1. The Common Core State Standards for 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
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.

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 K-8 Conceptual Category Grade Domain
Cluster
Standards
K-8
Grade
Domain
Cluster
Standards
(No pre-K Common Core Standards)

14. Format of High School Domain Cluster Standard
Note no grade level, different way of labeling domain in the gray box.

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
Finding the inverse of a function Is a part of the Common Core for all students (i.e., not STEM) but the ideas listed here are expected of STEM students

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
Congruence includes proving theorems and geometric constructions.

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 Cavalieri’s Principal for the formulas for the volume of solid figures
Note deriving equations of circles and parabolas is a part of the Common Core for all students
Note using Cavalieri’s Principal to find volume is a part of the Common Core for all students

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 Algebra and Geometry
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 NCTM’s Focus in High School Mathematics: Reasoning and Sense Making
For grades preK-8, a model of implementation can be found in NCTM’s Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics

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