CCSSI FOR MATHEMATICS
“STANDARDS OF PRACTICE”
Collegial Conversations
GRADES K – 1
Today’s Goal
 To explore the Standards for Content and
Practice for Mathematics
 Begin to consider how these new Standards
are likely to impact your classroom practices
What are the Common Core State
Standards?
 Aligned with college and work expectations
 Focused and coherent
 Included rigorous content and application of
knowledge through high-order skills
 Build upon strengths and lessons of current state
standards
 Internationally benchmarked so that all students are
prepared to succeed in our global economy and society
 Research and evidence based
 State led- coordinated by NGA Center and CCSSO
Focus
• Key ideas, understandings, and skills are
identified
• Deep learning of concepts is emphasized
– That is, time is spent on a topic and on learning it
well. This counters the “mile wide, inch deep”
criticism leveled at most current U.S. standards.
Benefits for States and Districts
•
•
•
•
Allows collaborative professional development based on best
practices
Allows development of common assessments and other tools
Enables comparison of policies and achievement across
states and districts
Creates potential for collaborative groups to get more
economical mileage for:
– Curriculum development, assessment, and professional
development
Common Core Development
• Initially 48 states and three territories signed
on
• As of November 29, 2010, 42 states have
officially adopted
• Final Standards released June 2, 2010, at
www.corestandards.org
• Adoption required for Race to the Top funds
Michigan’s Implementation Timeline
• Held October and November of 2010 rollouts
• District curricula and assessments that provide a
K-12 progression for meeting the MMC
requirements will require minimal adjustments to
meet CCSS
• Curriculum and assessment alignment in SY10-11
• Implementation SY11-12
• New assessment 2014-15 (Smarter Balanced
Assessment Consortium or SBAC – replaces MEAP
and MME)
Background
Responsibilities of States in the Consortium
Each State that is a member of the Consortium in 2014–
2015 also agrees to do the following:
 Adopt common achievement standards no later than the 2014–2015 school
year,
 Fully implement the Consortium summative assessment in grades 3–8 and
high school for both mathematics and English language arts no later than
the 2014–2015 school year,
 Adhere to the governance requirements,
 Agree to support the decisions of the Consortium,
 Agree to follow agreed-upon timelines,
 Be willing to participate in the decision-making process and, if a Governing
State, final decisions, and
 Identify and implement a plan to address barriers in State law, statute,
regulation, or policy to implementing the proposed assessment system and
address any such barriers prior to full implementation of the summative
assessment components of the system.
Technology Approach
SBAC Item Bank
• Partitioned into a secure item bank for
summative assessments and a non-secure
bank for the interim/benchmark assessments:
•
•
•
•
Traditional selected-response items
Constructed-response items
Curriculum-embedded performance events
Technology-enhanced items (modeled after
assessments in use by the U.S. military, the
architecture licensure exam, and NAEP)
HOW TO READ THE GRADE LEVEL
STANDARDS
Domains are large groups of related
standards. Standards from different
domains may sometimes be closely
related. Look for the name with the code
number on it for a Domain.
Common Core Format
Clusters are groups of related standards.
Standards from different clusters may
sometimes be closely related, because
mathematics is a connected subject.
• Clusters appear inside domains.
Common Core Format
Standards define what students should be
able to understand and be able to do –
part of a cluster.
•They are content statements. An example content
statement is: “Count to 100 by ones and by tens”,
K.CC.1. The “CC” stands for “Counting and Cardinality”. Please refer to page
three in your grade level appropriate Common Core document.
•Progressions of increasing complexity from grade to
grade
Common Core - Clusters
• May appear in multiple grade levels in the K-8
Common Core. There is increasing development
as the grade levels progress
• What students should know and be able to do
at each grade level
• Reflect both mathematical understandings and
skills, which are equally important
Common Core Format
K-8
High School
Grade
Conceptual Category
Domain
Domain
Cluster
Cluster
Standards
(There are no preK Common Core Standards)
Standards
Format of K-8 Standards
Grade Level
Domain
Format of K-8 Standards
Standard
Cluster
Standard
Cluster
Mathematics » Kindergarten » Introduction
In Kindergarten, instructional time should focus on two critical areas: (1) representing and comparing
whole numbers, initially with sets of objects; (2) describing shapes and space. More learning time in
Kindergarten should be devoted to number than to other topics.
1. Students use numbers, including written numerals, to represent quantities and to solve
quantitative problems, such as counting objects in a set; counting out a given number of objects;
comparing sets or numerals; and modeling simple joining and separating situations with sets of
objects, or eventually with equations such as 5 + 2 = 7 and 7 – 2 = 5. (Kindergarten students
should see addition and subtraction equations, and student writing of equations in kindergarten
is encouraged, but it is not required.) Students choose, combine, and apply effective strategies
for answering quantitative questions, including quickly recognizing the cardinalities of small sets
of objects, counting and producing sets of given sizes, counting the number of objects in
combined sets, or counting the number of objects that remain in a set after some are taken
away.
2. Students describe their physical world using geometric ideas (e.g., shape, orientation, spatial
relations) and vocabulary. They identify, name, and describe basic two-dimensional shapes, such
as squares, triangles, circles, rectangles, and hexagons, presented in a variety of ways (e.g., with
different sizes and orientations), as well as three-dimensional shapes such as cubes, cones,
cylinders, and spheres. They use basic shapes and spatial reasoning to model objects in their
environment and to construct more complex shapes.
Mathematics » Grade 1 » Introduction
In Grade 1, instructional time should focus on four critical areas: (1) developing understanding of addition, subtraction, and
strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value,
including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating
length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes.
1. Students develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. They
use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to
model add-to, take-from, put-together, take-apart, and compare situations to develop meaning for the operations of
addition and subtraction, and to develop strategies to solve arithmetic problems with these operations. Students
understand connections between counting and addition and subtraction (e.g., adding two is the same as counting on two).
They use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on
these properties (e.g., “making tens”) to solve addition and subtraction problems within 20. By comparing a variety of
solution strategies, children build their understanding of the relationship between addition and subtraction.
2. Students develop, discuss, and use efficient, accurate, and generalizable methods to add within 100 and subtract multiples
of 10. They compare whole numbers (at least to 100) to develop understanding of and solve problems involving their
relative sizes. They think of whole numbers between 10 and 100 in terms of tens and ones (especially recognizing the
numbers 11 to 19 as composed of a ten and some ones). Through activities that build number sense, they understand the
order of the counting numbers and their relative magnitudes.
3. Students develop an understanding of the meaning and processes of measurement, including underlying concepts such as
iterating (the mental activity of building up the length of an object with equal-sized units) and the transitivity principle for
indirect measurement.1
4. Students compose and decompose plane or solid figures (e.g., put two triangles together to make a quadrilateral) and build
understanding of part-whole relationships as well as the properties of the original and composite shapes. As they combine
shapes, they recognize them from different perspectives and orientations, describe their geometric attributes, and
determine how they are alike and different, to develop the background for measurement and for initial understandings of
properties such as congruence and symmetry.
K – 5 DOMAINS
Domains
Grade Levels
Counting and Cardinality
K only
Operations and Algebraic
Thinking
1-5
Number and Operations in
Base Ten
1-5
Number and Operations Fractions
3-5
Measurement and Data
1-5
Geometry
1-5
MIDDLE GRADES DOMAINS
Domains
Grade Levels
Ratio and Proportional
Relationships
6-7
The Number System
6-8
Expressions and Equations
6-8
Functions
8
Geometry
6-8
Statistics and Probability
6-8
Michigan GLCE vs. CCSS
Grade
Topic
Whole Number: Meaning
Whole Number: Operations
Measurement Units
Common Fractions
Equations & Formulas
Data Representation & Analysis
2-D Geometry: Basics
2-D Geometry: Polygons & Circles
Measurement: Perimeter, Area & Volume
Rounding & Significant Figures
Estimating Computations
Whole Numbers: Properties of Operations
Estimating Quantity & Size
Decimal Fractions
Relation of Common & Decimal Fractions
Properties of Common & Decimal Fractions
Percentages
Proportionality Concepts
Proportionality Problems
2-D Geometry: Coordinate Geometry
Geometry: Transformations
Negative Numbers, Integers, & Their Properties
Number Theory
Exponents, Roots & Radicals
Exponents and Orders of Magnitude
Measurement: Estimation & Errors
Constructions Using Straightedge & Compass
3-D Geometry
Geometry: Congruence & Similarity
Rational Numbers & Their Properties
Patterns, Relations & Functions
Proportionality: Slope & Trigonometry
Uncertainty & Probability
Real Numbers: Their Subsets & Properties
Topic intended in Michigan GLCE
Topic intended in CCSS
1
2
3
4
5
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
7
8
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
6
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
MAJOR SHIFTS K - 5
Numeration and operation intensified, and introduced
earlier
•Early place value foundations in Kindergarten
•Regrouping as composing/decomposing in Grade 2
•Decimals to hundredths in Grade 4
All three types of measurement simultaneously
•Non-standard, English and metric
Emphasis on fractions as numbers
Emphasis on number line as visualization/structure
Observations About Place Value
and Base Ten in the Early Grades
•Kindergarten
Foundation in bundling
Emphasis on the teen numbers
•Grade 1
•Extends to 10, 20, 30…
•Learn to compare
•Grade 2
•Extend to 100 as a bundle of ten 10s
•Extend to 100, 200, 300…
•Expanded notation and comparison
HOW IS THERE LESS?
•Backed off of algebraic patterns K – 5
•Backed off of statistics and probability in
K–5
•Delayed content like percent and ratios
and proportions
THE REASON
WHY WE ARE HERE
TODAY!
CCSSM
Mathematical
Practices
The Common Core proposes a set of
Mathematical Practices that all teachers should
develop in their students. These practices are
similar to NCTM’s Mathematical Processes from
the Principles and Standards for School
Mathematics.
Design and Organization
Mathematical Practice – expertise students
should acquire: (Processes & proficiencies)
• NCTM five process standards:
•
•
•
•
•
Problem solving
Reasoning and Proof
Communication
Connections
Representations
NCTM Process Standards and the
CCSS Mathematical Practice Standards
NCTM Process Standards
CCSS Mathematical Practices
Problem Solving
Make sense of problems and persevere
in solving them.
Use appropriate tools strategically
Reasoning and Proof
Reason abstractly and quantitatively.
Critique the reasoning of others.
Look for and express regularity in
repeated reasoning
Communication
Construct viable arguments
Connections
Attend to precision.
Look for and make use of structure
Representations
Model with mathematics.
Design and Organization
• Mathematical proficiency (National Research
Council’s report Adding It Up)
– Adaptive reasoning
– Strategic competence
– Conceptual understanding (comprehension of
mathematical concepts, operations, relations)
– Procedural fluency (skill in carrying out procedures flexibly,
accurately, efficiently, and appropriately)
– Productive disposition (ability to see mathematics as
sensible, useful, and worthwhile
Mathematics/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
Mathematics/Standards for Mathematical Practice
“The Standards for Mathematical Practice describe varieties of expertise that
mathematics educators at all levels should seek to develop in their students.
These practices rest on important “processes and proficiencies” with
longstanding importance in mathematics education.” CCSS, 2010
Standards for Mathematical Practice
• Carry across all grade levels
• Describe habits of a mathematically expert student
Standards for Mathematical Content
•
•
•
•
K-8 presented by grade level
Organized into domains that progress over several grades
Grade introductions give 2-4 focal points at each grade level
High school standards presented by conceptual theme (Number &
Quantity, Algebra, Functions, Modeling, Geometry, Statistics & Probability
Standards of Mathematical Practice
1. Choose a partner at your table and “Pair Share” the
Standards of Practice between you and your partner.
2. When you and your partner feel you understand
generally each of the standards, discuss the following
question:
What implications might the standards
of practice have on your classroom?
Transition from Current State Standards & Assessments
to New Common Core Standards
•
•
•
•
•
Develop Awareness
Needs Assessment/Gap Analysis
Planning
Capacity Building
Job-embedded Professional Development
Transition Planning
Next Steps:
• Alignment of CCSS with curriculum
• Gap analysis (content and skills that vary from
the MEAP and MME)
• What instructional practices will facilitate the
transition?
• What new assessment strategies will be
needed?
• Professional development needs?
Transition Planning
• Gather in teams from your schools and discuss
– What are your immediate needs as a classroom teacher
being asked to implement the CCSS?
– What professional development is needed?
– What initial gaps come to mind and how do you address
these gaps?
– As a school team, look at the eight Standards for
Mathematical Practice. What do they look like? Sound
like? What will students need in order to implement them?
What will teachers need? What are the implications for
assessment and grading?
Select a recorder, time keeper and someone to report out for
your group.
Questions?
Please contact:
PUT YOUR INFORMATION
HERE!
Have a great day!