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GENERIC EVALUATION CRITERIA
20010-2015
Mathematics
Geometry
Yes
R-E-S-P-O-N-S-E
No
N/A
CRITERIA
NOTES
I. INTER-ETHNIC
The instructional material meets the
requirements of inter-ethnic: concepts,
content and illustrations, as set by West
Virginia Board of Education Policy (Adopted
December 1970).
II. EQUAL OPPORTUNITY
The instructional material meets the
requirements of equal opportunity: concept,
content, illustration, heritage, roles
contributions, experiences and achievements
of males and females in American and other
cultures, as set by West Virginia Board of
Education Policy (Adopted May 1975).
1
INSTRUCTIONAL MATERIALS ADOPTION: 21st CENTURY LEARNING EVALUATION CRITERIA
GENERAL EVALUATION CRITERIA
20010-2015
Mathematics
Geometry
(Vendor/Publisher)
SPECIFIC LOCATION OF
CONTENT WITHIN PRODUCT
(IMR Committee) Responses
I=In-depth
A=Adequate
M=Minimal
N=Nonexistent
I
A
M
N
In addition to alignment of Content Standards and Objectives (CSOs), materials must also clearly connect to
Learning for the 21st Century which includes opportunities for students to develop
A.
Learning Skills

Thinking and Problem-Solving Skills/ Rigor and Depth of Content
Content is presented in a way that deepens student understanding
through engagement in meaningful, challenging mathematics that
builds on prior knowledge and promotes connections among
mathematical concepts.

Thinking and Problem-Solving Skills /Development of Conceptual
Understanding
Learning opportunities require students to develop their own viable
mathematical understandings and help them build connections
between mathematical ideas.

Information and Communication Skills/Mathematical Language
Appropriately introduce and reinforce in multiple ways all necessary
terms and symbols.

Personal and Work Place Productivity Skills
2
B.
21st Century Tools

Problem-solving tools (such as spreadsheets, decision support, design
tools)

Communication, information processing and research tools (such as word
processing, e-mail, groupware, presentation, Web development, Internet
search tools)

Personal development and productivity tools (such as e-learning, time
management/calendar, collaboration tools)
3
INSTRUCTIONAL MATERIALS ADOPTION: 21st Century Learning EVALUATION CRITERIA
The general evaluation criteria apply to each grade level and are to be evaluated for each grade level unless otherwise specified. These criteria consist of
information critical to the development of all grade levels. In reading the general evaluation criteria and subsequent specific grade level criteria, e.g. means
“examples of” and i.e. means that “each of” those items must be addressed. Eighty percent of the combined general and specific criteria must be met with I
(In-depth) or A (Adequate) in order to be recommended.
20010-2015
Mathematics
Geometry
(Vendor/Publisher)
SPECIFIC LOCATION OF
CONTENT WITHIN PRODUCT
(IMR Committee) Responses
I=In-depth
A=Adequate
M=Minimal
N=Nonexistent
I
A
M
N
For student mastery of content standards and objectives, the instructional materials will provide students with the opportunity to
4. Multimedia
1. offer appropriate multimedia (e.g., software, audio, visual, internet
access) materials.
2. provide a website which provides links to relevant sites as well as
lesson plans, student activities and parent resources.
4
3. Integrate technology seamlessly when appropriate to model
mathematical situations, analyze data, calculate results, and solve
problems.
B. Scientifically-Based Research Strategies
1. Consistently require students to link prior knowledge to new
information to construct their own viable understandings of
mathematical ideas.
2. Consistently provide opportunities for students to solve complex
problems that have multiple entry points and the possibility of multiple
solution processes.
3. Consistently provide opportunities for students to communicate their
mathematical thinking processes to others orally, in writing, or
pictorially.
4. Routinely require students to develop and defend mathematical
conjectures, arguments, reasoning and proof.
5. Provide opportunities for the students to be involved in investigations
that enable them to make connections among mathematical ideas.
6. Expect students to develop multiple representations of the
mathematics in order to depict reasoning used to explain real world
phenomena or solutions to relevant problems and move fluently
between those representations.
7. Present varied teaching models with emphasis on differentiated
instruction in content, process, and product.
5
C. Critical Thinking
1. emphasize questioning models to promote higher order thinking skills
based on depth of knowledge.
2.
Consistently require students to discuss mathematics with each other and
with the teacher, make arguments, conjecture and reason, and
justify/clarify their ideas in writing and orally in precise mathematical
symbols and language.
3. Present real world application that is current, engaging, integrated
throughout the instruction, and promotes and develops critical
thinking.
D. Life Skills
1. address life skills (e.g., reading road maps, using reference tools,
researching, reading a newspaper, using want ads, completing an
application, applying the interview process and goal setting).
2. address habits of mind activities (e.g., literacy skills, interpersonal
communications, problem solving and self-directional skills).
E. Classroom Management
1. include opportunities for large group, small group, and independent
learning.
2. Consistently require students to explore mathematical ideas,
individually and collaboratively, while integrating the process
standards (see Section I of this rubric).
3. provide suggestions for differentiated instruction (e.g., practice
activities, learning stations, assessment, lesson plans).
6
F. Instructional Materials
1. Are organized according to WV content standards or other increments
that allow students to investigate and explore major mathematical
ideas; provide a variety of lessons, activities, and projects from which
to choose; and emphasize connections between mathematical ideas.
2. Consistently integrate tasks that engage students and invite them to
speculate and hypothesize, are open-ended, and require them to
determine appropriate strategies.
3. Provide teachers with guiding questions to aid students’ development
of mathematical discourse to further mathematical understanding.
4. Provide additional resources that are organized in a way that is easy
to access and use.
5. Include various instructional models to address varied learning styles
of students.
6. Provide extensive and varied opportunities to differentiate individual
needs for skill-building.
7. Provide supplemental materials for intervention and enrichment.
8. Provide teachers with support to properly integrate the process
standards using the available resources.
9. Include a teacher resource that builds content knowledge for the
teacher.
10. Spiral previously taught skills and strategies with new content.
7
G. Assessment
1. provide assessment formats commensurate with WV assessment
programs (e.g., WESTEST, NAEP, State Writing Assessment,
informal assessments, PLAN, EXPLORE, ACT and SAT).
2. provide opportunities for assessment based on performance-based
measures, open-ended questioning, portfolio evaluation, rubrics and
multimedia simulations.
3. provide benchmark and ongoing progress monitoring.
4. provide rubric-based differentiated assessment.
5. provide an electronic system for managing assessment data to
facilitate the implementation of tiered instruction
6. integrate student self-assessment for and of learning by providing
tools and organizers that are linked to clearly identified learning goals.
7. Integrate formal and informal means of assessment in the materials
for diagnostic, formative, and summative purposes.
8. include various types of assessments: performance tasks, multiple
choice, short answer, and free response.
8
H. Process Standards
1. Problem Solving: Provide frequent opportunities for students to
formulate, grapple with, and solve complex problems that require a
significant amount of effort and have multiple viable solution paths.
2. Communication: Routinely challenge students to communicate their
thinking to others orally, in writing, and/or pictorially, using precise
mathematical language.
3. Reasoning and Proof: Provide frequent opportunities for students to
complete mathematical investigations with and without technology;
develop conjectures, mathematical arguments and proofs to confirm
those conjectures.
4. Connections with Mathematics: Consistently establish connections,
and provide opportunities for students to establish connections,
among mathematical concepts and their real-world applications.
5. Representations: Provide frequent opportunities for students to
develop multiple representations of the mathematics in order to depict
reasoning used to explain real world phenomena or solutions to
relevant problems and move fluently between those representations.
9
SPECIFIC EVALUATION CRITERIA
Mathematics
Geometry
Geometry objectives are designed for students who have completed the objectives for Algebra I. Study includes experiences and
activities that foster in students a feeling for the value of geometry in their lives. Emphasis is placed on development of conjectures by
inductive processes using manipulatives and computer software. Cooperative learning groups are particularly effective in allowing
students to become proficient in analyzing conjectures and in formulating both formal and informal proofs. Emphasis should be placed
on connections to other branches of mathematics and other disciplines, and on workplace applications. The West Virginia Standards for
21st Century Learning include the following components: 21st Century Content Standards and Objectives and 21st Century Learning
Skills and Technology Tools. All West Virginia teachers are responsible for classroom instruction that integrates learning skills,
technology tools and content standards and objectives.
Standard 3: Geometry
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the
field of mathematics, students will
 analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical
arguments about geometric relationships,
 specify locations and describe spatial relationships using coordinate geometry and other representational systems,
 apply transformations and use symmetry to analyze mathematical situations, and
 solve problems using visualization, spatial reasoning, and geometric modeling.
10
(Vendor/Publisher)
SPECIFIC LOCATION OF
CONTENT WITHIN PRODUCT
(IMR Committee) Responses
I=In-depth
A=Adequate
M=Minimal
N=Nonexistent
I
A
M
N
For student mastery of content standards and objectives, the instructional materials
will provide students with the opportunity to
A. Geometry
1. Investigate representations of geometric figures, such as
points, lines, planes, segments, rays, and angles
pictorially with proper identification and distinguish
between undefined and defined terms.
2. differentiate and apply inductive and deductive reasoning,
justify conclusions in real-world settings.
3. use the basic concepts of symbolic logic including
identifying the converse, inverse, and contrapositive of a
conditional statement and test the validity of conclusions
with methods that include Venn Diagrams.
4. investigate, validate, communicate, and apply conclusions
by constructing logical arguments using both formal and
informal methods with direct and indirect reasoning.
11
5. construct formal and informal proofs by applying
definitions, theorems, and postulates related to such
topics as
 complementary,
 supplementary,
 vertical angles,
 angles formed by perpendicular lines, and
justify the steps. Provide opportunities for student exploration
using interactive websites or software.
6. investigate, compare and contrast, and apply the
relationships between angles formed by two lines cut by a
transversal when lines are parallel and when they are not
parallel, and use the results to develop concepts that will
justify parallelism.
7. investigate relationships, and develop multiple conjectures
and justify the congruence relationships with an emphasis
on triangles and employ these relationships to solve real
world problems.
8. use interactive geometric software and/or manipulatives
(geoboards or patty paper) to investigate, develop, and
identify general properties and compare and contrast the
properties of convex and concave quadrilaterals
 parallelograms
 rectangles
 rhombuses
 squares
 trapezoids
12
9. identify a real life situation that involves similarity in two or
three dimensions; pose a question; make a hypothesis as
to the answer, develop, justify, and implement a method
to collect, organize, and analyze related data; generalize
the results to make a conclusion; compare the hypothesis
and the conclusion; present the project numerically,
analytically, graphically and verbally using the predictive
and analytic tools of algebra and geometry (with and
without technology).
10. investigate measures of angles and lengths of segments
to determine the existence of a triangle (triangle
inequality) and to establish the relationship between the
measures of the angles and the length of the sides (with
and without technology).
11. verify and justify the basis for the trigonometric ratios by
applying properties of similar triangles and use the results
to find inaccessible heights and distances. Using the
ratios of similar triangles to find unknown side lengths and
angle measures, construct a physical model that
illustrates the use of a scale drawing in a real-world
situation.
13
12. use applets, interactive software or websites to
investigate, model and apply the Pythagorean Theorem
and its converse to solve real-world problems and derive
the special right triangle relationships (i.e. 30-60-90, 4545-90).
13. use of strategies (graphic organizers foldables, interactive
geometric software, websites or applets) to investigate
measures of angles formed by chords, tangents, and
secants of a circle and draw conclusions for the
relationship to its arcs.
14. explorations to determine angle measures of interior and
exterior angles; given a polygon, find the length of sides
from given data; and use properties of regular polygons to
find any unknown measurements of sides or angles.
15. develop properties of tessellating figures and use those
properties to tessellate the plane.
16. derive and justify formulas for area, perimeter, surface
area, and volume using nets and apply them to solve realworld problems.
17. consistently apply concepts of analytical geometry such
as formulas for distance, slope, and midpoint and apply
these to finding dimensions of polygons on the coordinate
plane.
14
18. construct a triangle’s medians, altitudes, angle and
perpendicular bisectors using various methods; and
develop logical concepts about their relationships to be
used in solving real-world problems.
19. create and apply concepts using transformational
geometry and laws of symmetry, of a
 reflection,
 translation,
 rotation,
 glide reflection,
 dilation of a figure, and
 develop logical arguments for congruency and
similarity.
15
20. compare and contrast Euclidean geometry to other
geometries (i.e. spherical, elliptic) using various
forms of communication such as development of
physical models, oral or written reports.
21. approximate the area of irregularly shaped regions
based on the approximations and the attributes of
the related region, develop a formula for finding the
area of irregularly shaped regions. Plan, organize
and present results by justifying conclusions.
16