Unwrapping the Common Core State Standards for Administrators

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Unwrapping the Common Core State Standards for
Administrators
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Objectives

• Increase participants knowledge of the CCSS for
  Mathematics
• Increase participants knowledge of the shifts of
  the CCSS for Mathematics
• Increase participants ability to unpack content
  and mathematical practice standards

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Outcomes

• Knowledge to lead implementation of the Common
  Core State Standards.
• Vision to integrate the implementation of the
  Common Core State Standards into broad education
  improvement efforts.
• Metrics to clearly describe what successful
  progress in implementation looks like and
  facilitates a flexible cycle of change.
• Build capacity so that all members of the
  education landscape are learning together.

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Rationale for the CCSS

• Declining US competitiveness with other developed
  countries
• NAEP performance that is largely flat over the
  past 40 years in 8th grade
• Slight improvement at the 4th grade level
• Slight decline at the high school level
• High rates of college remediation

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Principles of the CCSS

• Aligned to requirements for college and career
  readiness
• Based on evidence
• Honest about time

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Activity
Digging into the Common Core
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Common Core State Standards for Mathematics Key
Shifts
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Mathematics 3 Shifts

1. Focus Focus strongly where the standards focus.

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Shift 1 Focus Strongly where the Standards Focus

• Significantly narrow the scope of content and
  deepen how time and energy is spent in the math
  classroom.
• Focus deeply on what is emphasized in the
  standards, so that students gain strong
  foundations.

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Traditional U.S. Approach
K 12
Number and Operations

Measurement and Geometry

Algebra and Functions

Statistics and Probability
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Focusing Attention Within Number and Operations
Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Expressions and Equations Expressions and Equations Expressions and Equations Algebra
Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking ? Expressions and Equations Expressions and Equations Expressions and Equations ? Algebra
Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Expressions and Equations Expressions and Equations Expressions and Equations Algebra
Algebra
Number and OperationsBase Ten Number and OperationsBase Ten Number and OperationsBase Ten Number and OperationsBase Ten Number and OperationsBase Ten Number and OperationsBase Ten ? The Number System The Number System The Number System Algebra
The Number System The Number System The Number System ? Algebra
Number and OperationsFractions Number and OperationsFractions Number and OperationsFractions ? The Number System The Number System The Number System Algebra


K 1 2 3 4 5 6 7 8 High School
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Engaging with the shift What do you think
belongs in the major work of each grade?
Grade Which two of the following represent areas of major focus for the indicated grade? Which two of the following represent areas of major focus for the indicated grade? Which two of the following represent areas of major focus for the indicated grade?
K Compare numbers Use tally marks Understand meaning of addition and subtraction
1 Add and subtract within 20 Measure lengths indirectly and by iterating length units Create and extend patterns and sequences
2 Work with equal groups of objects to gain foundations for multiplication Understand place value Identify line of symmetry in two dimensional figures
3 Multiply and divide within 100 Identify the measures of central tendency and distribution Develop understanding of fractions as numbers
4 Examine transformations on the coordinate plane Generalize place value understanding for multi-digit whole numbers Extend understanding of fraction equivalence and ordering
5 Understand and calculate probability of single events Understand the place value system Apply and extend previous understandings of multiplication and division to multiply and divide fractions
6 Understand ratio concepts and use ratio reasoning to solve problems Identify and utilize rules of divisibility Apply and extend previous understandings of arithmetic to algebraic expressions
7 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers Use properties of operations to generate equivalent expressions Generate the prime factorization of numbers to solve problems
8 Standard form of a linear equation Define, evaluate, and compare functions Understand and apply the Pythagorean Theorem
Alg.1 Quadratic inequalities Linear and quadratic functions Creating equations to model situations
Alg.2 Exponential and logarithmic functions Polar coordinates Using functions to model situations
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Key Areas of Focus in Mathematics
Grade Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding
K2 Addition and subtraction concepts, skills, and problem solving and place value
35 Multiplication and division of whole numbers and fractions concepts, skills, and problem solving
6 Ratios and proportional reasoning early expressions and equations
7 Ratios and proportional reasoning arithmetic of rational numbers
8 Linear algebra
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Mathematics 3 Shifts

1. Focus Focus strongly where the standards focus.
2. Coherence Think across grades, and link to major
   topics

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Shift 2 Coherence Think Across Grades, and
Link to Major Topics Within Grades

• Carefully connect the learning within and across
  grades so that students can build new
  understanding on foundations built in previous
  years.
• Begin to count on solid conceptual understanding
  of core content and build on it. Each standard is
  not a new event, but an extension of previous
  learning.

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Activity
Coherence
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Coherence Link to Major Topics Within Grades
Example Data Representation
Standard MACC.3.MD.2.3
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Coherence Link to Major Topics Within Grades
Example Geometric Measurement
MACC.3.MD.3 (cluster)
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Informing Grades 1-6 Mathematics Standards
Development What Can Be Learned from
High-Performing Hong Kong, Singapore, and Korea?
American Institutes for Research (2009, p. 13)
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Alignment in Context Neighboring Grades and
Progressions
Algebra Reasoning with Equations and Inequalities (A-REI.1-12) Understand solving equations as a process of reasoning and explain the reasoning Solve equations and inequalities in one variable Solve systems of equations Represent and solve equations and inequalities graphically Algebra Reasoning with Equations and Inequalities (A-REI.1-12) Understand solving equations as a process of reasoning and explain the reasoning Solve equations and inequalities in one variable Solve systems of equations Represent and solve equations and inequalities graphically
8.EE.7-8 Analyze and solve linear equations and pairs of simultaneous linear equations.
7.EE.3-4 Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
6.EE.5-8 Reason about and solve one-variable equations and inequalities.
5.OA.1-2 Write and interpret numerical expressions.
4.OA.1-3 Use the four operations with whole numbers to solve problems.
3.OA.1-4 Represent and solve problems involving multiplication and division.
2.OA.1 Represent and solve problems involving addition and subtraction.
1.OA.7-8 Work with addition and subtraction equations.
K.OA.1-5 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
One of several staircases to algebra designed in
the OA domain.

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Mathematics 3 Shifts

1. Focus Focus strongly where the standards focus.
2. Coherence Think across grades, and link to major
   topics
3. Rigor In major topics, pursue conceptual
   understanding, procedural skill and fluency, and
   application

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Shift 3 Rigor In Major Topics, Pursue
Conceptual Understanding, Procedural Skill and
Fluency, and Application

• The CCSSM require a balance of
• Solid conceptual understanding
• Procedural skill and fluency
• Application of skills in problem solving
  situations
• Pursuit of all three requires equal intensity in
  time, activities, and resources.

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Solid Conceptual Understanding

• Teach more than how to get the answer and
  instead support students ability to access
  concepts from a number of perspectives
• Students are able to see math as more than a set
  of mnemonics or discrete procedures
• Conceptual understanding supports the other
  aspects of rigor (fluency and application)

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Fluency

• The standards require speed and accuracy in
  calculation.
• Teachers structure class time and/or homework
  time for students to practice core functions such
  as single-digit multiplication so that they are
  more able to understand and manipulate more
  complex concepts

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Required Fluencies in K-6
Grade Standard Required Fluency
K K.OA.5 Add/subtract within 5
1 1.OA.6 Add/subtract within 10
2 2.OA.2 2.NBT.5 Add/subtract within 20 (know single-digit sums from memory) Add/subtract within 100
3 3.OA.7 3.NBT.2 Multiply/divide within 100 (know single-digit products from memory) Add/subtract within 1000
4 4.NBT.4 Add/subtract within 1,000,000
5 5.NBT.5 Multi-digit multiplication
6 6.NS.2,3 Multi-digit division Multi-digit decimal operations
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Fluency in High School
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Application

• Students can use appropriate concepts and
  procedures for application even when not prompted
  to do so.
• Teachers provide opportunities at all grade
  levels for students to apply math concepts in
  real world situations, recognizing this means
  different things in K-5, 6-8, and HS.
• Teachers in content areas outside of math,
  particularly science, ensure that students are
  using grade-level-appropriate math to make
  meaning of and access science content.

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Engaging with the shift Making a True Statement
Rigor ______ ________ _______

• This shift requires a balance of three discrete
  components in math instruction. This is not a
  pedagogical option, but is required by the
  standards. Using grade __ as a sample, find and
  copy the standards which specifically set
  expectations for each component.

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Discussion
Have you observed any of these shifts in your
schools with the implementation of NGSSS? What
have you seen?
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Common Core in Action?
Observe Mr. McKinneys class. Do you see the
shifts of CCSS incorporated into his teaching?

• Teaching the Pythagorean Theorem

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Activity
Reflecting on the Shifts for Mathematics
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Structure of CCSS
Standards for Mathematical Practice
Grade level or High School conceptual category
Domain
Cluster
Standard
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Standards for Mathematical Practice
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Activity
Standards of Mathematical Practice
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Strategies for Alignment

• Key questions to be asking
• What are your teachers including as questions on
  classroom assessments (formative and summative)?
• What do you value in PD?
• What do you look for in teacher observations?

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Discussion

• What policies, procedures, and/or work within
  your district, school, or classroom are impacted
  by the Common Core State Standards?

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Metrics What it Looks Like

• Everyone in the system needs clarity around the
  goals what it will look like when implemented.
• Metrics let us know what progress we are making
  in meeting goals.
• The system must be set up to collect progress
  data, and also monitor and adjust.

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Areas to Watch for Progress

• In relation to the shifts and your goals,
  consider
• Teacher knowledge and practice
• Instructional materials and resources
• Student work

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Activity
Unpacking Practice Standards
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Activity
Unpacking Content Standards
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Unpacking Content Standards

• Answers 2 questions
• What does that mean?
• What should I do to help my students demonstrate
  that?
• Product
• Clear explanations, definitions, and background
  research
• Ideas for tasks
• Guides differentiation and planning

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Unpacking Process
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Essential Element of Unpacking Process

• Read the standard.
• Identify and discuss the technical meaning of
  important words in the language of the standard.
• Explore research pertaining to the content in the
  standard, including common misconceptions related
  to the topic.
• Determine what the standard calls for students to
  know and be able to do.
• Determine how the standard relates to learning
  progressions, standards progressions, and big
  ideas.
• Determine how students will demonstrate
  proficiency.

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MACC.6.RP.1.3a

• MACC.6.RP.1.3
• Use ratio and rate reasoning to solve real-world
  and mathematical problems, e.g., by reasoning
  about tables of equivalent ratios, tape diagrams,
  double number line diagrams, or equations
• MACC.6.RP.1.3a
• Make tables of equivalent ratios relating
  quantities with whole-number measurements, find
  missing values in the tables, and plot the pairs
  of values on the coordinate plane. Use tables to
  compare ratios.

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MACC.6.RP.1.3a

• MACC.6.RP.1.3
• Use ratio and rate reasoning to solve real-world
  and mathematical problems, e.g., by reasoning
  about tables of equivalent ratios, tape diagrams,
  double number line diagrams, or equations
• MACC.6.RP.1.3a
• Make tables of equivalent ratios relating
  quantities with whole-number measurements, find
  missing values in the tables, and plot the pairs
  of values on the coordinate plane. Use tables to
  compare ratios.

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Assessable Instructional Objectives

• Students will relate quantities in a table of
  equivalent ratios (ratio table) by identifying
  how many times greater or less a quantity in one
  ratio is compared to a corresponding quantity in
  an equivalent ratio.
• Students will construct a table of equivalent
  ratios (ratio table) either in columns or rows to
  find a missing value in a real-world or
  mathematical problem. An additional column or row
  may be added for totaling quantities in cases
  where units are the same.
• Students will plot ratio pair values from a
  (ratio table) on a coordinate plane to solve
  problems. This method may be used to find missing
  values or to make a multiplicative comparison
  between equivalent ratios.
• Students will compare ratios from two different
  ratio tables to solve problems by finding
  corresponding quantities that have the same value
  on both tables.

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Elementary Middle High
MACC.5.NF.2.7c MACC.7.EE.2.3 MACC.912.A-CED.1.2
Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form convert between forms as appropriate and assess the reasonableness of answers using mental computation and estimation strategies. For example If a woman making 25 an hour gets a 10 raise, she will make an additional 1/10 of her salary an hour, or 2.50, for a new salary of 27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge this estimate can be used as a check on the exact computation. Create equations in two or more variables to represent relationships between quantities graph equations on coordinate axes with labels and scales.
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Build Capacity

• You are acting as lead learner this content is
  new to everyone.
• Not an issue of compliance.
• Teachers need opportunities to learn and process
  these expectations not just a new scope and
  sequence.
• Everyone in the system needs to appreciate this
  initiative for what it is, an opportunity to
  reform education.
• Recognize this as hard work, worth doing.

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Stages of Change

• Look for people to go through the stages of
  awareness, application and experimentation, and
  ownership.

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Activity
Building Capacity for the Work
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• You have just purchased an expensive Grecian urn
  and asked the dealer to ship it to your house. He
  picks up a hammer, shatters it into pieces, and
  explains that he will send one piece a day in an
  envelope for the next year. You object he says
  dont worry, Ill make sure that you get every
  single piece, and the markings are clear, so
  youll be able to glue them all back together.
  Ive got it covered. Absurd, no? But this is the
  way many school systems require teachers to
  deliver mathematics to their students one piece
  (i.e. one standard) at a time. They promise their
  customers (the taxpayers) that by the end of the
  year they will have covered the
  standards.
• Excerpt from The Structure is the Standards
• Phil Daro, Bill McCallum, Jason Zimba

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References

• www.achievethecore.org