CCSS: Mathematics
Julie Staton
August 9-10, 2012
Common Board Configuration
Date: August 9-10, 2012
Bell Ringer: Community Builder
Learning Goal: Participants will understand
the shifts in instruction for Mathematics under
the Common Core State Standards
Benchmark: To aid in building rigor in the
mathematics classroom.
Objective: By the end of the session,
participants will be able to identify the shifts in
instruction in the Mathematics CCSS, resulting
in participants being able to explain how the
increased rigor of the 8 Standards of
Mathematical Practice will impact
mathematics classrooms.
Essential Question: How will the increased
rigor of the 8 Standards of Mathematical
Practice facilitate a transition toward the CCSS
in all Mathematics Classrooms
Vocabulary: Fluency, Coherence
Agenda:
Bellringer
Shifts in Instruction
CCSS Mathematics Standards
Tools & Resources
Unpacking the 8 Standards of Mathematical
Practice
I do  We do You do
Summary
Summarizing Activity:
CBC review
Participant Scale
Essential Question Reflection
Homework: Evaluate the rigor of existing
programs and initiatives within your school
that will assist in the development of an
implementation plan for Mathematics in the
Common Core.
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and implementing the best practices in instructional methodology.
Summer Leadership Institute
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21
Century Skills
Tony Wagner, The Global Achievement Gap
1. Critical Thinking and Problem Solving
2. Collaboration and Leadership
3. Agility and Adaptability
4. Initiative and Entrepreneurialism
5. Effective Oral and Written Communication
6. Accessing and Analyzing Information
7. Curiosity and Imagination
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high effect size instructional and leadership
strategies with a causal relationship to student
learning growth constitute priority issues for
deliberate practice and faculty development.”
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Summer Leadership Institute
Classroom Teacher
High Effect Indicators







Learning Goal with Scales
Tracking Student Progress
Established Content
Standards
Multi-tiered System of
Supports
Clear Goals
Text Complexity
ESOL Students
School Leadership
High Effect Indicators
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
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Learning
Clear Goals and Expectations
Instructional Resources
High Effect Size Strategies
Instructional Initiatives
Monitoring Text Complexity
Interventions
Instructional Adaptations
ESOL Strategies
Summer Leadership Institute
CCSS Mathematics: Shifts in Instruction
Focus
Coherence
&
Spending more
time on fewer
things at any
given grade
Following the
progressions of
ideas and skills as
they unfold
across the grades.
CCSS Mathematics
CCSS Mathematics Content Standards:
Domains in Kindergarten - 8th Grade
CCSS Mathematics Content Standards:
Domains in High School
Tools & Resources in K-5
 Kindergarten & 1st Grade
 OnCore Resources
 Crosswalks
 Curriculum Maps (k-1 & 2-5)



Lesson Progression Sheets
Proficiency Scales
Web Resources
CCSS Mathematics:
8 Standards of Mathematical Practice
Derived from…
The NCTM process
standards:
•
•
•
•
•
Problem solving
Reasoning and proof
Communication
Representation
Connections
&
The Strands of
Mathematical
Proficiency –
Adding it Up
• Adaptive reasoning
• Strategic competence
• Conceptual
understanding
• Procedural fluency
• Productive disposition
CCSS Mathematics:
8 Standards of Mathematical Practice
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.
CCSS Mathematics:
8 Standards of Mathematical Practice
I do…
CCSS Mathematics:
8 Standards of Mathematical Practice
 Make sense of problems and persevere in solving them.
 Mathematically proficient students start by explaining to themselves the meaning
of a problem and looking for entry points to its solution. They analyze givens,
constraints, relationships, and goals. They make conjectures about the form and
meaning of the solution and plan a solution pathway rather than simply jumping
into a solution attempt. They consider analogous problems, and try special cases
and simpler forms of the original problem in order to gain insight into its solution.
They monitor and evaluate their progress and change course if necessary. Older
students might, depending on the context of the problem, transform algebraic
expressions or change the viewing window on their graphing calculator to get the
information they need. Mathematically proficient 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. Younger students might rely on using concrete objects or
pictures to help conceptualize and solve a problem. Mathematically proficient
students check their answers to problems using a different method, and they
continually ask themselves, “Does this make sense?” They can understand the
approaches of others to solving complex problems and identify correspondences
between different approaches.
I do…
CCSS Mathematics:
8 Standards of Mathematical Practice
 Make sense of problems and persevere in solving them.
 Mathematically proficient students start by explaining to themselves the
meaning of a problem and looking for entry points to its solution. They analyze
givens, constraints, relationships, and goals. They make conjectures about the
form and meaning of the solution and plan a solution pathway rather than simply
jumping into a solution attempt. They consider analogous problems, and try
special cases and simpler forms of the original problem in order to gain insight
into its solution. They monitor and evaluate their progress and change course if
necessary. Older students might, depending on the context of the problem,
transform algebraic expressions or change the viewing window on their graphing
calculator to get the information they need. Mathematically proficient 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. Younger students might rely on using concrete
objects or pictures to help conceptualize and solve a problem. Mathematically
proficient students check their answers to problems using a different method, and
they continually ask themselves, “Does this make sense?” They can understand the
approaches of others to solving complex problems and identify correspondences
between different approaches.
I do…
CCSS Mathematics:
8 Standards of Mathematical Practice
 Make sense of problems and persevere in solving them.
 Mathematically proficient students start by explaining to themselves the meaning
of a problem and looking for entry points to its solution. They analyze givens,
constraints, relationships, and goals. They make conjectures about the form and
meaning of the solution and plan a solution pathway rather than simply jumping
into a solution attempt. They consider analogous problems, and try special cases
and simpler forms of the original problem in order to gain insight into its solution.
They monitor and evaluate their progress and change course if necessary. Older
students might, depending on the context of the problem, transform algebraic
expressions or change the viewing window on their graphing calculator to get the
information they need. Mathematically proficient 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. Younger students might rely on using concrete objects or
pictures to help conceptualize and solve a problem. Mathematically proficient
students check their answers to problems using a different method, and they
continually ask themselves, “Does this make sense?” They can understand the
approaches of others to solving complex problems and identify correspondences
between different approaches.
I do…
CCSS Mathematics:
8 Standards of Mathematical Practice
 Make sense of problems and persevere in solving them.
 Mathematically proficient students start by explaining to themselves the meaning
of a problem and looking for entry points to its solution. They analyze givens,
constraints, relationships, and goals. They make conjectures about the form
and meaning of the solution and plan a solution pathway rather than simply
jumping into a solution attempt. They consider analogous problems, and try
special cases and simpler forms of the original problem in order to gain insight
into its solution. They monitor and evaluate their progress and change course if
necessary. Older students might, depending on the context of the problem,
transform algebraic expressions or change the viewing window on their graphing
calculator to get the information they need. Mathematically proficient 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. Younger students might rely on using concrete
objects or pictures to help conceptualize and solve a problem. Mathematically
proficient students check their answers to problems using a different method, and
they continually ask themselves, “Does this make sense?” They can understand the
approaches of others to solving complex problems and identify correspondences
between different approaches.
I do…
CCSS Mathematics:
8 Standards of Mathematical Practice
 Make sense of problems and persevere in solving them.
 Mathematically proficient students start by explaining to themselves the meaning
of a problem and looking for entry points to its solution. They analyze givens,
constraints, relationships, and goals. They make conjectures about the form
and meaning of the solution and plan a solution pathway rather than simply
jumping into a solution attempt. They consider analogous problems, and try
special cases and simpler forms of the original problem in order to gain insight
into its solution. They monitor and evaluate their progress and change course if
necessary. Older students might, depending on the context of the problem,
transform algebraic expressions or change the viewing window on their graphing
calculator to get the information they need. Mathematically proficient 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. Younger students might rely on using concrete
objects or pictures to help conceptualize and solve a problem. Mathematically
proficient students check their answers to problems using a different method, and
they continually ask themselves, “Does this make sense?” They can understand the
approaches of others to solving complex problems and identify correspondences
between different approaches.
I do…
CCSS Mathematics:
8 Standards of Mathematical Practice
 Make sense of problems and persevere in solving them.
 Mathematically proficient students start by explaining to themselves the meaning
of a problem and looking for entry points to its solution. They analyze givens,
constraints, relationships, and goals. They make conjectures about the form and
meaning of the solution and plan a solution pathway rather than simply jumping
into a solution attempt. They consider analogous problems, and try special cases
and simpler forms of the original problem in order to gain insight into its solution.
They monitor and evaluate their progress and change course if necessary. Older
students might, depending on the context of the problem, transform algebraic
expressions or change the viewing window on their graphing calculator to get the
information they need. Mathematically proficient 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. Younger students might rely on using concrete objects or
pictures to help conceptualize and solve a problem. Mathematically proficient
students check their answers to problems using a different method, and they
continually ask themselves, “Does this make sense?” They can understand the
approaches of others to solving complex problems and identify correspondences
between different approaches.
I do…
CCSS Mathematics:
8 Standards of Mathematical Practice
 Make sense of problems and persevere in solving them.
 Mathematically proficient students start by explaining to themselves the meaning
of a problem and looking for entry points to its solution. They analyze givens,
constraints, relationships, and goals. They make conjectures about the form and
meaning of the solution and plan a solution pathway rather than simply jumping
into a solution attempt. They consider analogous problems, and try special
cases and simpler forms of the original problem in order to gain insight into
its solution. They monitor and evaluate their progress and change course if
necessary. Older students might, depending on the context of the problem,
transform algebraic expressions or change the viewing window on their graphing
calculator to get the information they need. Mathematically proficient 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. Younger students might rely on using concrete
objects or pictures to help conceptualize and solve a problem. Mathematically
proficient students check their answers to problems using a different method, and
they continually ask themselves, “Does this make sense?” They can understand the
approaches of others to solving complex problems and identify correspondences
between different approaches.
I do…
CCSS Mathematics:
8 Standards of Mathematical Practice
 Make sense of problems and persevere in solving them.
 Mathematically proficient students start by explaining to themselves the meaning
of a problem and looking for entry points to its solution. They analyze givens,
constraints, relationships, and goals. They make conjectures about the form and
meaning of the solution and plan a solution pathway rather than simply jumping
into a solution attempt. They consider analogous problems, and try special cases
and simpler forms of the original problem in order to gain insight into its solution.
They monitor and evaluate their progress and change course if necessary. Older
students might, depending on the context of the problem, transform algebraic
expressions or change the viewing window on their graphing calculator to get the
information they need. Mathematically proficient 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. Younger students might rely on using concrete objects or
pictures to help conceptualize and solve a problem. Mathematically proficient
students check their answers to problems using a different method, and they
continually ask themselves, “Does this make sense?” They can understand the
approaches of others to solving complex problems and identify correspondences
between different approaches.
I do…
CCSS Mathematics:
8 Standards of Mathematical Practice
 Make sense of problems and persevere in solving them.
 Mathematically proficient students start by explaining to themselves the meaning
of a problem and looking for entry points to its solution. They analyze givens,
constraints, relationships, and goals. They make conjectures about the form and
meaning of the solution and plan a solution pathway rather than simply jumping
into a solution attempt. They consider analogous problems, and try special cases
and simpler forms of the original problem in order to gain insight into its solution.
They monitor and evaluate their progress and change course if necessary. Older
students might, depending on the context of the problem, transform algebraic
expressions or change the viewing window on their graphing calculator to get the
information they need. Mathematically proficient 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. Younger students might rely on using concrete objects or
pictures to help conceptualize and solve a problem. Mathematically proficient
students check their answers to problems using a different method, and they
continually ask themselves, “Does this make sense?” They can understand the
approaches of others to solving complex problems and identify
correspondences between different approaches.
I do…
CCSS Mathematics:
8 Standards of Mathematical Practice
 Make sense of problems and persevere in solving them.
 Mathematically proficient students start by explaining to themselves the meaning
of a problem and looking for entry points to its solution. They analyze givens,
constraints, relationships, and goals. They make conjectures about the form and
meaning of the solution and plan a solution pathway rather than simply jumping
into a solution attempt. They consider analogous problems, and try special cases
and simpler forms of the original problem in order to gain insight into its solution.
They monitor and evaluate their progress and change course if necessary. Older
students might, depending on the context of the problem, transform
algebraic expressions or change the viewing window on their graphing
calculator to get the information they need. Mathematically proficient
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. Younger
students might rely on using concrete objects or pictures to help conceptualize
and solve a problem. Mathematically proficient students check their answers to
problems using a different method, and they continually ask themselves, “Does
this make sense?” They can understand the approaches of others to solving
complex problems and identify correspondences between different approaches.
I do…
CCSS Mathematics:
8 Standards of Mathematical Practice
 #1 Make sense of problems and persevere in solving them.
 Mathematically proficient students start by explaining to themselves the meaning of
a problem and looking for entry points to its solution. They analyze givens,
constraints, relationships, and goals. They make conjectures about the form and
meaning of the solution and plan a solution pathway rather than simply jumping
into a solution attempt. They consider analogous problems, and try special cases
and simpler forms of the original problem in order to gain insight into its solution.
They monitor and evaluate their progress and change course if necessary. Older
students might, depending on the context of the problem, transform algebraic
expressions or change the viewing window on their graphing calculator to get the
information they need. Mathematically proficient 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. Younger students might rely on using concrete objects or
pictures to help conceptualize and solve a problem. Mathematically proficient
students check their answers to problems using a different method, and they
continually ask themselves, “Does this make sense?” They can understand the
approaches of others to solving complex problems and identify correspondences
between different approaches.
I do…
CCSS Mathematics:
8 Standards of Mathematical Practice
 #1 Make sense of problems and persevere in solving them.
 Determine entry points to solve a problem
 Develop a problem solving plan
 Carry out a problem solving plan
 Consider similar, simpler problems
 Determine the relationships between known and unknown
quantities.
 Monitor problem solving process and make changes if
necessary.
 Determine if solution makes sense.
 Evaluate different methods for solving the same problem and
explain the correspondences between different methods.
We do…
CCSS Mathematics:
8 Standards of Mathematical Practice
• #2 Reason abstractly and quantitatively.
• Mathematically proficient students make sense of quantities and
their relationships in problem situations. They bring two
complementary abilities to bear on problems involving quantitative
relationships: the ability to decontextualize—to abstract a given
situation and represent it symbolically and manipulate the
representing symbols as if they have a life of their own, without
necessarily attending to their referents—and the ability to
contextualize, to pause as needed during the manipulation process in
order to probe into the referents for the symbols involved.
Quantitative reasoning entails habits of creating a coherent
representation of the problem at hand; considering the units
involved; attending to the meaning of quantities, not just how to
compute them; and knowing and flexibly using different properties
of operations and objects.
We do…
CCSS Mathematics:
8 Standards of Mathematical Practice
• #2 Reason abstractly and quantitatively.
• makes sense of quantities
and their relationships
•able to decontextualize
•able to contextualize
•creates a coherent
representation of the problem
at hand
•considers the units involved
•attends to the meaning of
quantities, not just how to
compute them
•knows and flexibly uses
different properties of
operations and objects
You do…
CCSS Mathematics:
8 Standards of Mathematical Practice
 Activity
 Within your group, answer the following questions:
1.
2.
3.
What would this SMP look like in the classroom?
What would this SMP sound like in the classroom?
What items represent increased rigor?
CCSS Mathematics:
8 Standards of Mathematical Practice
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.
Common Board Configuration
Date: August 9-10, 2012
Bell Ringer: Community Builder
Learning Goal: Participants will understand
the shifts in instruction for Mathematics under
the Common Core State Standards
Benchmark: To aid in building rigor in the
mathematics classroom.
Objective: By the end of the session,
participants will be able to identify the shifts in
instruction in the Mathematics CCSS, resulting
in participants being able to explain how the
increased rigor of the 8 Standards of
Mathematical Practice will impact
mathematics classrooms.
Essential Question: How can the increased
rigor of the 8 Standards of Mathematical
Practice facilitate a transition toward the CCSS
in all Mathematics Classrooms
Vocabulary: Fluency, Coherence
Agenda:
Bellringer
Shifts in Instruction
CCSS Mathematics Standards
Tools & Resources
Unpacking the 8 Standards of Mathematical
Practice
I do  We do You do
Summary
Summarizing Activity:
CBC review
Essential Question Reflection
Participant Scale
Homework: Evaluate the rigor of existing
programs and initiatives within your school
that will assist in the development of an
implementation plan for Mathematics in the
Common Core.
Participant Scale and Reflection
(Please complete and turn in)
4-Innovating
•In addition to
criteria of
Applying,
enhanced
understanding,
implementation,
monitoring, and
execution take
aways
3-Applying
•Consistent
understanding
and
implementation
steps taken away
along with
monitoring
componets for
effective
execution
2-Developing
1-Beginning
0-Not Using
•Moderate
understanding
and
implementation
steps taken away
•Little
understanding
and inconsistent
implementation
steps taken away
•No
understanding
or
implementatio
n steps taken
away
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