Common Core State Standards for Mathematics

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Common Core State Standards for Mathematics

• Christine Downing, CCSS Consultant NH DOE
• Patty Ewen, Office of Early Childhood Education,
  NH DOE

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Whos in the room?

• Name, position, school/district
• Tell me something you already know about the CCSS
  for Mathematics?
• Now tell me something you hope to learn more
  about in terms of CCSS for Mathematics?

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Goals of Presentation

• Dig into the Common Core State Standards for
  Mathematics
• 2. Get down and dirty with SBAC
• Content Specifications, Assessment Claims, Item
  Specifications
• Throughout we will sift through and mix the
  resources!

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Instructional Shifts

• Focus
• Coherence
• Fluency
• Deep Understanding
• Application
• Dual Intensity

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Dig Into CCSS Mathematics
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Context for Treasure Hunt

• As you complete the treasure hunt, consider the
  following Common Core Message.
• CCSS Solve Three Specific Problems
• Increased Skills Demand and Competition
• Students Not College/Career Ready
• Variance Across the Country in Standards/Expectati
  ons
• Is there evidence in CCSS for Mathematics to
  support this?

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Treasure Hunt

• Form Small Groups that represent the grade ranges
  from K through 12
• As a group complete the Treasurer Hunt for
  Mathematics
• As you complete the Treasurer Hunt, keep track of
  what intrigues you? What do you want to
  investigate deeper? Also, what surprised you?

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Lets Do a Quick Overview of Mathematics

• Here are some common, key messages that can be
  used to begin the discussion
• Hang onits going to be quite a ride!

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Criteria for New Standards

• Fewer, clearer, and higher (Consistent, rigorous,
  and shared aligned with college and work
  expectations)
• Aligned with college and work expectations
• Include rigorous content and application of
  knowledge through high-order skills
• Build upon strengths and lessons of current state
  standards (think DNA of education)
• Internationally benchmarked, so that all students
  are prepared to succeed in our global economy and
  society
• Based on evidence and research

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Mathematics

• Focus and coherence
• Focus on key topics at each grade level.
• Coherent progressions across grade levels.
• Balance of concepts and skills
• Content standards require both conceptual
  understanding and procedural fluency.
• Mathematical practices (8 practices)
• Foster reasoning and sense making in mathematics.
• College and career readiness
• Level is ambitious but achievable.

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Topic Placement in Top Achieving Countries
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Topic Placement in the U.S.
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International Comparison
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CCSS Distribution of Emphasis
CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression
Domains K 1 2 3 4 5 6 7 8
Counting and Cardinality
Operations and Algebraic Thinking
Number and Operations in Base Ten
Number and Operations Fraction
Ratios and Proportional Reasoning
The Number System
Expressions and Equations
Functions
Measurement and Data
Geometry
Statistics and Probability
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CCSS versus GLE/GSE emphasis In NECAP
CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression
Domains K 1 2 3 4 5 6 7 8
Counting and Cardinality
Operations and Algebraic Thinking
Number and Operations in Base Ten
Number and Operations Fraction
Ratios and Proportional Reasoning
The Number System
Expressions and Equations
Functions
Measurement and Data
Geometry
Statistics and Probability
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NECAP Assessment Changes in Mathematics
Test Grade GLEs NOT Assessed in Fall 2013
NECAP Mathematics 3 DSP 2-4 Combinations
NECAP Mathematics 4 DSP 3-5 Probability
NECAP Mathematics 5 DSP 4-4, DSP 4-5, and GM 4-5 Combinations/Permutations Theoretical Probability Similarity
NECAP Mathematics 6 DSP 5-5 Experimental Theoretical Probability
NECAP Mathematics 7 DSP 6-4, DSP 6-5, FA 6-2, and GM 6-5 Combinations/Permutations Experimental Theoretical Probability Slope Similarity
NECAP Mathematics 8 FA 7-2 Slope Constant/Varying Rates of Change
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CCSS Mathematics-High School
The high school standards are listed in
conceptual categories Number and Quantity
Algebra Functions Modeling Geometry
Statistics and Probability
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Lets Pause for a Bit

• Lets Jigsaw the strands of mathematical
  proficiency.
• Please form groups of 5.
• All read pages 115 to 118 and 133 to 135
• Person 1 reads conceptual understanding
• Person 2 reads procedural fluency
• Person 3 reads strategic competence
• Person 4 reads adaptive reasoning
• Person 5 reads productive disposition

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• How do the strands of mathematical proficiency
  relate to the 8 mathematical habits of mind?

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National Council of Teachers of Mathematics NCTM

• Mathematical Process Standards
• Communication
• Connections
• Representations
• Problem Solving
• Reasoning
• Proof
• www.nctm.org

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New Hampshire Connection to 8 Mathematical
Practices
PreK-16 Numeracy Action Plan for the 21st
Century http//www.education.nh.gov/innovations/pr
e_k_num/index.htm
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Lets Dig a Little Deeper

• The new standards support improved curriculum and
  instruction due to increased
• FOCUS, via critical areas at each grade level
• COHERENCE, through carefully developed
  connections within and across grades
• CLARITY, with precisely worded standards that
  cannot be treated as a checklist
• RIGOR, including a focus on College and Career
  Readiness and Standards for Mathematical Practice
  throughout Pre-K-12

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Structure of Knowledge
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Structure of Knowledge in CCSS

• Critical Areas
• Domains
• Clusters
• Standards

Top Level
Similar to STRANDS from GLEs and GSEs
Middle Level
Similar to STEMS from GLEs and GSEs
Bottom Level
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Critical Areas

• There are typically two to four Critical Areas
  for instruction in the introduction for each
  grade level or course.
• They bring focus to the standards at each grade
  by grouping and summarizing the big ideas that
  educators can use to build their curriculum and
  to guide instruction.

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Example of a Critical Area

• __________________________________________________
  _____________________________________
• Kindergarten
• __________________________________________________
  _____________________________________
• In Kindergarten, instructional time should focus
  on two critical areas (1) representing,
  relating, and operating on
• whole numbers, initially with sets of objects
  and (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.
• The Standards for Mathematical Practice
  complement the content standards at each grade
  level so that students
• increasingly engage with the subject matter as
  they grow in mathematical maturity and expertise.
  

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How do critical areas promote focus?

• What is the number of critical areas per grade
  level/course?
• How will/could it improve teaching and learning
  in our school/district when each grade focuses on
  a few Critical Areas?

Grade level K 1 2 3 4 5 6 7 8
of Critical Areas 2 4 4 4 3 3 4 4 3
Course Alg I Geo Alg II Math I Math II Math III
of Critical Areas 5 6 4 6 6 4
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Main Activity Focusing on the Critical Areas

• In small groups, read the Critical Areas for a
  grade level including the description.
• Read each content standard, marking the recording
  sheet with a
• v when a standard strongly matches or supports
  your Critical Area and
• ? when you are not sure
• Leave blank if the standard does not match or
  support the Critical Area

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• Did every standard fall within a Critical Area?
• Are there standards that fall within more than
  one Critical Area?
• Do all the standards within a cluster fall within
  the same Critical Area?

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• How do the Critical Areas help organize and bring
  focus to your grade level standards?
• How should we as a school (or district) use what
  we have learned today about Critical Areas in
  planning for the implementation of the new
  standards?
• How could this work be linked to existing
  curriculum built on GLEs/GSEs?

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Down and Dirty with SBAC
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• Content Specifications
• Assessment Claims
• Item Specifications

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SMARTER Balanced

• Computer Adaptive
• Multiple Choice, Constructed Response, Technology
  Enhanced
• Performance Tasks
• Writing, listening and speaking
• Emphasis of mathematical practices

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Components of SBAC System

• Summative Assessments
• Grades 3-8 and 11 in ELA and Mathematics
• Computer Adaptive Testing
• Performance Tasks
• Interim Assessments
• Optional
• Progress of Students
• Linked to content clusters in CCSS
• Formative Tools and Processes
• Evidence of progress toward learning goals

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Mathematics ContentSpecs

• Claim 1 Conceptual Understanding and Procedural
  Fluency Students can explain and apply
  mathematical concepts and interpret and carry out
  mathematical procedures with precision and
  fluency.
• Claim 2 Problem Solving Students can solve a
  range of complex well-posed problems in pure and
  applied mathematics, making productive use of
  knowledge and problem solving strategies.

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Mathematics Content Specs

• Claim 3 Communicating Reasoning Students can
  clearly and precisely construct viable arguments
  to support their own reasoning and to critique
  the reasoning of others.
• Claim 4 Modeling and Data Analysis Students can
  analyze complex, real-world scenarios and can
  construct and use mathematical models to
  interpret and solve problems.

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Lets look at SBAC Resources

• Assessment Claims and Target Standards
• Claim 1 of the Content Specifications
• Design of Performance Tasks
• Sample Items from Showcase 2 and 3

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Where do you find all this for SBAC?

• www.smarterbalanced.org
• Now explore on your own!

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Share

• So what ahas did you have as you explored the
  wealth of information on SBAC?
• What concerns do you have?
• What will you do next?

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Other Math Resources

• MASS DOE presentation materials
• NCSM Alignment Tool for CCSS resources
• NCTM Reasoning and Sense Making Tools
• Indiana Resources new??
• North Carolina Unpacking

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Questions/Comments

• Thank you!
• Christine Downing
• Christine.downing_at_nh.gov
• Patty Ewen
• Patricia.ewen_at_doe.nh.gov