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GENERIC EVALUATION CRITERIA
20010-2015
Mathematics
Algebra III
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
Algebra III
(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
Algebra III
(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
Algebra III
Algebra III is intended for students who have mastered the concepts of Algebra I, Geometry, and Algebra II. Algebra III objectives
develop and extend properties of higher degree polynomial functions, rational functions, exponential functions and logarithmic functions
using the common concepts and language of algebraic, graphical, and tabular representations. The use of analytic geometry for sense
making, conceptual understanding of abstract ideas and modeling real world applications is stressed, making use of calculators,
computers, and interactive activities. 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 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.
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. Algebra
1. Provide a variety of examples and exercises to use
properties of analytic geometry that
 justify and use the distance and
 midpoint formulas and
 negative reciprocal criterion for non-vertical
perpendicular lines.
2. Provide opportunities to factor higher order polynomials
by using techniques that can be applied to the factoring of
second degree polynomials.
3. Provide a variety of examples and exercises to relate
factored forms of polynomials to graphs, tables, and
solutions to problems in context.
11
4. Provide opportunities for students to relate analytical
attributes such as:
 characteristics of zeros,
 x- and y- intercepts,
 symmetry,
 asymptotes,
 end behavior,
 maximum and minimum points,
 and domain and range
 to graphical and algebraic representations of
polynomials and rational functions.
5. Provide exercises that allow students to analyze the
discriminant to classify the roots of quadratic equations
with real coefficients, and relate the existence of xintercepts of the graph to information obtained from the
discriminant.
6. Provide opportunities for students to solve equations with
extraneous roots and explain, using precise mathematical
language, why the extraneous roots are excluded from the
solution set.
7. Allow students the opportunity to compare and contrast
the use of interval notation, set notation, and number line
representations to express the domain and range of
functions.
12
8. Provide the opportunity to compare and contrast the
domain and range of a modeling function with the
restricted domain and range used in a real world situation;
justify the restricted domain and range choice for a
problem in context.
9. Provide a variety of examples and exercises to:
 differentiate between functions and relations;
 evaluate, add, subtract, multiply, divide, rationalize,
simplify, and compose functions (including rational,
radical and those with fractional exponents);
 express domain and range of functions.
10. Provide the opportunity to formulate strategies to solve
real life problems including compound interest and
exponential growth and decay.
11. Appropriately introduce and reinforce how to restrict the
possible rational zeros of a polynomial function by using
the Rational Zeros Theorem and Descartes’ Rule of
Signs; confirm the real zeros of a polynomial function by
using the Remainder and Factor Theorems.
12. Provide the opportunity to approximate zeros of a
polynomial or rational function using a graphing utility and
the Intermediate Value Theorem.
13
13. Provides students the opportunity to compare and
contrast the cases when 0<a<1 and a>1 for the general
exponential function f(x) =ax: graphs, asymptotes, domain
and range, and transformations. Interpret the number e
as a limit and use e to build exponential functions
modeling real world applications.
14. Provide students examples of Interpreting the number e
as a limit and use e to build exponential functions
modeling real world applications.
15. Provides students with the opportunity to use common
and natural logarithms in the evaluation of logarithmic
functions whose base is neither 10 nor e.
16. Provide students the opportunity to incorporate the
change of base formula and properties of logarithms to
simplify and expand algebraic expressions and to solve
logarithmic and exponential equations.
17. Provides a variety of examples and exercise to solve
equations involving
 radical,
 exponential,
 and logarithmic expressions
18. Provides students with opportunities to formulate
strategies to solve real life problems involving compound
interest and exponential growth and decay.
14
19. Builds conceptual understanding through opportunities for
students to build on the skills of solving linear equations in
two variables using elimination, substitution, or matrix
methods to solve systems with three or more unknowns
involving real world applications and to categorize
systems of equations as zero, one, or infinitely many
solutions, by both geometric and algebraic methods.
20. Provide students with materials and resources that
support their work in groups to choose a real life
situation that could be modeled by a polynomial, rational,
exponential, or logarithmic function, and make a
hypothesis, design an experiment, gather data, analyze
data, refine the hypothesis into an appropriate
mathematical model, use the model to make a prediction,
test the prediction using the experimental setup, and
compare the results. Present the collaboration as a
project using words, graphs, tables, equations, and
appropriate presentation tools.
15
21. Provide opportunities for students to
 convert between graphs and equations of circles
identifying important features from either
representation;
 translate from general form to standard form by
completing the square and describe readily usable
characteristics of each form;
 represent a circle as two functions graphically and
algebraically.
22. Provide a variety of examples and exercises to
 analyze a piecewise defined function in multiple
representations,
 to give its domain, intercepts, range, constituent
pieces as elementary functions, and end behavior;
 apply to real world data.
23. Enable students to:
 determine the average rate of change of a function
between any two points on its graph and use this rate
to find the equation of a secant line;
 interpret the average rate of change to solve real
world problems;
 relate signs of average rate of change to the function
increasing or decreasing;
 and demonstrate a geometrical and conceptual
understanding of the difference quotient.
16
24. Provide a variety of examples and exercises to
 use synthetic division to divide a polynomial,
 verify a factor,
 and determine its roots;
 compare and contrast synthetic division to long
division.
25. Provide opportunities to investigate how the multiplicity of
zeros of polynomial functions affects the graph;
characterize a polynomial given the zeros, the behavior of
the graph at the zeros, and the end-behavior.
26. Use of multiple strategies, interactive software, websites,
and/or applets to investigate the characteristics of a
transformation involving
 polynomial,
 radical,
 absolute value,
 logarithmic,
 or exponential functions,
 unravel the effect of a series of transformations using
multiple representations
17
27. Define and discusses one-to-one functions including:
 the role of the Vertical and Horizontal Line Tests;
 uses multiple representations in describing the
relationship between a function and its inverse,
including the domain and range of each;
 identifies and explains the need for appropriate
restrictions necessary to guarantee an inverse
function;
 discusses the symmetrical relationship associated
with the line y=x between the function and its inverse
and explain the geometric reason the symmetry exists;
 demonstrates how to algebraically verify that two
functions are inverses of each other.
28. Provides students the opportunity to prioritize relevant
techniques to graph a given rational function:
 explaining the relevance of symmetry, end behavior,
and domain and range;
 using zeros of the denominator to differentiate
between vertical asymptotes and points of
discontinuity;
 using long division to determine end behavior and
explain the role of quotient and remainder in the
process;
 explaining how the factors of the numerator and
denominator can be used to analytically and
graphically determine where the graph will fall above
or below the x-axis.
18