Partnership for Assessment of Readiness for College and Careers (PARCC) Assessment Practices and Mathematical Reasoning Syllabus

Assessment Practices and Mathematical Reasoning syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Assessment Practices and Mathematical Reasoning in Partnership for Assessment of Readiness for College and Careers (PARCC), not a summary of it.

1. 1

   Standards for Mathematical Practice

   4 topics

   • Reasoning and Sense-Making
     • Making sense of problems and persevering
     • Reasoning abstractly and quantitatively
   • Argument and Critique
     • Constructing viable arguments
     • Critiquing the reasoning of others
   • Modeling and Tools
     • Modeling with mathematics
     • Using appropriate tools strategically
   • Precision and Structure
     • Attending to precision
     • Looking for and making use of structure and repeated reasoning
2. 2

   PARCC Mathematics Task Types

   3 topics

   • Type I: Concepts, Skills, and Procedures
     • Machine-scored fluency and procedure items
     • Conceptual understanding items
   • Type II: Expressing Mathematical Reasoning
     • Written justifications and critiques
     • Constructing and evaluating arguments
   • Type III: Modeling and Applications
     • Multi-step real-world modeling
     • Interpreting results in context
3. 3

   Test Format and Administration

   3 topics

   • Computer-Based Test Navigation
     • Online equation editor and tools
     • Item types and response interfaces
   • Accessibility Features and Accommodations
     • Text-to-speech and embedded supports
     • Accommodations for eligible students
   • Performance Levels and Scoring
     • Five performance levels and college/career readiness
     • Scale scores and reporting categories
4. 4

   Test-Taking Strategies

   3 topics

   • Time Management Across Units
     • Pacing within timed sections
     • Allocating time to constructed-response tasks
   • Evidence and Annotation Skills
     • Highlighting and note-taking tools
     • Planning written responses
   • Error-Checking and Review
     • Verifying mathematical work
     • Proofreading writing for conventions

Assessment Practices and Mathematical Reasoning flashcards for Partnership for Assessment of Readiness for College and Careers (PARCC)

24 of 50 cards from the Assessment Practices and Mathematical Reasoning deck — real questions with worked answers.

1. In PARCC mathematics, what does the practice of 'Reasoning and Sense-Making' require a student to do?

   To make sense of problems by understanding what is being asked, to look for entry points and structure, and to reason quantitatively and abstractly so that answers are evaluated for whether they make sense in context.

2. What is the difference between 'reasoning quantitatively' and 'reasoning abstractly' in mathematical sense-making?

   Reasoning quantitatively means attending to the meaning of quantities and their units in context; reasoning abstractly means decontextualizing a problem into symbols, manipulating them, and then re-contextualizing the result.

3. In sense-making, what does it mean to 'check the reasonableness' of an answer?

   Estimating the expected magnitude, verifying units, and confirming the solution fits the real-world constraints of the problem before accepting it as correct.

4. What does 'making sense of problems and persevering in solving them' (the first Standard for Mathematical Practice) entail?

   Analyzing givens, constraints, and goals; planning a solution pathway; monitoring progress; and changing course when needed instead of giving up.

5. In PARCC's 'Argument and Critique' practice, what are students expected to do with mathematical claims?

   Construct viable arguments using definitions, assumptions, and logical reasoning, and critique the reasoning of others by detecting flaws or justifying validity.

6. What is a 'viable argument' in mathematics?

   A logically sound justification built from stated assumptions, definitions, and previously established results that leads validly to the conclusion.

7. What distinguishes a counterexample from a proof when critiquing reasoning?

   A counterexample is a single case that disproves a universal claim, while a proof must show the claim holds for all cases within its scope.

8. When critiquing another student's argument on PARCC, what two outcomes should the response address?

   Whether the reasoning is correct (and why it works) or flawed (identifying the specific error and explaining why it fails).

9. What is the 'Modeling and Tools' practice in PARCC mathematics?

   Applying mathematics to real-world situations by building models, and strategically selecting and using appropriate tools such as calculators, graphs, diagrams, or technology.

10. List the typical steps of the mathematical modeling cycle.

    Identify variables and make assumptions, formulate a model, perform operations/analyze, interpret the results, validate against reality, and report or revise the model.

11. What does 'use appropriate tools strategically' mean as a mathematical practice?

    Knowing which tool (e.g., ruler, calculator, spreadsheet, graphing software) is helpful for a given task, recognizing its limitations, and using it to deepen understanding rather than as a crutch.

12. In modeling, what is the role of 'assumptions and simplifications'?

    They reduce a messy real situation to a tractable mathematical form; good modeling states assumptions explicitly so the model's validity and limits can be judged.

13. What does the 'Precision' practice (attend to precision) require?

    Communicating precisely with clear definitions and correct symbols, using accurate units and labels, and computing/expressing answers to an appropriate degree of accuracy.

14. What does 'look for and make use of structure' mean in mathematics?

    Recognizing patterns, forms, or composition in expressions and figures (e.g., seeing 7x+7y as 7(x+y)) to simplify or solve problems.

15. What does 'look for and express regularity in repeated reasoning' mean?

    Noticing when calculations repeat, then generalizing the process into a shortcut, rule, or formula while keeping oversight of the overall process.

16. Why is attending to units considered part of precision in PARCC tasks?

    Correct units ensure the answer is meaningful and comparable; mismatched or missing units indicate a reasoning error and can cost evidence/precision credit.

17. What does a PARCC Type I task assess, and how is it scored?

    Type I assesses Concepts, Skills, and Procedures; it uses machine-scorable items (often multiple-choice or technology-enhanced) and is the only task type that contributes to the calculator/no-calculator skill demonstration in full.

18. What is the primary focus of PARCC Type I items?

    Demonstrating fluency, conceptual understanding, and application of skills and procedures, balanced across the major, additional, and supporting content of the grade.

19. What does a PARCC Type II task assess?

    Type II tasks call for 'Expressing Mathematical Reasoning'—written arguments, justifications, critiques of reasoning, and precise explanations.

20. How are PARCC Type II tasks primarily scored?

    On the quality of the mathematical reasoning and the validity of the argument or critique, using a reasoning-focused rubric rather than just the final answer.

21. What does a PARCC Type III task assess?

    Type III tasks assess 'Modeling and Applications'—applying mathematics to real-world problems by modeling, interpreting, and connecting multiple concepts.

22. How are PARCC Type III tasks scored compared to Type I?

    Type III uses a modeling/application rubric that credits the modeling process, interpretation, and accuracy, whereas Type I is machine-scored for correct answers/procedures.

23. Match each PARCC math task type to its emphasis: Type I, Type II, Type III.

    Type I = concepts, skills, and procedures; Type II = expressing mathematical reasoning; Type III = modeling and applications.

24. Which PARCC math task types are hand-scored against rubrics rather than purely machine-scored?

    Type II (reasoning) and Type III (modeling) include human/rubric scoring of student-constructed responses; Type I is primarily machine-scored.

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