Transcript Mathematics Building Mathematical Foundations

Domains of Study/Conceptual Categories
Learning Progressions/Trajectories
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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
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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.
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Grade
Course
Domain
Cluster
Standard
K-8
Conceptual Category
Domain
Cluster
Standard
9-12
 Domain
 Cluster
 Standards
Domain:
Overarching “big ideas” that connect
content across the grade levels.
Cluster:
Group of related standards below a
domain.
Standards: Define what a student should
know
(understand) and do at the conclusion of a
course or grade.
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Overarching big ideas that connect
mathematics across high school
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Illustrate progression of increasing
complexity
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May appear in all courses
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Organize high school standards
Number &
Quantity
Algebra
Functions
The Real
Number
System
Seeing
Structure in
Expressions
Interpreting
Functions
Quantities
Arithmetic
with
Polynomials
& Rational
Expressions
Building
Functions
The Complex
Number
System
Creating
Equations
Linear,
Quadratic and
Exponential
Models
Vector and
Matrix
Quantities
Reasoning
with
Equations
and
Inequalities
Trigonometric
Functions
Modeling
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
(★).
Geometry
Statistics &
Probability
Congruence
Interpreting
Categorical and
Quantitative
Data
Similarity,
Right
Triangles, and
Trigonometry
Making
Inferences and
Justifying
Conclusions
Circles
Conditional
Probability and
the Rules of
Probability
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
Grade to Grade
9-12 Cluster
Algebra I
Interpret the structure of expressions.
(Linear, exponential, quadratic.)
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]
Algebra II with Trigonometry
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]
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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.
Modeling
Geometry
Number Functions
&
Quantity
Algebra
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.
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
1
2
3
4
5
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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 Proof
Confrey (2007)
“Developing sequenced obstacles and challenges for
students…absent the insights about 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
Number and Operations –
Fractions
Ratios and Proportional
Relationships
The Number System
Number and
Quantity
Expressions and Equations
Algebra
Operations and Algebraic Thinking
Functions
Geometry
Measurement and Data
Functions
Geometry
Statistics and Probability
Statistics and
Probability
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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
The Number System
Number and Operations –
Fractions
Number and
Quantity
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Beginning at the lowest grade examine the domain and
conceptual category, cluster and standards at your grade level
- 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.
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Summary and/or representation of how the
concept of the use of numbers grows
throughout your grade band.
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.
Read the posters for your grade band.
 Discuss similarities and differences
between the posters.
 Establish a clear vision for your grade
band.
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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?
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Know what to expect about students’ preparation.
More readily manage the range of preparation of
students in your class.
Know what teachers in the next grade expect of
your students.
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
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ALSDE Office of Student Learning
Curriculum and Instruction
Cindy Freeman, Mathematics Specialist
 Phone: 334.353.5321
E-mail: [email protected]