Regents Exams: Mathematics – Geometry Sample Items

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UPDATE 12/23/2014: Geometry Sample Items - Fall 2014 now available from downloadable resources below.

New York State Common Core Sample Questions: Regents Examination in Geometry (Common Core)

With the adoption of the New York P-12 Common Core Learning Standards (CCLS) in ELA/Literacy and Mathematics, the Board of Regents signaled a shift in both instruction and assessment. Educators around the state have already begun instituting Common Core instruction in their classrooms. To aid in this transition, we are providing sample Regents Examination in Geometry (Common Core) questions to help students, parents, and educators better understand the instructional shifts demanded by the Common Core and the rigor required to ensure that all students are on track to college and career readiness.

These Questions Are Teaching Tools
The sample questions emphasize the instructional shifts demanded by the Common Core. These questions include multiple-choice and constructed response. The sample questions are teaching tools for educators and can be shared freely with students and parents. They are designed to help clarify the way the Common Core should drive instruction and how students will be assessed on the Geometry Regents Examination in Geometry measuring CCLS beginning in June 2015. NYSED is eager for feedback on these sample questions. Your input will guide us as we develop future exams.

These Questions Are NOT Test Samplers
While educators from around the state have helped craft these sample questions, they have not undergone the same extensive review, vetting, and field testing that occurs with actual questions used on the State exams. The sample questions were designed to help educators think about content, NOT to show how operational exams look exactly or to provide information about how teachers should administer the test.

How to Use the Sample Questions

  • Interpret how the standards are conceptualized in each question.
  • Note the multiple ways the standards are assessed throughout the sample questions.
  • Look for opportunities for mathematical modeling, i.e., connecting mathematics with the real world by conceptualizing, analyzing, interpreting, and validating conclusions in order to make decisions about situations in everyday life, society, or the workplace.
  • Consider the instructional changes that will need to occur in your classroom.
  • Notice the application of mathematical ways of thinking to real-world issues and challenges.
  • Pay attention to the strong distractors in each multiple-choice question.
  • Don’t consider these questions to be the only way the standards will be assessed.
  • Don’t assume that the sample questions represent a mini-version of future State exams.

Understanding Math Sample Questions

Multiple-Choice Questions
Sample multiple-choice math questions are designed to assess CCLS math standards. Math multiple-choice questions assess procedural fluency and conceptual understanding. Unlike questions on past math exams, many require the use of multiple skills and concepts. Within the sample questions, all distractors will be based on plausible missteps.

Constructed Response Questions
Math constructed response questions are similar to past questions, asking students to show their work in completing one or more tasks or more extensive problems. Constructed response questions allow students to show their understanding of math procedures, conceptual understanding, and application.

Format of the Math Sample Questions Document
The Math Sample Questions document is formatted so that headings appear below each item to provide information for teacher use to help interpret the item, understand measurement with the CCLS, and inform instruction. A list of the headings with a brief description of the associated information is shown below.

Key: This is the correct response or, in the case of multiple-choice items, the correct option.

Measures CCLS: This item measures the knowledge, skills, and proficiencies characterized by the standards within the identified cluster.

Mathematical Practices: If applicable, this is a list of mathematical practices associated with the item.

Commentary: This is an explanation of how the item measures the knowledge, skills, and proficiencies characterized by the identified cluster.

Rationale: For multiple-choice items, this section provides the correct option and demonstrates one method for arriving at that response. For constructed response items, one possible approach to solving the item is shown followed by the scoring rubric that is specific to the item. Note that there are often multiple approaches to solving each problem. The rationale section provides only one example. The scoring rubrics should be used to evaluate the efficacy of different methods of arriving at a solution.

Downloadable Resources

Resources may contain links to sites external to the website. These sites may not be within the jurisdiction of NYSED and in such cases NYSED is not responsible for its content.