The Common Core State Standards for Mathematics

1
The Common CoreState Standardsfor Mathematics

• High School

2
Common Core Development

• Initially 48 states and three territories signed
  on
• Final Standards released June 2, 2010, and can be
  downloaded at www.corestandards.org
• As of November 29, 2010, 42 states had officially
  adopted
• Adoption required for Race to the Top funds

3
Common Core Development

• Each state adopting the Common Core either
  directly or by fully aligning its state standards
  may do so in accordance with current state
  timelines for standards adoption, not to exceed
  three (3) years.
• States that choose to align their standards with
  the Common Core Standards accept 100 of the core
  in English language arts and mathematics. States
  may add additional standards.

4
(No Transcript)
5
Benefits for States and Districts

• Allows collaborative professional development to
  be based on best practices
• Allows the 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 mileage from
• Curriculum development, assessment, and
  professional development

6
Characteristics

• Fewer and more rigorous. The goal was increased
  clarity.
• Aligned with college and career expectations
  prepare all students for success on graduating
  from high school.
• Internationally benchmarked, so that all students
  are prepared for succeeding in our global economy
  and society.
• Includes rigorous content and application of
  higher-order skills.
• Builds on strengths and lessons of current state
  standards.
• Research based.

7
Intent of the Common Core

• The same goals for all students
• Coherence
• Focus
• Clarity and specificity

8
Coherence

• Articulated progressions of topics and
  performances that are developmental and connected
  to other progressions
• Conceptual understanding and procedural skills
  stressed equally
• NCTM states coherence also means that
  instruction, assessment, and curriculum are
  aligned.

9
Focus

• Key ideas, understandings, and skills are
  identified
• Deep learning of concepts is emphasized
• That is, adequate time is devoted to a topic and
  learning it well. This counters the mile wide,
  inch deep criticism leveled at most current U.S.
  standards.

10
Clarity and Specificity

• Skills and concepts are clearly defined.
• An ability to apply concepts and skills to new
  situations is expected.

11
CCSS Mathematical Practices

• The Common Core proposes a set of Mathematical
  Practices that all teachers should develop in
  their students. These practices are similar to
  the mathematical processes that NCTM addresses in
  the Process Standards in Principles and Standards
  for School Mathematics.

12
CCSS Mathematical Practices

• 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.

13
Common Core Format

• High School
• Conceptual Category
• Domain
• Cluster
• Standards

K-8 Grade Domain Cluster Standards (No
pre-K Common Core Standards)
14
Format of High School
Domain
Cluster
Standard
15
Format of High School Standards
Regular Standard
Modeling
STEM
16
High School Conceptual Categories

• The big ideas that connect mathematics across
  high school
• A progression of increasing complexity
• Description of the mathematical content to be
  learned, elaborated through domains, clusters,
  and standards

17
Common Core - Domain

• Overarching big ideas that connect topics
  across the grades
• Descriptions of the mathematical content to be
  learned, elaborated through clusters and
  standards

18
Common Core - Clusters

• May appear in multiple grade levels with
  increasing developmental standards as the grade
  levels progress
• Indicate WHAT students should know and be able to
  do at each grade level
• Reflect both mathematical understandings and
  skills, which are equally important

19
Common Core - Standards

• Content statements
• Progressions of increasing complexity from grade
  to grade
• In high school, this may occur over the course of
  one year or through several years

20
High School Pathways

• The CCSS Model Pathways are NOT required. The two
  sequences are examples, not mandates
• Two models that organize the CCSS into coherent,
  rigorous courses
• Four years of mathematics
• One course in each of the first two years
• Followed by two options for year 3 and a variety
  of relevant courses for year 4
• Course descriptions
• Define what is covered in a course
• Are not prescriptions for the curriculum or
  pedagogy

21
High School Pathways

• Pathway A Consists of two algebra courses and a
  geometry course, with some data, probability, and
  statistics infused throughout each (traditional)
• Pathway B Typically seen internationally,
  consisting of a sequence of 3 courses, each of
  which treats aspects of algebra geometry and
  data, probability, and statistics.

22
Conceptual Categories

• Number and Quantity
• Algebra
• Functions
• Modeling
• Geometry
• Statistics and Probability

23
Numbers and Quantity

• Extend the Real Numbers to include work with
  rational exponents and study of the properties of
  rational and irrational numbers
• Use quantities and quantitative reasoning to
  solve problems.

24
Numbers and Quantity

• Required for higher math and/or STEM
• Compute with and use the Complex Numbers, use the
  Complex Number plane to represent numbers and
  operations
• Represent and use vectors
• Compute with matrices
• Use vector and matrices in modeling

25
Algebra and Functions

• Two separate conceptual categories
• Algebra category contains most of the typical
  symbol manipulation standards
• Functions category is more conceptual
• The two categories are interrelated

26
Algebra

• Creating, reading, and manipulating expressions
• Understanding the structure of expressions
• Includes operating with polynomials and
  simplifying rational expressions
• Solving equations and inequalities
• Symbolically and graphically

27
Algebra

• Required for higher math and/or STEM
• Expand a binomial using the Binomial Theorem
• Represent a system of linear equations as a
  matrix equation
• Find the inverse if it exists and use it to solve
  a system of equations

28
Functions

• Understanding, interpreting, and building
  functions
• Includes multiple representations
• Emphasis is on linear and exponential models
• Extends trigonometric functions to functions
  defined in the unit circle and modeling periodic
  phenomena

29
Functions

• Required for higher math and/or STEM
• Graph rational functions and identify zeros and
  asymptotes
• Compose functions
• Prove the addition and subtraction formulas for
  trigonometric functions and use them to solve
  problems

30
Functions

• Required for higher math and/or STEM
• Inverse functions
• Verify functions are inverses by composition
• Find inverse values from a graph or table
• Create an invertible function by restricting the
  domain
• Use the inverse relationship between exponents
  and logarithms and in trigonometric functions

31
Modeling

• Modeling has no specific domains, clusters or
  standards. Modeling is included in the other
  conceptual categories and marked with a asterisk.

32
Modeling

• Modeling links classroom mathematics and
  statistics to everyday life, work, and
  decision-making. Technology is valuable in
  modeling.
• A model can be very simple, such as writing total
  cost as a product of unit price and number
  bought, or using a geometric shape to describe a
  physical object.

33
Modeling

• Planning a table tennis tournament for 7 players
  at a club with 4 tables, where each player plays
  against each other player.
• Analyzing stopping distance for a car.
• Modeling savings account balance, bacterial
  colony growth, or investment growth.

34
Geometry

• Understanding congruence
• Using similarity, right triangles, and
  trigonometry to solve problems
• Congruence, similarity, and symmetry are
  approached through geometric transformations

35
Geometry

• Circles
• Expressing geometric properties with equations
• Includes proving theorems and describing conic
  sections algebraically
• Geometric measurement and dimension
• Modeling with geometry

36
Geometry

• Required for higher math and/or STEM
• Non-right triangle trigonometry
• Derive equations of hyperbolas and ellipses given
  foci and directrices
• Give an informal argument using Cavalieris
  Principal for the formulas for the volume of
  solid figures

37
Statistics and Probability

• Analyze single a two variable data
• Understand the role of randomization in
  experiments
• Make decisions, use inference and justify
  conclusions from statistical studies
• Use the rules of probability

38
Interrelationships

• Algebra and Functions
• Expressions can define functions
• Determining the output of a function can involve
  evaluating an expression
• Algebra and Geometry
• Algebraically describing geometric shapes
• Proving geometric theorems algebraically

39
Additional Information

• For the secondary level, please see NCTMs Focus
  in High School Mathematics Reasoning and Sense
  Making
• For grades preK-8, a model of implementation can
  be found in NCTMs Curriculum Focal Points for
  Prekindergarten through Grade 8 Mathematics

www.nctm.org/FHSM
www.nctm.org/cfp
40
Acknowledgments

• Thanks to the Ohio Department of Education and
  Eric Milou of Rowan University for providing
  content and assistance for this presentation

41
(No Transcript)