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GENERIC EVALUATION CRITERIA
20010-2015
Mathematics
College Transition
Yes
R-E-S-P-O-N-S-E
No
N/A
CRITERIA
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).
NOTES
INSTRUCTIONAL MATERIALS ADOPTION: 21st CENTURY LEARNING EVALUATION CRITERIA
GENERAL EVALUATION CRITERIA
20010-2015
Mathematics
College Transition
(Vendor/Publisher)
SPECIFIC LOCATION OF
CONTENT WITHIN PRODUCT
(IMR Committee) Responses
I=In-depth
A=Adequate
M=Minimal
N=Nonexistent
I
A
M
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
N
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)
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
20010-2015
Mathematics
College Transition
(Vendor/Publisher)
SPECIFIC LOCATION OF
CONTENT WITHIN PRODUCT
(IMR Committee) Responses
I=In-depth
A=Adequate
M=Minimal
N=Nonexistent
I
A
M
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.
N
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.
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).
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.
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.
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.
SPECIFIC EVALUATION CRITERIA
Mathematics
College Transition
The WVDE has recognized the need to identify students prior to high school graduation, who will be unprepared for college and/or who
will be enrolled in remedial mathematics courses, in order to provide additional instruction for these students. Students in grade 11 who
are either in the professional pathway, or are college bound in the skilled pathway and are not achieving the state assessment college
readiness benchmark in mathematics, will be required in grade 12 to take the college mathematics transition course. Since high school
students are allowed to choose the sequence of the mathematics courses in which they enroll, there is no specific mathematics course
required of all grade 11 students. Students in grade 11 can take Algebra I, Geometry, Algebra II, Trigonometry and/or higher level
mathematics courses. Specific objectives were identified as aligning to the West Virginia Higher Education Mathematics College
Readiness Standards.
For mathematics, there is a 100% alignment between the West Virginia Higher Education Mathematics College Readiness Standards
and the identified mathematics objectives. Following are the number and percent of objectives identified by course: Algebra I 12
objectives 32% Algebra II 7 objectives 18% Geometry 17 objectives 45% Trigonometry 2 objectives 05%. The college transition
mathematics course may be counted as a required mathematics credit for high school graduation. Rigorous benchmarks (cut scores) to
determine college readiness will be determined; it is important to note that mastery on the Grade 11 Mathematics WESTEST 2 may be
different from the benchmark for college readiness.
Standard 2: Algebra
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the
field of mathematics, students will
 demonstrate understanding of patterns, relations and functions,
 represent and analyze mathematical situations and structures using algebraic symbols,
 use mathematical models to represent and understand quantitative relationships, and
 analyze change in various contexts.
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.
(Vendor/Publisher)
SPECIFIC LOCATION OF
CONTENT WITHIN PRODUCT
(IMR Committee) Responses
I=In-depth
A=Adequate
M=Minimal
N=Nonexistent
I
A
M
For student mastery of content standards and objectives, the instructional materials
will provide students with the opportunity to
A. Algebra
1. Provide various opportunities to create and solve multistep linear equations, absolute value equations, and linear
inequalities in one variable, (with and without technology);
apply skills toward solving practical problems such as
distance, mixtures or motion and judge the
reasonableness of solutions.(A1.2.2)
N
2. Provide opportunities to investigate and develop and test
hypotheses to derive the laws of exponents and use them
to perform operations on expressions with integral
exponents. (A1.2.4)
3. Provide opportunities to investigate and analyze a given
set of data and prove the existence of a pattern
numerically, algebraically and graphically, write equations
from the patterns and make inferences and predictions
based on observing the pattern. (A1.2.5)
4. Provide opportunities to investigate and analyze situations
and solve problems by determining the equation of a line
given a graph of a line, two points on the line, the slope
and a point, or the slope and y intercept.(A1.2.7)
5. Provide various opportunities to extrapolate data
represented by graphs, tables and formulas to make
inferences and predictions on rate of change (slope) and
justify when communicating results within a project based
investigation. (A1.2.8)
6. Provide examples and exercises to create and solve
systems of linear equations graphically and numerically
using the elimination method and the substitution method,
given a real-world situation. (A1.2.9)
7. Provide examples and exercises to simplify and evaluate
algebraic expressions, add and subtract polynomials,
multiply and divide binomials by binomials or monomials
(A1.2.10)
8. Provide examples and exercises to simplify radical
expressions through adding, subtracting, multiplying and
dividing exact and approximate forms (A1.2.13)
9. Provide various opportunities to solve quadratic equations
by graphing (with and without technology), factoring,
quadratic formula, and draw reasonable conclusions
about a situation being modeled. (A1.2.14)
10. Provide examples and exercises to simplify and evaluate
rational expressions, add, subtract, multiply and divide
determine when an expression is undefined. (A1.2.16)
11. Provide opportunities to investigate and gather data to
create histograms, box plots, scatter plots and normal
distribution curves and use them to draw and support
conclusions about the data. (A1.2.19)
12. Provide opportunities to design experiments to model and
solve problems using the concepts of sample space and
probability distribution. (A1.2.20)
13. Provide various opportunities to factor higher order
polynomials by applying various methods including
factoring by grouping and the sum and difference of two
cubes; analyze and describe the relationship between the
factored form and the graphical representation. (A2.2.2)
14. Provide opportunities to investigate properties of complex
numbers, simplify powers of ‘i’, perform basic operations
with complex numbers, and give answers as complex
numbers in simplest form. (A2.2.3)
15. Provide examples and exercises to simplify expressions
involving radicals and fractional exponents, convert
between the two forms, and solve equations containing
radicals and exponents. (A2.2.4)
16. Provide various opportunities to solve quadratic equations
over the set of complex numbers: apply the techniques of
factoring, completing the square, and the quadratic
formula; use the discriminate to determine the number
and nature of the roots; identify the maxima and minima;
use words, graphs, tables, and equations to generate and
analyze solutions to practical problems.(A2.2.5)
17. Provide various opportunities to define a function and find
its zeros; express the domain and range using interval
notation; find the inverse of a function; find the value of a
function for a given element in its domain; and perform
basic operations on functions including composition of
functions.(A2.2.7)
18. Provide opportunities to investigate and analyze families
of functions and their transformations; recognize linear,
quadratic, radical, absolute value, step, piece-wise, and
exponential functions; analyze connections among words,
graphs, tables and equations when solving practical
problems with and without technology.(A2.2.8)
19. Provide examples and exercises to solve absolute value
inequalities graphically, numerically and algebraically and
express the solution set in interval notation. (A2.2.13)
B. Geometry
1. Provide opportunities to investigate and apply differentiate
and apply inductive and deductive reasoning, justify
conclusions in real-world settings.(G.3.2)
2. Provide various opportunities to validate conclusions by
constructing logical arguments using both formal and
informal methods with direct and indirect reasoning.
(G.3.4)
3. Provide various opportunities to 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. (G.3.5)
4. Provide opportunities to investigate and compare and
contrast 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. (G.3.6)
5. Provide opportunities to investigate and make conjectures
and justify congruence relationships with an emphasis on
triangles and employ these relationships to solve
problems. (G.3.7)
6. Provide opportunities to investigate and apply the general
properties of and compare and contrast the properties of
convex and concave quadrilaterals, parallelograms,
rectangles, rhombuses, squares and trapezoids (G.3.8)
7. Provide opportunities to investigate and draw conclusions
in problem solving situations that include two and three
dimensions of figures based on the properties of similarity.
(G.3.9)
8. Provide opportunities to 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). (G.3.10)
9. Provide opportunities to investigate, 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. (G.3.11)
10. Provide opportunities to investigate and apply the
Pythagorean Theorem and its converse to solve realworld problems and derive the special right triangle
relationships (i.e. 30-60-90, 45-45-90). (G.3.12)
11.
Provide opportunities to investigate and apply measures
of angles formed by chords, tangents, and secants of a
circle and draw conclusions for the relationship to its arcs.
(G.3.13)
12. Provide examples and exercises to find 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.(G.3.14)
13. Provide opportunities to investigate and develop
properties of tessellating figures and use those properties
to tessellate the plane. (G.3.15)
14. Provide opportunities to investigate, derive and justify
formulas for area, perimeter, surface area, and volume
using nets and apply them to solve real-world problems.
(G.3.16)
15. Provide opportunities to investigate and 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.(G.3.17)
16. Provide opportunities to investigate and construct a
triangle’s medians, altitudes, angle and perpendicular
bisectors using various methods; and develop their
relationships to be used in solving real-world problems.
(G.3.18)
17. Provide various opportunities to 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. (G.3.19)
18. Provide opportunities to investigate and apply the right
triangle definition of the six trigonometric functions of an
angle to determine the values of the function values of an
angle in standard position given a point on the terminal
side of the angle. determine the value of the other
trigonometric functions given the value of one of the
trigonometric functions and verify these values with
technology.using geometric principles and the
Pythagorean Theorem, determine the six function values
for the special angles and the quadrantal angles and use
them in real-world problems.(T.3.1)
19. Provide opportunities to investigate and compare circular
functions and the trigonometric function values to draw
inferences about coterminal angles and cofunctions.(T.3.1)
20. Provide resources that identify real-world problems within
a project based investigation involving triangles using the
trigonometric functions, the law of sines and the law of
cosines,. (T.3.8)