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Regents Examination in Geometry (Common Core)

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Regents Examination in Geometry (Common Core)

• Test Guide• Question Types & Development• Clarifications• Sample Items & Comparisons

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Test Guide

Educator Guide to theRegents Examination in

Geometry (Common Core)

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Conceptual Categories are the highest organizing level in the high school CCLS for Mathematics.

The two conceptual categories for Geometry (Common Core) are Modeling and Geometry.

The Modeling conceptual category is woven throughout various standards.

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Test GuideThe Geometry conceptual category is divided into domains, clusters, and standards.

• Domains are larger groups of related clusters and standards. Standards from different domains may be closely related.

• Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject.

• Standards define what students should understand and be able to do. In some cases, standards are further articulated into lettered components.

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Test GuideRegents Examination in Geometry (Common Core) Blueprint

Conceptual Category Domains in Geometry Percent of Test

By Credit

Geometry

Congruence (G-CO) 27% - 34%

Similarity, Right Triangles, and Trigonometry (G-SRT) 29% - 37%

Circles (G-C) 2% - 8%

Expressing Geometric Properties with Equations (G-GPE) 12% - 18%

Geometric Measurement & Dimensions (G-GMD) 2% - 8%

Modeling with Geometry (G-GMD) 8% - 15%

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Test GuideContent Chart

Conceptual Category Domain Cluster Cluster Emphasis Standard

Geometry

Congruence27% - 34%

Experiment with transformations in the plane Supporting

G-CO.1G-CO.2G-CO.3G-CO.4G-CO.5

Understand congruence in terms of rigid motions

Major

G-CO.6G-CO.7G-CO.8

Prove geometric theoremsG-CO.9

G-CO.10G-CO.11

Make geometric constructions Supporting G-CO.12G-CO.13

Similarity, Right Triangles, & Trigonometry

29% - 37%

Understand similarity in terms of similarity transformations

Major

G-SRT.1aG-SRT.1bG-SRT.2G-SRT.3

Prove theorems involving similarity G.SRT.4G.SRT.5

Define trigonometric ratios and solve problems involving right trianglesG.SRT.6G.SRT.7G.SRT.8

Circles2% - 8%

Understand and apply theorems about circlesAdditional

G.C.1G.C.2G.C.3

Find arc lengths and areas of sectors of circles G.C.5

Expressing Geometric Properties with Equations

12% - 18%

Translate between the geometric description and the equation for a conic section Additional G.GPE.1

Use coordinates to prove simple geometric theorems algebraically Major

G.GPE.4G.GPE.5G.GPE.6G.GPE.7

Geometric Measurement & Dimensions

2% - 8%

Explain volume formulas and use them to solve problemsAdditional

G.GMD.1G.GMD.3

Visualize relationships between two-dimensional and three-dimensional objects G.GMD.4

Modeling with Geometry8% - 15% Apply geometric concepts in modeling situations Major

G.MG.1G.MG.2G.MG.3

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Test Guide

Regents Examination in Geometry (Common Core) Design

Test Component Number of Questions

Credits per Question

Total Credits in Section

Part I 24 2 48Part II 8 2 16Part III 4 4 16Part IV 1 6 6Total 37 - 86

Question FormatPart I – Multiple-Choice QuestionsParts II, III, IV – Constructed-Response Questions

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Test GuideMathematics Tools for the Regents Examination in Geometry (Common Core)

• Graphing Calculator• Straightedge• Compass

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Test GuideReference Sheet

• Same as Algebra I

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Question Types & Development

Question Types

• Multiple-Choice Questions• Constructed-Response Questions

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Question Types & Development

Question Types

Multiple-Choice Questions• primarily used to assess procedural fluency and

conceptual understanding• measure the Standards for Mathematical Content • may incorporate Standards for Mathematical

Practices and real-world applications• some questions require multiple steps

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Question Types & Development

Question Types

Constructed-Response Questions (2-credit)• students are required to show their work• may involve multiple steps• the application of multiple mathematics skills• real-world applications• may require students to explain or justify their

solutions and/or show their process of problem solving

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Question Types & Development

Question TypesConstructed-Response Questions (4-,6-credit)• require students to show their work in completing more

extensive problems which may involve multiple tasks and concepts

• students will need to reason abstractly and quantitatively• students may need to construct viable arguments to justify

and/or prove geometric relationships in order to demonstrate procedural and conceptual understanding

6-credit constructed-response questions• students will develop multi-step, extended logical arguments

and proofs involving major content and/or use modeling to solve real-world and mathematical application problems

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Development: Item-Writing GuidelinesThese guidelines for writing multiple-choice and constructed-response items serve to ensure that the items included on operational exams meet certain standards for alignment to curriculum, fairness, clarity, and overall quality.

• Using these guidelines to draft questions is one of many steps employed to help ensure a valid, fair, and quality assessment.

• Draft questions that meet these criteria are allowed to move forward in the development process. The next step is for the items to be reviewed, and edited when necessary, by a Committee of certified New York State educators.  Only items that are approved by the educator panel are allowed to be field-tested.

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Standards ClarificationsIn an effort to ensure that the standards can be interpreted by teachers and used effectively to inform classroom instruction, several standards of the Geometry curriculum have been identified as needing some clarification. These clarifications are outlined below.

• G-CO.3Trapezoid is defined as “A quadrilateral with at least one pair of parallel sides.”

• G-CO.10, G-CO.11, G-SRT.4Theorems include but are not limited to the listed theorems.

• G-CO.12Constructions include but are not limited to the listed constructions.

• G-SRT.5ASA, SAS, SSS, AAS, and Hypotenuse-Leg theorem are valid criteria for triangle congruence.AA, SAS, and SSS are valid criteria for triangle similarity.

• G-C.2Relationships include but are not limited to the listed relationships.

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Sample Items & Comparison

Let’s take an in-depth look at some of the Sample Items.

We’ll look at:• Selected Sample Items• Annotations• Rubric• Compares to past regents questions

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MC Sample Question1 What are the coordinates of the point on the directed line segment from K(–5,–4) to L(5,1) that partitions the segment into a ratio of 3 to 2? 

 

 

 

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2pt CR Sample Question

 

 

A B3

5

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5 Two stacks of 23 quarters each are shown below. One stack forms a cylinder but the other stack does not form a cylinder.

Use Cavalieri’s principle to explain why the volumes of these two stacks of quarters are equal.

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Question

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D C

N

L

A

 

 

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Question

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9 As shown below, a canoe is approaching a lighthouse on the coastline of a lake. The front of the canoe is 1.5 feet above the water and an observer in the lighthouse is 112 feet above the water.

At 5:00, the observer in the lighthouse measured the angle of depression to the front of the canoe to be 6°. Five minutes later, the observer measured and saw the angle of depression to the front of the canoe had increased by 49°. Determine and state, to the nearest foot per minute, the average speed at which the canoe traveled toward the lighthouse.

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Question

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12Trees that are cut down and stripped of their branches for timber are approximately cylindrical. A timber company specializes in a certain type of tree that has a typical diameter of 50 cm and a typical height of about 10 meters. If the density of the wood is 380 kilograms per cubic meter, and the wood can be sold by mass at a rate of $4.75 per kilogram, determine and state the minimum number of whole trees that must be sold to raise $50,000.

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Question

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AB

C

D

O

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Question

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Questions?