Transcript Presentation

Regents Examination in
Geometry (Common Core)
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Regents Examination in
Geometry (Common Core)
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Test Guide
Question Types & Development
Clarifications
Sample Items & Comparisons
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Test Guide
Educator Guide to the
Regents Examination in
Geometry (Common Core)
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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.
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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.
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Test Guide refer to page 3
Regents Examination in Geometry (Common Core) Blueprint
Conceptual
Category
Domains in Geometry
Congruence (G-CO)
27% - 34%
Similarity, Right Triangles, and
Trigonometry (G-SRT)
29% - 37%
Circles (G-C)
Geometry
Percent of Test
By Credit
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 Guide refer to page 4
Content Chart
Conceptual Category
Domain
Cluster
Experiment with transformations in the plane
Congruence
27% - 34%
Cluster
Emphasis
Supporting
Understand congruence in terms of rigid motions
Major
Prove geometric theorems
Make geometric constructions
Supporting
Understand similarity in terms of similarity transformations
Similarity, Right Triangles,
& Trigonometry
29% - 37%
Geometry
Prove theorems involving similarity
Major
Define trigonometric ratios and solve problems involving right triangles
Circles
2% - 8%
Understand and apply theorems about circles
Additional
Find arc lengths and areas of sectors of circles
Expressing Geometric
Properties with Equations
12% - 18%
Geometric Measurement
& Dimensions
2% - 8%
Modeling with Geometry
8% - 15%
Translate between the geometric description and the equation for a
conic section
Use coordinates to prove simple geometric theorems algebraically
Apply geometric concepts in modeling situations
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G-CO.1
G-CO.2
G-CO.3
G-CO.4
G-CO.5
G-CO.6
G-CO.7
G-CO.8
G-CO.9
G-CO.10
G-CO.11
G-CO.12
G-CO.13
G-SRT.1a
G-SRT.1b
G-SRT.2
G-SRT.3
G.SRT.4
G.SRT.5
G.SRT.6
G.SRT.7
G.SRT.8
G.C.1
G.C.2
G.C.3
G.C.5
Additional
Major
Explain volume formulas and use them to solve problems
Visualize relationships between two-dimensional and threedimensional objects
Standard
Additional
G.GPE.1
G.GPE.4
G.GPE.5
G.GPE.6
G.GPE.7
G.GMD.1
G.GMD.3
G.GMD.4
Major
G.MG.1
G.MG.2
G.MG.3
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Test Guide refer to page 6
Question Format
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
Part II
Part III
Part IV
Total
24
8
4
1
37
2
2
4
6
-
48
16
16
6
86
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Test Guide refer to page 7
Mathematics Tools for the Regents
Examination in Geometry (Common Core)
• Graphing Calculator
• Straightedge
• Compass
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Test Guide refer to page 8
Reference 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 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
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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.
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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.
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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 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?
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2pt CR Sample Question refer to page 13
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A
B
3
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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.
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4pt CR Sample Question refer to page 29
L
D A
C
N
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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.
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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.
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6pt CR Sample Question refer to page 49
A
B
O
C
D
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Questions?
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