# Domains of Study/Conceptual Categories Learning Progressions/Trajectories

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13 Δεκ 2013 (πριν από 4 χρόνια και 7 μήνες)

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Domains of Study/Conceptual Categories

Learning Progressions/Trajectories

Aligned with college and work expectations

Written in a clear, understandable, and consistent
format

Designed to include rigorous content and
application of knowledge through high
-
order skills

Formulated upon strengths and lessons of current
state standards

Informed by high
-
performing mathematics
curricula in other countries to ensure all students
are prepared to succeed in our global economy and
society

Grounded on sound evidence
-
based research

Coherent

Rigorous

Well
-
Articulated

Enables Students to Make Connections

Articulated progressions of topics and
performances that are developmental
and connected to other progressions.

Conceptual understanding and
procedural skills stressed equally.

Real
-
world/Situational application
expected.

Key ideas, understandings, and skills
are identified.

Deep learning stressed.

K
-
8

9
-
12

Domain

Cluster

Standard

Course

Conceptual
Category

Domain

Cluster

Standard

Domain

Cluster

Standards

Domain:

Overarching
“big ideas” that connect

Cluster:

Group
of related standards
below a
domain.

Standards:

Define what a student should know
(understand) and do at
the
conclusion of a

Overarching big ideas that connect
mathematics across high school

Illustrate progression of increasing
complexity

May appear in all courses

Organize high school standards

Number &
Quantity

Algebra

Functions

Modeling

Geometry

Statistics &
Probability

The Real
Number
System

Seeing
Structure in
Expressions

Interpreting
Functions

Modeling is
best
interpreted
not as a
collection of
isolated

topics but
rather in
relation to
other
standards.
Making
mathematical
models is

a Standard
for
Mathematical
Practice, and
specific
modeling
standards
appear

throughout
the high
school
standards
indicated by a
star symbol
(

).

Congruence

Interpreting
Categorical and
Quantitative

Data

Quantities

Arithmetic
with

Polynomials
& Rational
Expressions

Building
Functions

Similarity,
Right
Triangles, and
Trigonometry

Making
Inferences

and
Justifying
Conclusions

The Complex
Number
System

Creating
Equations

Linear,
Exponential
Models

Circles

Conditional
Probability and
the Rules of
Probability

Vector and
Matrix
Quantities

Reasoning
with
Equations
and
Inequalities

Trigonometric
Functions

Expressing
Geometric

Properties with
Equations

Using Probability

to Make
Decisions

Geometric
Measurement
and Dimension

Modeling with
Geometry

Multiple Courses

Illustrate Progression of
Increasing Complexity from

Algebra I

Algebra II with Trigonometry

Interpret the structure of expressions.

7. Interpret expressions that represent
a

quantity in
terms of its context.*

[A
-
SSE1
]

a.
Interpret parts of an expression such as
terms, factors, and coefficients. [A
-
SSE1a]

b.
Interpret complicated expressions by
viewing one or more of their parts as a
single entity. [A
-
SSE1b]

8. Use the structure of an expression to

identify ways
to rewrite it. [A
-
SSE2]

Interpret the structure of expressions.
(Polynomial and rational.)

6. Interpret expressions that represent
a

quantity

in terms of its context.*

[
A
-
SSE1]

a.
Interpret parts of an expression such as
terms, factors, and coefficients.

[
A
-
SSE1a]

a.
Interpret complicated expressions by
viewing one or more of their parts as a
single entity. [A
-
SSE1b]

7. Use the structure of an expression
to

identify
ways
to rewrite it. [A
-
SSE2]

9
-
12 Cluster

Content standards in this document contain
minimum required content.

Each content standard completes the phrase

Students will.”

Reflect both mathematical understandings
and skills, which are equally important.

Geometry

Modeling

Algebra

Functions

Number

&

Quantity

Statistics

&

Probability

3.
Explain why the sum or product of two rational numbers is rational;
that
the sum of a rational number and an irrational number is
irrational; and that the product of a nonzero rational number and an
irrational number is irrational. [N
-
RN3]

AI.3.1.

Explain why the
sum of
two rational numbers is rational.

AI.3.2.

Explain why the product of two rational numbers is rational.

AI.3.3.

Explain
that the sum of a rational number and an
irrational
number
is
irrational
.

AI.3.4.

Explain
that the product of a nonzero rational number and an
irrational
number is irrational.

K

1

2

3

4

5

6

7

8

Counting and Cardinality

Operations and Algebraic Thinking

Number and Operations in Base Ten

Measurement and Data

Geometry

Number and Operations: Fractions

Ratios and Proportional Reasoning

The Number System

Expressions and Equations

Statistics and Probability

Functions

K
-
2

Number
and
number
sense.

3
-
5

Operations
and Properties

(Number and
Geometry)

Fractions

6
-
8

Algebraic and
Geometric
Thinking

Data Analysis
and using
Properties

High
School

Functions,
Statistics,
Modeling
and Proo
f

Confrey (2007)

“Developing sequenced obstacles and challenges for
meaning

that derive
from careful study of learning, would be unfortunate and
unwise.”

CCSS, p. 4

“…
the development of these Standards began with
research
-
based learning progressions

detailing what is
known today about how students’ mathematical
knowledge, skill,
and understanding
develop over time.”

K

1

2

3

4

5

6

7

8

HS

Counting and
Cardinality

Number and Operations in Base Ten

Ratios and Proportional
Relationships

Number and
Quantity

Number and Operations

Fractions

The Number System

Operations and Algebraic Thinking

Expressions and Equations

Algebra

Functions

Functions

Geometry

Geometry

Measurement and Data

Statistics and Probability

Statistics and
Probability

Domains provide common learning
progressions.

Curriculum and teaching methods are
not dictated.

Standards are not presented in a
specific instructional order.

Standards should be presented in a
manner that is consistent with local
collaboration.

K

1

2

3

4

5

6

7

8

HS

Counting and
Cardinality

Number and Operations in Base Ten

Ratios and Proportional
Relationships

Number and
Quantity

Number and Operations

Fractions

The Number System

Beginning at the lowest grade examine the domain and
-

identify how
the use of numbers and number systems
change
from K
-

12.

K
-
2

-

Counting & Cardinality (CC)

Number and Operations in Base Ten (NBT)

3
-
5

-

Number and Operations in Base Ten (NBT)

Number and Operations

Fractions (NF)

6
-
8

-

The Number System (NS)

9
-
12

-

Number and Quantity (N)

Look at the grade level above and grade level below (to see the
context).

Make notes that reflect a logical progression, increasing
complexity.

As a table group share a vertical progression (bottom

up or
top
-
down) on chart paper.

Summary and/or representation of how the
concept of the use of numbers grows

Easy for others to interpret or understand.

Visual large enough for all to see.

More than just the letters and numbers of
the standards

include key words or
phrases.

Display posters side
-
by
-
side and in
order on the wall.

Begin at the grade band you studied.

Discuss similarities and differences
between the posters.

band.

As a table group, consider your
journey through the 2010 ACOS as
you studied the concept of the use of
numbers K
-
12.

What did you learn?

What surprised you?

What questions do you still have?

Know what to expect about students’ preparation.

More readily manage the range of preparation of

Know what teachers in the next grade expect of

Identify clusters of related concepts at grade level.

Clarity about the student thinking and discourse
to focus on conceptual development.

Engage in rich uses of classroom assessment.

2003 ACOS

2010 ACOS

Contains bullets

Does not contain bullets

Does not contain

a glossary

Contains a glossary

.

.

.

.

.

.

ALSDE Office of Student Learning

Curriculum and
Instruction

Cindy Freeman, Mathematics Specialist

Phone: 334.353.5321

E
-
mail:
cfreeman@alsde.edu