1. PARCC Mathematics

2. High School vs Middle School The standards are arranged by grade level standards for mathematics in grades K–8, and high school standards are organized by content areas. Teaching Math in 2015 - Best Practices  Choose engaging tasks  Balance struggle and success  Talk less; listen more From NJ Core Content Standards to Common Core Standards

3. CCSS Mathematical Practices 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.

4. From NJ Core Content Standards to Common Core Standards The CCSS bring three key shifts to mathematics instruction and assessment. 1.Focus strongly where the standards focus 2.Coherence: think across grades, and link to major topics within grades 3.Rigor: in major topics pursue: conceptual understanding, procedural skill and fluency, and application with equal intensity.

5. FOCUS Shift 1: Focus strongly where the Standards focus FromTo Cover content that is a “mile- wide and an inch-deep” Assess fewer topics at each grade (as required by the Standards) Give equal importance to all content Dedicate large majority of score points to the major work* of the grade

6. Focus in High School The mile-wide inch-deep problem looks different in high school. In earlier grades it’s a matter of having too many topics. In high school it’s a matter of having too many separately memorized techniques, with no overall understanding of the structure to tie them altogether. So narrowing and deepening the curriculum is not so much a matter of eliminating topics, as seeing the structure that ties them together. –Prof. William McCallum CCSS Mathematics Author

7. Coherence FromTo Assessment as a checklist of individual standards Items that connect standards, clusters, and domains (as is natural in mathematics) as well as items that assess individual standards Each topic in each year is treated as an independent event Consistent representations are used for mathematics across the grades, and Content connects to and builds on previous knowledge

8. Coherence Across Grades Seeing the Structure “The Standards were not so much assembled out of topics as woven out of progressions.” What It Means Aligning items to grade-level expectations requires understanding of all the standards at that grade and understanding how the standard fits into a progression with previous and future grades Why It Matters for Assessment The Standards were woven out of connected topics (the progressions) and so assessments should also rely on the connections between topics (coherence across grades).

9. Rigor Shift 3: Rigor: in major topics pursue conceptual understanding, procedural skill and fluency, and application with equal intensity FromTo Unbalanced emphasis on procedure or application Assessment of all three aspects of rigor in balance A lack of items that require conceptual understanding Items that require students to demonstrate conceptual understanding of the mathematics, not just the procedures Fluency items that are only routine and ordinary Fluency items that are presented in new ways, as well as some that are routine and ordinary Application of mathematics to routine and contrived word problems Application of mathematics to authentic non-routine problems and real-world situations

10. Rigor The word “rigor” is widely used, but it’s rarely understood or defined, and often it merely passes as code for “better” or “harder”. Non-rigorous Tasks may be more “difficult,” but have no purpose (for example, adding 7ths and 15ths without any real context) require minimal effort focus on quantity (more pages to do) do not connect to other mathematical ideas contain routine procedures with little relevance follow a rote procedure require memorization of rules and procedures without understanding

11. Algebra I Overview The Real Number System (N-RN) Extend the properties of exponents to rational exponents Use properties of rational and irrational numbers Quantities (N-Q) Reason quantitatively and use units to solve problems Seeing Structure in Expressions (A-SSE) Interpret the structure of expressions Write expressions in equivalent forms to solve problems Arithmetic with Polynomials and Rational Expressions (A-APR) Perform arithmetic operations on polynomials

12. Algebra I Overview Creating Equations (A-CED) Create equations that describe numbers or relationships Reasoning with Equations and Inequalities (A-REI) 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 Interpreting Functions (F-IF) 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

13. Algebra I Overview Building Functions (F-BF) Build a function that models a relationship between two quantities Build new functions from existing functions Linear, Quadratic, and Exponential Models (F-LE) Construct and compare linear, quadratic, and exponential models and solve problems Interpret expressions for functions in terms of the situation they model Interpreting Categorical and Quantitative Data (S-ID) Summarize, represent, and interpret data on a single count or measurement variable Summarize, represent, and interpret data on two categorical and quantitative variables Interpret linear models

14. Algebra II Overview Seeing Structure in Expressions (A-SSE) Interpret the structure of expressions Write expressions in equivalent forms to solve problems The Complex Number System (N-CN) Perform arithmetic operations with complex numbers Use complex numbers in polynomial identities and equations Arithmetic with Polynomials and Rational Expressions (A-APR) Perform arithmetic operations on polynomials Understand the relationship between zeros and factors of polynomials Use polynomial identities to solve problems Rewrite rational expressions

15. Algebra II Overview Creating Equations (A-CED) Create equations that describe numbers or relationships Interpreting Functions (F-IF) Interpret functions that arise in applications in terms of the context Analyze functions using different representation Reasoning with Equations and Inequalities (A-REI) Understand solving equations as a process of reasoning and explain the reasoning Represent and solve equations and inequalities graphically

16. Algebra II Overview Building Functions (F-BF) Build a function that models a relationship between two quantities Build new functions from existing functions Linear, Quadratic, and Exponential Models (F-LE) Construct and compare linear, quadratic, and exponential models and solve problems Trigonometric Functions (F-TF) Extend the domain of trigonometric functions using the unit circle Model periodic phenomena with trigonometric functions Prove and apply trigonometric identities

17. Algebra II Overview Interpreting categorical and quantitative data (S-ID) Summarize, represent, and interpret data on a single count or measurement variable Making Inferences and Justifying Conclusions (S-IC) Understand and evaluate random processes underlying statistical experiments Make inferences and justify conclusions from sample surveys, experiments and observational studies Using Probability to Make Decisions (S-MD) Use probability to evaluate outcomes of decisions

18. Geometry Overview Congruence (G-CO) Experiment with transformations in the plane Understand congruence in terms of rigid motions Prove geometric theorems Make geometric constructions Modeling with Geometry (G-MG) Apply geometric concepts in modeling situations Circles (G-C) Understand and apply theorems about circles Find arc lengths and areas of sectors of circles Geometric measurement and dimension (G-GMD) Explain volume formulas and use them to solve problems Visualize relationships between two-dimensional and three-dimensional objects

19. Geometry Overview Similarity, Right Triangles, and Trigonometry (G- SRT) Understand similarity in terms of similarity transformations Prove theorems using similarity Define trigonometric ratios and solve problems involving right triangles Apply trigonometry to general triangles Expressing Geometric Properties with Equations (G-GPE) Translate between the geometric description and the equation of a conic section Use coordinates to prove simple geometric theorems algebraically Conditional Probability and the Rules of Probability (S-CP) Understand independence and conditional probability and use them to interpret data Use the rules of probability to compute probabilities of compound events in a uniform probability model Use Probability to Make Decisions (S- MD) Use probability to evaluate outcomes of decisions

20. Task Types Task TypeDescription of Task Type I. Tasks assessing concepts, skills and procedures Balance of conceptual understanding, fluency, and application Can involve any or all mathematical practice standards Machine scorable including innovative, computer-based formats Will appear on the End of Year and Performance Based Assessment components II. Tasks assessing expressing mathematical reasoning Each task calls for written arguments / justifications, critique of reasoning, or precision in mathematical statements (MP.3, 6). Can involve other mathematical practice standards May include a mix of machine scored and hand scored responses Included on the Performance Based Assessment component III. Tasks assessing modeling / applications Each task calls for modeling/application in a real-world context or scenario (MP.4) Can involve other mathematical practice standards May include a mix of machine scored and hand scored responses Included on the Performance Based Assessment component

21. Item Counts per Assessment Assessment Items Algebra I Algebra I Geometry Geometry Algebra II Algebra II End of Year Assessment (EOY) After 90% of school year Type I 1 Point 21 19 19 Type I 2 Point 11 12 12 Type I 4 Point 3 3 3 EOYTOTALEOYTOTAL Type I Type I 35 34 34 Performance Based Assessment (PBA) After 75% of school year Type I 1Point 10 10 10 Type I 2 Point - - - Type II 3 Point 2 2 2 Type II 4 Point 2 2 3 Type III 3 Point 2 2 2 Type III 6 Point 2 2 3 PBATOTAL PBATOTAL Type I Type I 10 10 10 Type II Type II 4 4 5 Type III Type III 4 4 5

22. Type 1 (2 points) This application task requires students to understand a diagram and formula, and then use expressions within that formula to represent a quantity in terms of its context. Expectation is for the student to drag and drop the proper expression into each text box

23. Type 2 (3 points) Expectation is for the student to describe the geometric construction to prove angle congruency The student must construct chains of reasoning that will justify that the construction shown in the animation actually creates a bisector of the given angle. Unlike traditional multiple choice, it is difficult to guess the correct answer or use a choice elimination strategy, and the item is scored using a clearly defined rubric that awards partial credit for a variety of valid partial responses.

24. Type 3 (3 points) This item requires students to model the given situation using equations, then students use that model to determine who will win the race and their margin of victory

25. How Can You Help Your Child? Encourage your child to practice:  typing Mathematical formulas using Equation Editor  the tutorial on the PARCC test Nav website  using an online graphing calculator  using the practice assessments

26. How Can You Help Your Child? A word about Graphing Calculators There will be an online graphing calculator available for the calculator active sections. If your child has their own graphing calculator and wishes to use it…..  Ensure that it is fully charged, or has fresh batteries  it must be cleared prior to testing – remind your child to backup/save their programs before the test

27. Links PARCC Parent Information http://parcconline.org/for-parents PARCC Test Nav Tutorials – testing platform and equation editor http://parcc.pearson.com/tutorial/ http://epat-parcc.testnav.com/client/index.html#tests Online graphing calculators http://www.meta-calculator.com/online/ http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html https://www.desmos.com/calculator PARCC Practice Tests/Sample Items http://parcc.pearson.com/practice-tests/math/ http://parcc.pearson.com/sample-items/