7th Grade Mathematics Standards & Assessment Framework
Colorado Academic Standards 7th Grade Level Expectations:
Number Sense, 1. Proportional reasoning involves comparisons and multiplicative
Properties, and
relationships among rates. (CCSS Focus 1)
Operations
2. Formulate, represent, and use algorithms with rational numbers flexibly,
accurately, and efficiently. (CCSS Focus 2)
Patterns,
Functions, and
Algebraic
Structures
Data Analysis,
Statistics, and
Probability
Shape,
Dimension,
and Geometric
Relationships
1. Properties of arithmetic can be used to generate equivalent expressions.
2. Equations and expressions model quantitative relationships and
phenomena. (CCSS Focus 2)
1. Statistics can be used to gain information about populations by examining
samples. (CCSS Focus 4)
2. Mathematical models are used to determine probability.
1. Modeling geometric figures and relationships leads to informal spatial
reasoning and proof. (CCSS Focus 3)
2. Linear measure, angle measure, area, and volume are fundamentally
different and require different units of measure. (CCSS Focus 3)
Math Practice Standards
1. Make sense of problems and
persevere in solving them.
2. Reason abstractly and
quantitatively.
3. Construct viable arguments
and critique the reasoning of
others.
4. Model with mathematics
5. Use appropriate tools
strategically.
6. Attend to precision.
7. Look for and make use of
structure.
8. Look for and express
regularity in repeated
reasoning.
Common Core State Standards (CCSS)
Areas of Instructional Focus:
1. Developing understanding of and
applying proportional relationships.
2. Developing understanding of operations
with rational numbers and working with
expressions and linear equations.
3. Solving problems involving scale
drawings and informal geometric
constructions, and working with twoand three- dimensional shapes to solve
problems involving area, surface area,
and volume.
4. Drawing inferences about populations
based on samples.
PARCC Assessment Framework:
Sub-Claim A:
Major Content



Proportional
Relationships
(CCSS Focus 1)
Operations with
Fractions
(CCSS Focus 2)
Expressions,
Equations, and
Inequalities
(CCSS Focus 2)
Sub-Claim B:
Supporting Content




Representing
Geometric Figures
(CCSS Focus 3)
Drawings and
Measurement
(CCSS Focus 3)
Random Sampling
and Comparative
Inferences
(CCSS Focus 4)
Chance Processes
and Probability
Models
Sub-Claim C:
Practice Standards
3&6
 Properties of
Operations
 Concrete Referents
and Diagrams
 Distinguish Correct
Explanation/
Reasoning from that
which is Flawed
Sub-Claim D:
Practice Standard 4
(may include 1, 2, 5, 7, & 8)

Modeling
Grade 5
Grade 6
Grade 7
Ratios and
Proportional
Reasoning
The concepts of multiplication and
division can be applied to multiply
and divide fractions.
Quantities can be
expressed and
compared using ratios
and rates. (CCSS Focus)
Operations
and
Algorithmic
Thinking
Formulate, represent, and use
algorithms with multi-digit whole
numbers and decimals with
flexibility, accuracy, and
efficiency. (CCSS Focus)
Formulate, represent, and use
algorithms to add and subtract
fractions with flexibility, accuracy,
and efficiency. (CCSS Focus)
The decimal number system
describes place value patterns and
relationships that are repeated in
large and small numbers and
forms the foundation for efficient
algorithms. (CCSS Focus)
Formulate, represent,
and use algorithms
with positive rational
numbers with
flexibility, accuracy,
and efficiency. (CCSS
Focus)
Proportional reasoning
involves comparisons and
multiplicative
relationships among
ratios. (CCSS Focus)
Formulate, represent, and
use algorithms with
rational numbers flexibly,
accurately, and efficiently.
(CCSS Focus)
Number Patterns are based on
operations and relationships.
Algebraic expressions
can be used to
generalize properties of
arithmetic. (CCSS
Focus)
Variables are used to
represent unknown
quantities within
equations and
inequalities. (CCSS
Focus)
Visual displays and
summary statistics of
one-variable data
condense the
information in data
sets into usable
knowledge. (CCSS
Focus)
Statistics can be used to
gain information about
populations by examining
samples. (CCSS Focus)
The Number
System
Expression
and Equation
Properties
Functions
and Modeling
Statistics
Visual displays are used to
interpret data.
Grade 8
High School
In the real number system, rational and
irrational numbers are in one to one
correspondence to points on the
number line.
The complex number system includes real numbers and
imaginary numbers.
Properties of arithmetic
can be used to generate
equivalent expressions.
Properties of algebra and equality are
used to solve linear equations and
systems of equations. (CCSS Focus)
Equations and expressions
model quantitative
relationships and
phenomena. (CCSS Focus)
Linear functions model situations with
a constant rate of change and can be
represented numerically, algebraically,
and graphically. (CCSS Focus)
Graphs, tables and equations can be
used to distinguish between linear and
nonlinear functions. (CCSS Focus)
Expressions can be represented in multiple, equivalent
forms. (PARCC Math I Focus)
Solutions to equations, inequalities and systems of
equations are found using a variety of tools. (PARCC Math I
Focus)
Functions model situations where one quantity determines
another and can be represented algebraically, graphically,
and using tables. (PARCC Math I Focus)
In the real number
system, rational
numbers have a unique
location on the number
line and in space. (CCSS
Focus)
Visual displays and summary statistics of
two-variable data condense the
information in data sets into usable
knowledge.
Mathematical models are
used to determine
probability
Probability
Geometric
Measurements
Properties of multiplication and
addition provide the foundation
for volume, an attribute of solids.
(CCSS Focus)
Geometric
Relationships
Geometric figures can be described
by their attributes and specific
locations in the plane.
Objects in space and
their parts and
attributes can be
measured and analyzed.
Quantitative reasoning is used to make sense of quantities
and their relationships in problem situations.
Quantitative relationships in the real world can be modeled
and solved using functions.
Visual displays and summary statistics condense the
information in data sets into usable knowledge. (PARCC
Math I Focus)
Statistical methods take variability into account supporting
informed decision making through quantitative studies
designed to answer specific questions.
Probability models outcomes for situations in which there is
inherent randomness.
Linear measure, angle
measure, area, and
volume are fundamentally
different and require
different units of
measure. (CCSS Focus)
Direct and indirect measurements can
be used to define the concepts of
congruence and similarity. (CCSS Focus)
Modeling geometric
figures and relationships
leads to informal spatial
reasoning and proof.
(CCSS Focus)
Transformations of objects can be used
to define the concepts of congruence
and similarity. (CCSS Focus)
Objects in the plane can be described and analyzed
algebraically.
Attributes of two-and three-dimensional objects are
measurable and can be quantified.
Objects in the real world can be modeled using geometric
concepts.
Objects in the plane can be transformed, and those
transformations can be described and analyzed
mathematically. (PARCC Math I Focus)
Concepts of similarity are foundational to geometry and its
applications.