2011 NYS P-12 Common Core
Learning Standards in
Mathematics
Please visit www.engageNY.org for additional
information regarding the Common Core Learning
Standards
NYS Mathematics
Common Core
Learning Standards
Common Core Learning Standards
Instructional Shifts . . .
Instructional Shifts . . .
Instructional Shifts in Mathematics
Shift 1 Focus
Teachers use the power of the eraser and
significantly narrow and deepen the scope of
how time and energy is spent in the math
classroom. They do so in order to focus deeply
on only the concepts that are prioritized in
the standards so that students reach strong
foundational knowledge and deep conceptual
understanding and are able to transfer
mathematical skills and understanding across
concepts and grades.
Shift 2 Coherence
Principals and teachers carefully connect the
learning within and across grades so that, for
example, fractions or multiplication spiral
across grade levels and students can build
new understanding onto foundations built in
previous years. Teachers can begin to count on
deep conceptual understanding of core
content and build on it. Each standard is not a
new event, but an extension of previous
learning.
Shift 3 Fluency
Students are expected to have speed and
accuracy with simple calculations; teachers
structure class time and/or homework time
for students to memorize, through repetition,
core functions (found in the attached list of
fluencies) such as multiplication tables so that
they are more able to understand and
manipulate more complex concepts.
Shift 4 Deep Understanding
Teachers teach more than “how to get the
answer” and instead support students’ ability
to access concepts from a number of
perspectives so that students are able to see
math as more than a set of mnemonics or
discrete procedures. Students demonstrate
deep conceptual understanding of core math
concepts by applying them to new situations.
as well as writing and speaking about their
understanding.
Shift 5 Applications
Students are expected to use math and choose
the appropriate concept for application even
when they are not prompted to do so.
Teachers provide opportunities at all grade
levels for students to apply math concepts in
“real world” situations. Teachers in content
areas outside of math, particularly science,
ensure that students are using math – at all
grade levels – to make meaning of and access
content.
Shift 6 Dual Intensity
Students are practicing and understanding. There is
more than a balance between these two things in
the classroom – both are occurring with intensity.
Teachers create opportunities for students to
participate in “drills” and make use of those skills
through extended application of math concepts. The
amount of time and energy spent practicing and
understanding learning environments is driven by
the specific mathematical concept and therefore,
varies throughout the given school year.
Standards for Mathematical Practice
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
Content Standards
The content standards are organized by
domains across grade levels and each grade
level begins with a narrative description of
the grade level, followed by the standards
for mathematical practice, a list of the “Big
Ideas” for the specific grade level, and then
the content standards by domain.
How to read the grade level standards in Mathematics
Standards define what students should understand and be able to do.
Clusters summarize groups of related standards. Note that standards from different clusters may sometimes be
closely related, because mathematics is a connected subject.
Domains are larger groups of related standards. Standards from different domains may sometimes be closely
related.
These Standards do not dictate curriculum or teaching methods. For example, just because topic A appears before
topic B in the standards for a given grade, it does not necessarily mean that topic A must be taught before topic B. A
teacher might prefer to teach topic B before topic A, or might choose to highlight connections by teaching topic A
and topic B at the same time. Or, a teacher might prefer to teach a topic of his or her own choosing that leads, as a
byproduct, to students reaching the standards for topics A and B.
What students can learn at any particular grade level depends upon what they have learned before. Ideally then, each
standard in this document might have been phrased in the form, “Students who already know A should next come to
learn B.” But at present this approach is unrealistic—not least because existing education research cannot specify all
such learning pathways. Of necessity therefore, grade placements for specific topics have been made on the basis of
state and international comparisons and the collective experience and collective professional judgment of educators,
researchers and mathematicians. One promise of common state standards is that over time they will allow research
on learning progressions to inform and improve the design of standards to a much greater extent than is possible
today. Learning opportunities will continue to vary across schools and school systems, and educators should make
every effort to meet the needs of individual students based on their current understanding.
These Standards are not intended to be new names for old ways of doing business. They are a call to take the next
step. It is time for states to work together to build on lessons learned from two decades of standards based reforms. It
Progressions
Because progressions are so important in the
Standards, suggestions for places to begin are
not a laundry list of topics but rather a menu
of progressions. Experts recommend
organizing implementation work according to
progressions because the instructional
approach to any given topic should be
informed by its place in an overall flow of
ideas.
Progressions
They emphasize the word menu. If a curriculum
provider delivers a single coherent progression
of materials to a district, then that provider
has added value. If a math coach helps
elementary school teachers in a district better
understand a single coherent progression,
then that coach has added value. The
quantum of improvement is not the textbook
series.
Progressions
• Counting and Cardinality and Operations and Algebraic
Thinking: grades K–2
• Operations and Algebraic Thinking: multiplication and division
in grades 3–5, tracing the evolving meaning of multiplication,
from equal-groups thinking with whole numbers in grade 3 to
scaling-oriented thinking with fractions in grade 5.
• Number and Operations—Base Ten: addition and subtraction
in grades 1–4
• Number and Operations—Base Ten: multiplication and
division in grades 3–6
• Number and Operations—Fractions: fraction addition and
subtraction in grades 4–5, including parallel development of
fraction equivalence in grades 3–5
Progressions
• Number and Operations—Fractions: fraction multiplication
and division in grades 4–6
• The Number System: grades 6–7
• Expressions and Equations: grades 6–8, including how this
extends prior work in arithmetic
• Ratio and Proportional Reasoning: its development in grades
6–7, its relationship to functional thinking in grades 6–8, and
its connection to lines and linear equations in grade 8
• Geometry: work with the coordinate plane in grades 5–8,
including connections to ratio, proportion, algebra and
functions in grades 6–HS
• Geometry: congruence and similarity of figures in grades 8–
HS, with emphasis on real-world and mathematical problems
involving scales and connections to ratio and proportion
Progressions
• Modeling with equations and inequalities in high school,
development from simple modeling tasks such as word
problems to richer more open-ended modeling tasks
• Seeing Structure in Expressions, from expressions appropriate
to 8th–9th grade to expressions appropriate to 10th–11th
grade
• Statistics and Probability: comparing populations and drawing
inferences in grades 6–HS.
• Additionally, one of the important ―invisible themes in the
Standards involves units as a cross-cutting theme in the areas
of measurement, geometric measurement, base-ten
arithmetic, unit fractions, and fraction arithmetic, including
the role of the number line.
Summarized Objectives in Mathematics
for the Next Six Months are:
Materials:
– Focus
– Clear indication of fewer concepts at each grade level represented by
curriculum documents, district formative assessments
• Teachers:
– Identify focus areas and fluencies of grade level
– Shift in time spent on areas of in-depth instruction
• Students:
– Demonstrated fluency and understanding
– Display fluencies for the grade level and understand focus areas
Assessments . . .
• Spring 2012 NYS Grades 3-8 Assessments will focus on
the 2005 NYS Core Curriculums in ELA and mathematics
• Spring 2013 the NYS Grades 3-8 Assessments will focus
on the 2011 Common Core Learning Standards in ELA
and mathematics
• Spring 2015 PARCC Assessments (Grades 3-8 and High
School) administered for the first time
Questions . . .
Jane Landry
landry_jane@cves.org
Teri Calabrese-Gray
Gray_teri@cves.org