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1 Regents Examination in Geometry (Common Core)

2 EngageNY.org2 Regents Examination in Geometry (Common Core) Test Guide Question Types & Development Clarifications Sample Items & Comparisons

3 EngageNY.org3 Test Guide Educator Guide to the Regents Examination in Geometry (Common Core)

4 EngageNY.org4 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. refer to page 2 Test Guide

5 EngageNY.org5 Test Guide The 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. refer to page 2

6 EngageNY.org6 Test Guide Regents 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% refer to page 3

7 EngageNY.org7 Test Guide Content Chart Conceptual CategoryDomainCluster Cluster Emphasis Standard Geometry Congruence 27% - 34% Experiment with transformations in the planeSupporting G-CO.1 G-CO.2 G-CO.3 G-CO.4 G-CO.5 Understand congruence in terms of rigid motions Major G-CO.6 G-CO.7 G-CO.8 Prove geometric theorems G-CO.9 G-CO.10 G-CO.11 Make geometric constructionsSupporting G-CO.12 G-CO.13 Similarity, Right Triangles, & Trigonometry 29% - 37% Understand similarity in terms of similarity transformations Major G-SRT.1a G-SRT.1b G-SRT.2 G-SRT.3 Prove theorems involving similarity G.SRT.4 G.SRT.5 Define trigonometric ratios and solve problems involving right triangles G.SRT.6 G.SRT.7 G.SRT.8 Circles 2% - 8% Understand and apply theorems about circles Additional G.C.1 G.C.2 G.C.3 Find arc lengths and areas of sectors of circlesG.C.5 Expressing Geometric Properties with Equations 12% - 18% Translate between the geometric description and the equation for a conic section AdditionalG.GPE.1 Use coordinates to prove simple geometric theorems algebraicallyMajor G.GPE.4 G.GPE.5 G.GPE.6 G.GPE.7 Geometric Measurement & Dimensions 2% - 8% Explain volume formulas and use them to solve problems Additional G.GMD.1 G.GMD.3 Visualize relationships between two-dimensional and three- dimensional objects G.GMD.4 Modeling with Geometry 8% - 15% Apply geometric concepts in modeling situationsMajor G.MG.1 G.MG.2 G.MG.3 refer to page 4

8 EngageNY.org8 Test Guide Regents Examination in Geometry (Common Core) Design Test Component Number of Questions Credits per Question Total Credits in Section Part I24248 Part II8216 Part III4416 Part IV166 Total37-86 Question Format Part I – Multiple-Choice Questions Parts II, III, IV – Constructed-Response Questions refer to page 6

9 EngageNY.org9 Test Guide Mathematics Tools for the Regents Examination in Geometry (Common Core) Graphing Calculator Straightedge Compass refer to page 7

10 EngageNY.org10 Test Guide Reference Sheet Same as Algebra I refer to page 8

11 EngageNY.org11 Question Types & Development Question Types Multiple-Choice Questions Constructed-Response Questions

12 EngageNY.org12 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

13 EngageNY.org13 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

14 EngageNY.org14 Question Types & Development Question Types Constructed-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

15 EngageNY.org15 Development: Item-Writing Guidelines These 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.

16 EngageNY.org16 Standards Clarifications In 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.3 Trapezoid is defined as “A quadrilateral with at least one pair of parallel sides.” G-CO.10, G-CO.11, G-SRT.4 Theorems include but are not limited to the listed theorems. G-CO.12 Constructions include but are not limited to the listed constructions. G-SRT.5 ASA, 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.2 Relationships include but are not limited to the listed relationships.

17 EngageNY.org17 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

18 EngageNY.org18 MC Sample Question 1What 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? refer to page 1

19 EngageNY.org19 2pt CR Sample Question AB 3 5 refer to page 13

20 EngageNY.org20 5Two 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. refer to page 17 2pt CR Sample Question

21 EngageNY.org21 D C N L A refer to page 29 4pt CR Sample Question

22 EngageNY.org22 9As 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. refer to page 33 4pt CR Sample Question

23 EngageNY.org23 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. refer to page 45 4pt CR Sample Question

24 EngageNY.org24 A B C D O refer to page 49 6pt CR Sample Question

25 EngageNY.org25 Questions?

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