Transcript NCSM Fall 2010: Connecting to The Common Core State Standards

Essential, Immediate Actions to
Implement the Common Core
State Standards for Mathematics
Grades 3 - 5
Diane J. Briars
NCSM Immediate Past President
Mathematics Education Consultant
[email protected]
October 20, 2011
2011 NCTM Regional Conference and Exposition
Atlantic City, NJ
FYI
Presentation slides will be posted on the
NCSM website:
mathedleadership.org
or
email me at
[email protected]
Briars, June 2011
Today’s Goals
• Examine critical differences between
CCSS and current practice.
• Consider how the CCSS-M are likely to
effect your mathematics program.
• Identify productive starting points for
beginning implementation of the CCSS-M.
• Learn about tools and resources to support
the transition to CCSS.
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What is NCSM?
International organization of and for mathematics
education leaders:
Coaches and mentors
Curriculum leaders
Department chairs
District supervisors/leaders
Mathematics consultants
Mathematics supervisors
Principals
Professional developers
Publishers and authors
Specialists and coordinators
State and provincial directors
Superintendents
Teachers
Teacher educators
Teacher leaders
www.mathedleadership.org
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NCSM Position Papers
1.
2.
3.
4.
5.
6.
7.
8.
Effective and Collaborative Teams
Sustained Professional Learning
Equity
Students with Special Needs
Assessment
English Language Learners
Positive Self-Beliefs
Technology
mathedleadership.org
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“ The Common Core State Standards represent an
opportunity – once in a lifetime – to form effective
coalitions for change.” Jere Confrey, August 2010
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CCSS: A Major
Challenge/Opportunity
• College and career readiness expectations
• Rigorous content and applications
• Stress conceptual understanding as well as
procedural skills
• Organized around mathematical principles
• Focus and coherence
• Designed around research-based learning
progressions whenever possible.
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Common Core State Standards for
Mathematics
• Introduction
– Standards-Setting Criteria
– Standards-Setting Considerations
• Application of CCSS for ELLs
• Application to Students with Disabilities
• Mathematics Standards
– Standards for Mathematical Practice
– Contents Standards: K-8; HS Domains
• Appendix A: Model Pathways for High School Courses
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Expanded CCSS and Model Pathways available at
www.mathedleadership.org/
What’s different about CCSS?
• Accountability
• Accountability
• Accountability
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What’s different about CCSS?
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 is time to recognize that standards are not
just promises to our children, but promises we
intend to keep.
— CCSS (2010, p.5)
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Assessment Consortia
• Partnership for the Assessment of
Readiness for College and Careers
(PARCC)
http://www.fldoe.org/parcc/
• SMARTER Balanced Assessment
Consortium
http://www.k12.wa.us/SMARTER/
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Implementing CCSS
• Challenge:
– CCSS assessments not available for several
years (2014-2015 deadline).
• Where NOT to start-– Aligning CCSS standards grade-by-grade with
existing mathematics standards.
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Implementing CCSS:
Where to Start?
• Mathematical practices
• Progressions within and among content clusters
and domains
• “Key advances”
• Conceptual understanding
• Research-Informed C-T-L-A Actions
• Assessment tasks
– Balanced Assessment Tasks (BAM)
– State released tasks
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Collaborate!
Engage teachers in working in
collaborative teams
• Grade level/course/department meetings
– Common assessments
– Common unit planning
– Differentiating instruction
• Cross grade/course meetings
– End-of-year/Beginning-of-year expectations
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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)
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Underlying Frameworks
National Council of Teachers of Mathematics
5 Process Standards
•
•
•
•
•
Problem Solving
Reasoning and Proof
Communication
Connections
Representations
NCTM (2000). Principles and Standards for
School Mathematics. Reston, VA: Author.
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Underlying Frameworks
Strands of Mathematical Proficiency
Conceptual
Understanding
Strategic
Competence
Adaptive
Reasoning
Productive
Disposition
Procedural
Fluency
NRC (2001). Adding It Up. Washington, D.C.:
National Academies Press.
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Strands of Mathematical Proficiency
• Conceptual Understanding – comprehension of
mathematical concepts, operations, and relations
• Procedural Fluency – skill in carrying out
procedures flexibly, accurately, efficiently, and
appropriately
• Strategic Competence – ability to formulate,
represent, and solve mathematical problems
• Adaptive Reasoning – capacity for logical
thought, reflection, explanation, and justification
• Productive Disposition – habitual inclination to
see mathematics as sensible, useful, and
worthwhile, coupled with a belief in diligence and
one’s own efficacy.
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Standards for Mathematical Practice
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in
solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the
reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated
reasoning.
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The Standards for
Mathematical Practice
Take a moment to examine the first three
words of each of the 8 mathematical
practices… what do you notice?
Mathematically Proficient Students…
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The Standards for [Student]
Mathematical Practice
What are the verbs that illustrate the
student actions for your assigned
mathematical practice?
Circle, highlight or underline them
for your assigned practice…
Discuss with a partner:
What jumps out at you?
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The Standards for [Student]
Mathematical Practice
SMP1: Explain and make conjectures…
SMP2: Make sense of…
SMP3: Understand and use…
SMP4: Apply and interpret…
SMP5: Consider and detect…
SMP6: Communicate precisely to others…
SMP7: Discern and recognize…
SMP8: Notice and pay attention to…
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The Standards for [Student]
Mathematical Practice
On a scale of 1 (low) to 6 (high),
to what extent is your school promoting
students’ proficiency in the practice you
discussed?
Evidence for your rating?
Individual rating
Team rating
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Standards for Mathematical Practice
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in
solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the
reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated
reasoning.
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Standards for Mathematical Practice
• Describe the thinking processes, habits of
mind and dispositions that students need to
develop a deep, flexible, and enduring
understanding of mathematics; in this
sense they are also a means to an end.
SP1. Make sense of problems
“….they [students] analyze givens, constraints,
relationships and goals. ….they monitor and evaluate
their progress and change course if necessary. …. and
they continually ask themselves “Does this make
sense?”
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Standards for Mathematical Practice
AND….
• Describe mathematical content students
need to learn.
SP1. Make sense of problems
“……. students can explain correspondences between
equations, verbal descriptions, tables, and graphs or
draw diagrams of important features and
relationships, graph data, and search for regularity or
trends.”
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Buttons Task
Gita plays with her grandmother’s collection of black & white buttons.
She arranges them in patterns. Her first 3 patterns are shown below.
Pattern #1
1.
2.
3.
4.
Pattern #2
Pattern #3
Pattern #4
Draw pattern 4 next to pattern 3.
How many white buttons does Gita need for Pattern 5 and Pattern
6? Explain how you figured this out.
How many buttons in all does Gita need to make Pattern 11?
Explain how you figured this out.
Gita thinks she needs 69 buttons in all to make Pattern 24. How
do you know that she is not correct?
How many buttons does she need to make Pattern 24?
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Button Task
1. Individually complete parts 1 - 3.
2. Then work with a partner to compare your
work. Look for as many ways to solve part 3 as
possible.
3. Which mathematical practices are needed to
complete the task?
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www.Inside Mathematics.org
A reengagement
lesson using the
Button Task
Francis Dickinson
San Carlos Elementary
Grade 5
• http://www.insidemathematics.org/index.php/classroom-videovisits/public-lessons-numerical-patterning/218-numerical-patterninglesson-planning?phpMyAdmin=NqJS1x3gaJqDM-1-8LXtX3WJ4e8
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Learner A
Pictorial Representation
What does Learner A see staying the same? What does Learner A see changing?
Draw a picture to show how Learner A sees this pattern growing through the first
3 stages. Color coding and modeling with square tiles may come in handy.
Verbal Representation
Describe in your own words how Learner A sees this pattern growing. Be sure to
mention what is staying the same and what is changing.
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Learner B
Pictorial Representation
What does Learner B see staying the same? What does Learner B see changing?
Draw a picture to show how Learner B sees this pattern growing through the first
3 stages. Color coding and modeling with square tiles may come in handy.
Verbal Representation
Describe in your own words how Learner B sees this pattern growing. Be sure
to mention what is staying the same and what is changing.
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Button Task Revisited
• Which of the Standards of Mathematical Practice
did you see the students working with?
• What did Mr. Dickinson get out of using the same
math task two days in a row, rather than switching
to a different task(s)?
• How did the way the lesson was facilitated support
the development of the Standards of Practice for
students?
• What implications for implementing CCSS does
this activity suggest to you?
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Standards for [Student] Mathematical
Practice
“Not all tasks are created equal, and different
tasks will provoke different levels and kinds
of student thinking.”
Stein, Smith, Henningsen, & Silver, 2000
“The level and kind of thinking in which
students engage determines what they
will learn.”
Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human, 1997
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The Standards for [Student]
Mathematical Practice
The 8 Standards for Mathematical Practice –
place an emphasis on student demonstrations
of learning…
Equity begins with an understanding of how
the selection of tasks, the assessment of
tasks, the student learning environment
creates great inequity in our schools…
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Learners should
• Acquire conceptual knowledge as well as
skills to enable them to organize their
knowledge, transfer knowledge to new
situations, and acquire new knowledge.
• Engage with challenging tasks that involve
active meaning-making
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What Are Mathematical Tasks?
Mathematical tasks are a set of problems
or a single complex problem the purpose
of which is to focus students’ attention on
a particular mathematical idea.
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Why Focus on Mathematical Tasks?
• Tasks form the basis for students’ opportunities to learn
what mathematics is and how one does it;
• Tasks influence learners by directing their attention to
particular aspects of content and by specifying ways to
process information;
• The level and kind of thinking required by mathematical
instructional tasks influences what students learn; and
• Differences in the level and kind of thinking of tasks used
by different teachers, schools, and districts, is a major
source of inequity in students’ opportunities to learn
mathematics.
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Why Focus on Mathematical Tasks?
• Tasks form the basis for students’ opportunities to learn
what mathematics is and how one does it;
• Tasks influence learners by directing their attention to
particular aspects of content and by specifying ways to
process information;
• The level and kind of thinking required by mathematical
instructional tasks influences what students learn; and
• Differences in the level and kind of thinking of tasks used
by different teachers, schools, and districts, is a major
source of inequity in students’ opportunities to learn
mathematics.
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Increasing Task Cognitive Demand:
The Handshake Problem
Version 1
How many handshakes will
there be if each person in
your group shakes the hand
of every person once?
 Tell who was in your group
 How did you get your
answer?
 Try to show your solution on
paper
Version 2

How many handshakes will there
be if one more person joins your
group?
 How many handshakes will there
be if two more people join your
group?
 How many handshakes will there
be if three more people join your
group?
Organize your data into a table.
Do you see a pattern?
 How many handshakes will there
be if 100 more people join your
group?
Generalization: What can be said
about the relationship between the
number of people in a group and the
total number of handshakes?
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Blanton & Kaput, 2003
Compare the Two Versions of the
Handshake Problem
How are the two versions of the
handshake task the same?
How are they different?
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Blanton & Kaput, 2003
Cognitive Level of Tasks
• Lower-Level Tasks
(e.g., Handshakes Version 1)
• Higher-Level Tasks
(e.g., Handshakes Version 2)
The Quasar Project
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Lower-Level Tasks
• Memorization
– What are the decimal equivalents for the
fractions ½ and ¼?
• Procedures without connections
– Convert the fraction 3/8 to a decimal.
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Higher-Level Tasks
•
Procedures with connections
–
•
Using a 10 x 10 grid, identify the decimal and
percent equivalents of 3/5.
Doing mathematics
–
Shade 6 small squares in a 4 x 10 rectangle. Using
the rectangle, explain how to determine:
a)
The decimal part of area that is shaded;
b) The fractional part of area that is shaded.
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Implementation Issue
Do all students have the opportunity to
engage in mathematical tasks that
promote students’ attainment of the
mathematical practices on a regular basis?
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Opportunities for all students to
engage in challenging tasks?
• Examine tasks in your instructional materials:
– Higher cognitive demand?
– Lower cognitive demand?
• Where are the challenging tasks?
• Do all students have the opportunity to grapple
with challenging tasks?
• Examine the tasks in your assessments:
– Higher cognitive demand?
– Lower cognitive demand?
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Insidemathematics.org
Briars, June 2011
Insidemathematics.org
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“Algebrafying” Instructional Materials
Transforming problems with a single
numerical answer to opportunities for
pattern building, conjecturing,
generalizing, and justifying
mathematical facts and relationships.
Blanton & Kaput, 2003, p.71
Briars, June 2011
Increasing Task Cognitive Demand:
The Handshake Problem
Version 1
How many handshakes will
there be if each person in
your group shakes the hand
of every person once?
 Tell who was in your group
 How did you get your
answer?
 Try to show your solution on
paper
Version 2

How many handshakes will there
be if one more person joins your
group?
 How many handshakes will there
be if two more people join your
group?
 How many handshakes will there
be if three more people join your
group?
Organize your data into a table.
Do you see a pattern?
 How many handshakes will there
be if 100 more people join your
group?
Generalization: What can be said
about the relationship between the
number of people in a group and the
total number of handshakes?
Briars, June 2011
Blanton & Kaput, 2003
Algebrafy This Task
Jack wants to save to buy a CD player that
costs $35. He makes $5 per hour
babysitting. How many hours will he need
to work in order to buy the CD player?
Blanton & Kaput, 2003
Briars, June 2011
Creating A Classroom Culture and Practices
that Promote Algebraic Reasoning
• Incorporate conjecture, argumentation,
and generalization in purposeful ways so
that students consider arguments as ways
to build reliable knowledge
• Respect and encourage these activities as
standard daily practice, not as occasional
“enrichment” separate from the regular
work of learning and practicing arithmetic
Blanton & Kaput, 2003, p.74
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Leading with the
Mathematics Practices
• Build upon/extend work on NCTM
Processes and NRC Proficiencies
• Phase in implementation
• Consider relationships among the
practices
• Analyze instructional tasks in terms of
opportunities for students to regularly
engage in practices.
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Standards for Mathematical Content
• Counting and Cardinality
(K)
• Operations and Algebraic
Thinking (K-5)
• Number and Operations in
Base Ten (K-5)
• Measurement and Data
(K-5)
• Geometry (K-HS)
• Number and Operations —
Fractions (3-5)
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• Ratios and Proportional
Relationships (6-7)
• The Number System (6-8)
• Expressions and Equations
(6-8)
• Statistics and Probability
(6-HS)
• Functions (8-HS)
• Number and Quantity (HS)
• Algebra (HS)
• Modeling (HS)
56
Grade Level Standards
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Progressions within and across
Domains
K- 5
6-8
Operations and
Algebraic Thinking
Expressions
and
Equations
High School
Algebra
Number and
Operations―Base Ten
Number and
Operations
―Fractions
The Number
System
Daro, 2010
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Key Advances
1. Operations and the problems they solve
2. Properties of operations: Their role in arithmetic
and algebra
3. Mental math and “algebra” vs. algorithms
4. Units and unitizing
a. Unit fractions
b. Unit rates
5. Defining similarity and congruence in terms of
transformations
6. Quantities-variables-functions-modeling
7. Number-expression-equation-function
Daro, 2010
8. Modeling
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Write a word problem that could be
modeled by
a+b=c
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a×b=p
Word problems for
a + b = c or a x b = p
• Result unknown; e.g. 5 + 3 = ?, 3 x 6 = ?
– Mike has 8 pennies. Sam gives him 3 more.
How many does Mike have now?
– There are 3 bags with 6 plums in each bag?
How many plums are there in all?
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Word problems for
a+b=c
• Change or part unknown; e.g., 5 + ? = 8
– Mike has 5 pennies. Sam gives him some more. Now
he has 8. How many did he get from Sam?
• Start unknown; e.g., ? + 3 = 8
– Mike has some pennies. He gets 3 more. Now he has
11. How many did he have at the beginning?
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Word problems for
axb=p
• Number of groups (a) or number in each group (b)
unknown?
–
If 18 plums are to be packed 6 to a bag, then how many bags are
needed?
– If 18 plums are to packed into 6 bags, then how many plums will
be in each bag?
– Contexts: Equal groups? Arrays? Area? Size comparison?
• Scale factor or smaller quantity unknown
– Crista earned $18 babysitting. Ann only earned $6. How many
times as much money did Crista earn than Ann?
– Crista earned $18 babysitting. That was 3 times as much as Ann
earned. How much money did Ann earn?
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Common Addition and Subtraction Situations
Common Addition and Subtraction Situations
Common Multiplication and Division Situations
Does It Always Work?
Looking for “Key Words” or “Clue Words” is
sometimes taught to children to help them choose the
operation to solve a word problem. Does it always
work?
• Try to solve each type of problem in the table using
“key words.”
• Did you always get the correct answer using this
method? For which problems does it work? For
which problems, if any, doesn’t it work?
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Operations and
the Problems They Solve
• To what extent do your instructional
materials provide opportunities for
students to develop proficiency with the
full range of situations that can be modeled
by multiplication/division or ratios/rates?
• To what extent are students expected to
write equations to describe these
situations?
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Key Advances
1. Operations and the problems they solve
2. Properties of operations: Their role in arithmetic
and algebra
3. Mental math and “algebra” vs. algorithms
4. Units and unitizing
a. Unit fractions
b. Unit rates
5. Defining similarity and congruence in terms of
transformations
6. Quantities-variables-functions-modeling
7. Number-expression-equation-function
Daro, 2010
8. Modeling
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Mental Math and “Algebra” vs.
Algorithms
48 + 27 =
93 - 37 =
29 x 12 =
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Operations and
Algebraic Thinking
1
Understand and apply
properties of operations and
the relationship between
addition and subtraction.
2
3
4
Numbers and Operations in
Base Ten
Use place value understanding and
properties of operations to add and
subtract.
Use place value understanding and
properties of operations to add and
subtract.
Understand properties of
multiplication and the
relationship between
multiplication and division.
Use place value understanding and
properties of operations to perform
multi-digit arithmetic.
A range of algorithms may be used.
Use place value understanding and
properties of operations to perform
multi-digit arithmetic.
Fluently add and subtract multi-digit whole
numbers using the standard algorithm.
5
Fractions
Perform operations with multi-digit
whole numbers and with decimals to
hundredths.
Fluently multiply multi-digit whole numbers
using the standard algorithm.
Build fractions from unit
fractions by applying and
extending previous
understandings of
operations on whole
numbers.
Apply and extend previous
understandings of
multiplication and division
to multiply and divide
fractions.
Operations and
Algebraic Thinking
1
Understand and apply
properties of operations and
the relationship between
addition and subtraction.
2
3
4
Numbers and Operations in
Base Ten
Use place value understanding and
properties of operations to add and
subtract.
Use place value understanding and
properties of operations to add and
subtract.
Understand properties of
multiplication and the
relationship between
multiplication and division.
Use place value understanding and
properties of operations to perform
multi-digit arithmetic.
A range of algorithms may be used.
Use place value understanding and
properties of operations to perform
multi-digit arithmetic.
Fluently add and subtract multi-digit whole
numbers using the standard algorithm.
5
Fractions
Perform operations with multi-digit
whole numbers and with decimals to
hundredths.
Fluently multiply multi-digit whole numbers
using the standard algorithm.
Build fractions from unit
fractions by applying and
extending previous
understandings of
operations on whole
numbers.
Apply and extend previous
understandings of
multiplication and division
to multiply and divide
fractions.
Operations and
Algebraic Thinking
1
Understand and apply
properties of operations and
the relationship between
addition and subtraction.
2
3
4
Numbers and Operations in
Base Ten
Use place value understanding and
properties of operations to add and
subtract.
Use place value understanding and
properties of operations to add and
subtract.
Understand properties of
multiplication and the
relationship between
multiplication and division.
Use place value understanding and
properties of operations to perform
multi-digit arithmetic.
A range of algorithms may be used.
Use place value understanding and
properties of operations to perform
multi-digit arithmetic.
Fluently add and subtract multi-digit whole
numbers using the standard algorithm.
5
Fractions
Perform operations with multi-digit
whole numbers and with decimals to
hundredths.
Fluently multiply multi-digit whole
numbers using the standard algorithm.
Build fractions from unit
fractions by applying and
extending previous
understandings of
operations on whole
numbers.
Apply and extend previous
understandings of
multiplication and division
to multiply and divide
fractions.
Strategies vs. Algorithms
• Computational strategy:
– Purposeful manipulations that may be chosen for
specific problems, may not have a fixed order, and
may be aimed at converting one problem into another.
• Computational algorithm:
– A set of predetermined steps applicable to a class of
problems that gives the correct results in every case
when the steps are carried out correctly.
• Which 48 + 27 methods are strategies?
Algorithms?
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74
Multiplication Algorithms
CCSS Numbers and Operations in Base-Ten Progression, April 2011
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75
Multiplication Algorithms
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CCSS Numbers and Operations in Base-Ten Progression, April 2011
76
Multiplication Algorithms
CCSS Numbers and Operations in Base-Ten Progression, April 2011
77
Multiplication Algorithms
CCSS Numbers and Operations in Base-Ten Progression, April 2011
78
Key Advances
1. Operations and the problems they solve
2. Properties of operations: Their role in arithmetic
and algebra
3. Mental math and “algebra” vs. algorithms
4. Units and unitizing
a. Unit fractions
b. Unit rates
5.
6.
7.
8.
Quantities-variables-functions-modeling
Number-expression-equation-function
Modeling
Practices
Daro, 2010
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79
Units Matter
What fractional part is shaded?
CCSS Number and Operations-Fractions Progression, 8/2011
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80
Units are things you count
•
•
•
•
•
•
•
Objects
Groups of objects
1
10
100
¼ unit fractions
Numbers represented as expressions
Daro, 2010
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81
Units add up
•
•
•
•
•
•
•
3 pennies + 5 pennies = 8 pennies
3 ones + 5 ones = 8 ones
3 tens + 5 tens = 8 tens
3 inches + 5 inches = 8 inches
3 ¼ inches + 5 ¼ inches = 8 ¼ inches
3(1/4) + 5(1/4) = 8(1/4)
3(x + 1) + 5(x+1) = 8(x+1)
Daro, 2010
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82
Benefits of Unit Fraction Approach
• Increase understanding of fractions
• Apply whole number concepts and skills to
fractions
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83
Unitizing links fractions to whole
number arithmetic
• Students’ expertise in whole number
arithmetic is the most reliable expertise
they have in mathematics
• It makes sense to students
• If we can connect difficult topics like
fractions and algebraic expressions to
whole number arithmetic, these difficult
topics can have a solid foundation for
students.
Daro, 2011
Briars, June 2011
Fraction Equivalence
Grade 3:
– Fractions of areas that are the same size, or
fractions that are the same point (length from
0) are equivalent
– Recognize simple cases: ½ = 2/4 ; 4/6 = 2/3
– Fraction equivalents of whole numbers 3 =
3/1, 4/4 =1
– Compare fractions with same numerator or
denominator based on size in visual diagram
Briars, June 2011
Fraction Equivalence
Grade 4:
– Explain why a fraction a/b = na/nb using
visual models; generate equivalent fractions
– Compare fractions with different numerators
and different denominators, e.g., by creating
common denominators or numerators, or by
comparing to a benchmark fraction such as ½.
Briars, June 2011
Fraction Equivalence
Grade 5:
– Use equivalent fractions to add and subtract
fractions with unlike denominators
Briars, June 2011
Grade 4: Comparing Fractions
1. Which is closer to 1, 4/5 or 5/4?
How do you know?
2. Which is greater, 3/7 or 3/5?
How do you know?
3. Which is greater, 3/7 or 5/9?
How do you know?
CCSS Number and Operations-Fractions Progression, 8/2011
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Key Advances
1. Operations and the problems they solve
2. Properties of operations: Their role in arithmetic
and algebra
3. Mental math and “algebra” vs. algorithms
4. Units and unitizing
a. Unit fractions
b. Unit rates
5. Defining congruence and similarity in terms of
transformations
6. Quantities-variables-functions-modeling
7. Number-expression-equation-function
8. Modeling
Daro, 2010
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Implementing CCSS:
Where to Start?
• Mathematical practices
• Progressions within and among content clusters
and domains
• “Key advances”
• Conceptual understanding
• Research-Informed C-T-L-A Actions
• Assessment tasks
– Balanced Assessment Tasks (BAM)
– State released tasks
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Reflections
• What next steps will you take to
implement CCSS?
• Who will you need to work with?
• What support/information/resources will
you need?
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Thank You!
[email protected]
mathedleadership.org
Briars, June 2011