Common core state standards A closer look at the ccss for mathematics Presented By: Beatriz Alday
The common core state standards: Are aligned with college and work expectations; Are clear, understandable and consistent; Include rigorous content and application of knowledge through high-order skills; Build upon strengths and lessons of current state standards; Are informed by other top performing countries, so that all students are prepared to succeed in our global economy and society; and Are evidence-based.
Standards for Mathematical Practice • 1. Make sense of problems and persevere in solving them. • 2. Reason abstractly and quantitatively. • 3. Construct viable arguments and critique the reasoning of others. • 4. Model with mathematics. • 5. Use appropriate tools strategically. • 6. Attend to precision. • 7. Look for and make use of structure. • 8. Look for and express regularity in repeated reasoning
Standards for Mathematical Content • The standards for mathematical content are designed as learning progressions through the grades and define what students should understand and be able to do in mathematics. For K-8, there are grade-specific standards. • At the high school level, the standards are organized by “conceptual categories.” Each of these sets of standards includes a number of “domains,” which group related standards to provide coherence around key mathematical ideas.
Grades 9-12 • The standards at the high-school level outline the mathematics expected of all students in order to be prepared for college and a career. • They also include additional mathematics for students who choose to take advanced level courses. • The high school standards are organized by “conceptual categories,” each providing a “coherent view of high school mathematics.”
Number and quantity overview The Real Number System • Extend the properties of exponents to rational exponents • Classify numbers as rational or irrational Quantities • Reason quantitatively and use units to solve problems The Complex Number System • Perform arithmetic operations with complex numbers • Represent complex numbers and their operations on the complex plane • Use complex numbers in polynomial identities and equations Vector and Matrix Quantities • Represent and model with vector quantities. • Perform operations on vectors. • Perform operations on matrices and use matrices in applications.
Algebra overview Seeing Structure in Expressions • Interpret the structure of expressions • Write expressions in equivalent forms to solve problems Arithmetic with Polynomials and Rational Functions • Perform arithmetic operations on polynomials • Understand the relationship between zeros and factors of polynomials • Use polynomial identities to solve problems • Rewrite rational functions Creating Equations • Create equations that describe numbers or relationships Reasoning with Equations and Inequalities • 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
Functions overview Interpreting Functions • Understand the concept of a function and use function notation • Interpret functions that arise in applications in terms of the context • Analyze functions using different representations Building Functions • Build a function that models a relationship between two quantities • Build new functions from existing functions Linear, Quadratic, and Exponential Models • Construct and compare linear and exponential models and solve problems • Interpret expressions for functions in terms of the situation they model Trigonometric Functions • Extend the domain of trigonometric functions using the unit circle • Model periodic phenomena with trigonometric functions • Prove and apply trigonometric identities.
Modeling overview It involves: • (1) identifying variables in the situation and selecting those that represent essential features, • (2) formulating a model by creating and selecting geometric, graphical, tabular, algebraic, or statistical representations that describe relationships between the variables, • (3) analyzing and performing operations on these relationships to draw conclusions, • (4) interpreting the results of the mathematics in terms of the original situation, • (5) validating the conclusions by comparing them with the situation, and then either improving the model or, if it is acceptable, • (6) reporting on the conclusions and the reasoning behind them.
Geometry overview Congruence • Experiment with transformations in the plane • Understand congruence in terms of rigid motions • Prove geometric theorems • Make geometric constructions Similarity, Right Triangles, and Trigonometry • Understand similarity in terms of similarity transformations • Prove theorems involving similarity • Define trigonometric ratios and solve problems involving right triangles • Apply trigonometry to general triangles Circles • Understand and apply theorems about circles • Find arc lengths and areas of sectors of circles Expressing Geometric Properties with Equations • Translate between the geometric description and the equation for a conic section • Use coordinates to prove simple geometric theorems algebraically Geometric Measurement and Dimension • Explain volume formulas and use them to solve problems • Visualize relationships between two-dimensional and three-dimensional objects Modeling with Geometry • Apply geometric concepts in modeling situations
Statistics and probability overview The Real Number System • Extend the properties of exponents to rational exponents • Classify numbers as rational or irrational Quantities • Reason quantitatively and use units to solve problems The Complex Number System • Perform arithmetic operations with complex numbers • Represent complex numbers and their operations on the complex plane • Use complex numbers in polynomial identities and equations Vector and Matrix Quantities • Represent and model with vector quantities. • Perform operations on vectors. • Perform operations on matrices and use matrices in applications.
How will the standards be assessed? • Two consortia of states—the Washington-based SMARTER Balanced Assessment Consortium and Achieve’s Partnership for the Assessment of Readiness for College and Careers—have received Race to the Top funding to begin designing both summative and formative assessments that can be used by states adopting the CCSS. • These assessments are expected to be available during the 2014–2015 school year. Assessment comparisons will become easier among states with common assessments: Students who achieve proficiency in one state should also meet proficiency in another.
When will the CCSS be implemented? • The implementation of the common core will be a collaborative process. The ROEs will be an integral part in defining and supporting the roll out by providing initial information to districts on short and long term planning and developing and providing professional development to local districts. It is important to understand the implementation of common core will be a work in progress for at least the next twelve - eighteen months.
What Can Teachers Do Now To Prepare for CCSS Implementation? • Begin by reading the CCSS for your grade level and in your subject area. Consider these questions: • • How do Illinois state standards compare with the CCSS? Which standards are similar? Which standards appear at a grade level above or below your state’s standards? Which standards are new? • • How do your classroom, end-of course, and/or formative assessments align with the learning expectations outlined in the CCSS? • • How does the math district curriculum and instructional materials align with the CCSS? Will you need to develop new lessons and units? • • How will adoption of the new CCSS impact your work? What supports will you need to help students learn the knowledge and skills in the standards?