Regents Examination in Geometry (Common Core) Not all slides have annotations. Slides that contain the targeted information do not have annotations. Slides that do not already contain the “talking points” have annotations. These slides are mainly the Sample Items slides. Please note that the “refer to page . . . “ in the top right corner of the slide is the page reference to the appropriate NTI document; Educator Guide to the Regents Examination in Geometry (Common Core), Question Types and Development, or Sample and Comparison Items. EngageNY.org

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

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

Test Guide refer to page 2 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. EngageNY.org

Test Guide refer to page 2 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. EngageNY.org

Percent of Test By Credit Test Guide refer to page 3 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) Modeling with Geometry (G-GMD) 8% - 15% This chart shows the distribution of credits per test for each Domain level in Geometry. This information will help teachers to determine the level of classroom focus for the various domains. EngageNY.org

Test Guide refer to page 4 Content Chart EngageNY.org Conceptual Category Domain Cluster Cluster Emphasis Standard Geometry Congruence 27% - 34% Experiment with transformations in the plane Supporting 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 constructions G-CO.12 G-CO.13 Similarity, Right Triangles, & Trigonometry 29% - 37% Understand similarity in terms of similarity transformations 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 circles G.C.5 Expressing Geometric Properties with Equations 12% - 18% Translate between the geometric description and the equation for a conic section G.GPE.1 Use coordinates to prove simple geometric theorems algebraically G.GPE.4 G.GPE.5 G.GPE.6 G.GPE.7 Geometric Measurement & Dimensions Explain volume formulas and use them to solve problems 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 situations G.MG.1 G.MG.2 G.MG.3 This chart shows the Cluster within each Domain and the Standards associated with each Cluster. It also shows the cluster emphasis identifying which clusters hold the greatest focus (Major), which clusters support the Major clusters (Supporting), and those clusters that may not connect tightly or explicitly to the major work of the Geometry course (Additional). EngageNY.org

Test Guide Question Format refer to page 6 Part I – Multiple-Choice Questions Parts II, III, IV – Constructed-Response Questions Regents Examination in Geometry (Common Core) Design Test Component Number of Questions Credits per Question Total Credits in Section Part I 24 2 48 Part II 8 16 Part III 4 Part IV 1 6 Total 37 - 86 This chart shows the Test breakdown by question and credits. EngageNY.org

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

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

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

Question Types & Development 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 EngageNY.org

Question Types & Development 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 EngageNY.org

Question Types & Development 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 EngageNY.org

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. EngageNY.org

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. EngageNY.org

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 The Sample Items are examples of shifts in Geometry (Common Core) from the 2005 NYS Learning Standards. EngageNY.org

MC Sample Question refer to page 1 1 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?         This question demonstrates new content. The method of finding the coordinates of a point that divides a directed line segment into a given ratio is a generalization of the midpoint formula. This gives students a stronger foundation and a more versatile understanding of analytic geometry. In the past it was find the midpoint. Now students will not only need to find the point that divides a segment into a ratio of 1:1 (page 3 - find the midpoint) but also find a point that divides a directed line segment into other ratios such as 3 to 2. Please note that the directed line segment also corresponds to the direction of the ratio. EngageNY.org

2pt CR Sample Question refer to page 13 A B 3 5 EngageNY.org   A B 3 5   This question demonstrates new content. Similar circles can be determined by describing the similarity transformations that map one circle onto the other. Typically this will include describing the translation mapping the center of one circle (circle A) onto the center of the other circle (B). Then, describe the dilation by identifying the center of dilation and the scale factor to map one circle (A) onto the other (B). EngageNY.org

2pt CR Sample Question refer to page 17 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. This question requires students to use Cavalieri’s principle to explain why these volumes are equal. Where as in the past (page 19), students used a procedure to find a missing dimension. This shift allows a student to demonstrate a greater understanding of volume. EngageNY.org

4pt CR Sample Question refer to page 29 L A D C N EngageNY.org   L A D C N   Similar to past questions, this question requires that students prove two triangles are congruent. As this question shows, students may also be require the student to describe a sequence of rigid motions that map one triangle onto the other, demonstrating the connection between rigid motion and congruence. Please note that you can have a sequence of one rigid motion.   EngageNY.org

4pt CR Sample Question refer to page 33 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. This question shows right triangle trigonometry, a new topic to the Geometry course which was previously covered in Integrated Algebra (page 36). The students are required to use trigonometric functions to solve multi-step application problems that model right triangles. It also integrates the use of prior knowledge of unit rates from previous grade-levels to answer the question. EngageNY.org

4pt CR Sample Question refer to page 45 12 Trees 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. Students are required to solve modeling problems using shapes, their measures, and their properties. This Common Core Sample Question is a multi-step question that draws on multiple ideas such as density and volume. EngageNY.org

6pt CR Sample Question refer to page 49 A B C O D EngageNY.org   A B C D O   Students are required to use similarity criteria to prove relationships in geometric figures rather than using these relationships only to solve a procedural problem as found on page 52. This questions demonstrates the use of auxiliary lines in order to prove this theorem. This is also an example of a theorem that is not explicitly listed in the CCLS. EngageNY.org

Questions? EngageNY.org