Chance event
Associate numbers
close to zero with
unlikely events, and
numbers close to one
with likely events,
Compare likelihoods
of given events by
associating larger
numbers with the more
likely events.
Knowledge
Skills
Understanding
Resources
Using different
representations and
descriptors of a
data set can be
useful in seeing
important features
Characteristics
of the situation
and definitions of Describe the
mean, median,
distribution of a set of being investigated,
interquartile
data by referring to
range, and mean measures of center, Statistical
absolute deviation. spread, and shape,
measures of center
and variability that
Draw inferences describe data sets
can be used to
about populations
compare data sets
from sample data,
and answer
questions.
Justify answers to
statistical questions
involving comparison
of two populations by
using a variety of
representations of
sample data.
representing data,
(e.g., line plots,
coordinate
graphs),
(e.g. putting data in
order to find the
median, displaying in
a graph to see overall
shape),
Students know:
Students will be able Students
to:
understand that:
Relationships
between
numerically
represented
probabilities and
expressions of
likelihood.
Describe the
relationship of the
likelihood of a chance
event and its
probability.
The probability
of a chance event
is a number
between 0 and 1
that expresses the
likelihood that the
event occurs.
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Resources
Grade 7
CCRS Standard
22. 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.
Example: When rolling
a number cube 600
times, predict that a 3
or 6 would be rolled
roughly 200 times, but
probably not exactly
200 times.
Mathematics CCRS Standards and Alabama COS
Standard ID
Statistics &
Probability
Investigate
chance
processes and
develop, use,
and evaluate
probability
models.
7.SP.6
Evidence of Student
Attainment
Students:
Given the description of a
chance event, (e.g.,
rolling a certain number
on a number cube,
getting heads when
flipping a coin, drawing a
red card from a deck of
playing cards, etc.),
Teacher
Vocabulary
Probability
Chance event
Plan a data collection
process, collect and
organize the relevant
data and use the longrun relative frequency to
justify an approximation
of the probability of the
event.
Predict and justify
the approximate relative
frequency for a given
number of occurrences,
(e.g., if a number cube is
rolled 600 times, predict
that a 3 or a 6 would be
rolled roughly 200 times,
but probably not exactly
200 times).
Statistics &
Franklin County Schools
Students:
Students will
know:
Skills
Understanding
Resources
Students will be able Students
to:
understand that:
Methods for
Long-run relative collecting and
organizing data
frequency
collected from
observing chance
events,
Given the description of a
chance event and its
probability,
23. Develop a
Knowledge
Probability
Plan a data
The observed
collection process for relative frequency
chance event
of a particular
occurrences,
outcome of a
chance event may
be used to
Collect and
approximate the
organize data from
Methods for
repeated occurrences theoretical
probability of that
calculating and/or of a chance event,
outcome in any
expressing relative
random occurrence
frequency.
Calculate relative
of the event,
frequency of a
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specific outcome of a
As the number access all ALEX
chance event,
of observations of a resources aligned
chance event gets to this standard.
Justify
large, the relative
approximations of the
frequency of
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probability of a
occurrence of any
Resources
chance event
particular outcome
occurrence based on tends to more
relative frequency of
closely match the
observed outcomes,
theoretical
probability of that
Predict and justify outcome.
approximate relative
frequency of
occurrence of a
specific outcome
based on the
probability of a
chance event.
Students know:
Students will be able Students will
Click below to
Grade 7
CCRS Standard
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.
Mathematics CCRS Standards and Alabama COS
Standard ID
Probability
Investigate
chance
processes and
develop, use,
and evaluate
probability
models.
7.SP.7
a. Develop a uniform
probability model by
assigning equal
probability to all
outcomes, and use the
model to determine
probabilities of events.
Example: If a student is
selected at random
from a class, find the
probability that Jane
will be selected and the
probability that a girl
will be selected.
b. Develop a probability
model (which may not
be uniform) by
observing frequencies
in data generated from
a chance process.
Example: Find the
approximate probability
that a spinning penny
will land heads up or
that a tossed paper cup
will land open-end
down. Do the outcomes
for the spinning penny
appear to be equally
Franklin County Schools
Evidence of Student
Attainment
Given the description of a
chance event, (e.g.,
rolling a certain number
on a number cube,
getting heads when
flipping a coin, drawing a
red card from a deck of
playing cards, etc.),
Find and describe the
probability of the event
by developing probability
models based on
assigning equal
probabilities to each of
the possible outcomes
(uniform probability
model) and test whether
or not this model may or
may not fit the observed
situation when the
chance event occurs,
Explain possible
sources of discrepancy
between developed
probability models, (e.g.,
uniform probability model
or other models) and
observed frequencies.
Teacher
Vocabulary
Knowledge
model
Uniform
probability model
Observed
frequencies
Skills
to:
Methods for
collecting and
organizing data
collected from
observing chance
events,
Understanding
understand that:
Develop models that The observed
assign equal
relative frequency
probabilities to each of a particular
possible outcome of a outcome of a
chance event,
chance event may
be used to
Methods for
Develop models approximate the
calculating and/or to observe and record theoretical
expressing relative relative frequencies of probability of that
frequency,
a particular outcome outcome in any
of a chance event in random occurrence
order to approximate of the event,
Methods for
modeling chance the probability of a
As the number
specific outcome,
events by
of observations of a
assigning equal
chance event gets
Use logical
probabilities to
each outcome for reasoning to explain large, the relative
frequency of
the event.
sources of
discrepancy between occurrence of any
particular outcome
the probability of a
specific outcome of a tends to more
closely match the
chance event, as
theoretical
determined by a
probability of that
uniform probability
outcome.
model and an
experimental
observation.
Resources
access all ALEX
resources aligned
to this standard.

ALEX
Resources
Grade 7
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
likely based on the
observed frequencies?
Franklin County Schools
Evidence of Student
Attainment
Teacher
Vocabulary
Knowledge
Skills
Understanding
Resources
Grade 7
CCRS Standard
Mathematics CCRS Standards and Alabama COS
Standard ID
24. Find probabilities of
compound events using
organized lists, tables,
tree diagrams, and
simulation.
Statistics &
Probability
Investigate
chance
processes and
develop, use,
a. Understand that, just and evaluate
probability
as with simple events,
models.
the probability of a
compound event is the 7.SP.8
fraction of outcomes in
the sample space for
which the compound
event occurs.
b. Represent sample
spaces 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.
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?
Franklin County Schools
Evidence of Student
Attainment
Teacher
Vocabulary
Probability
Students:
Given the description of a
compound event, (e.g.,
Compound event
rolling a sum of seven
with two dice),
Tree diagram
Use models, (e.g.,
organized lists, tables,
tree diagrams, and
simulations) to find and
explain the possible
outcomes in the event
and find the probability
of each outcome.
Given a contextual or
mathematical situation
involving probability
related to a compound
event,
Develop a simulation
and data collection
process, collect and
organize the relevant
data, and use the longrun relative frequency to
justify an approximation
of the probability of the
event and an answer to
the original question.
Sample space
Knowledge
Students know:
Methods for
modeling
compound events,
(e.g., organized
lists, tables, tree
diagrams,
simulation),
Skills
Understanding
Resources
Students will be able Students
to:
understand that:
Calculate
The observed
probability of a
relative frequency
specific outcome of a of a particular
compound event,
outcome of a
chance event,
Strategically use including
models of compound compound events,
Methods for
events to determine approximates the
calculating and/or the possible outcomes theoretical
probability of that
expressing relative and their
outcome in any
frequency,
probabilities,
random occurrence
of the event,
Methods for
Use mathematical
calculating
vocabulary to justify
Click below to
probability from
solutions and solution As the number access all ALEX
of observations of a resources aligned
models of
paths for solving
chance event gets to this standard.
probability for
problems involving
large, the relative
compound events. the probability of
frequency of
specific events in a
 ALEX
occurrence of any
compound event,
Resources
particular outcome
tends to more
Set up and
closely match the
conduct simulations
theoretical
that model particular
probability of that
chance events and
outcome.
use the data from the
simulation to
approximate
probabilities
associated with the
chance event.
Grade 7
Franklin County Schools
Mathematics CCRS Standards and Alabama COS