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GENERIC EVALUATION CRITERIA
20010-2015
Eighth Grade Mathematics
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
Eighth Grade Mathematics
(Vendor/Publisher)
SPECIFIC LOCATION OF
CONTENT WITHIN PRODUCT
I
(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
Eighth Grade Mathematics
(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
Eighth Grade Mathematics
Eighth grade objectives provide an alternative course for students who do not take Algebra I in the eighth grade. In addition to
reinforcing the concepts presented in seventh grade, this course extends problem solving to a more sophisticated level. Linear
equations, systems of linear equations, proportional reasoning and rate of change are emphasized in the Algebra strand in preparation
for the formal Algebra I course. Lessons involving cooperative learning, manipulatives, or technology strengthen understanding of
concepts while fostering communication and reasoning skills. Calculator use is emphasized for all mathematical tasks including
assessment. 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 1: Number and Operations
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the
field of mathematics, students will
 demonstrate understanding of numbers, ways of representing numbers, and relationships among numbers and number
systems,
 demonstrate meanings of operations and how they relate to one another, and
 compute fluently and make reasonable estimates.
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
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.
Standard 4: Measurement
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the
field of mathematics, students will
 demonstrate understanding of measurable attributes of objects and the units, systems, and processes of
measurement, and
 apply appropriate techniques, tools and formulas to determine measurements.
Standard 5: Data Analysis and Probability
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the
field of mathematics, students will
 formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them,
 select and use appropriate statistical methods to analyze data,
 develop and evaluate inferences and predictions that are based on models, and
 apply and demonstrate an understanding of basic concepts of probability.
11
(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 …
A. Number and Operations
1. provide opportunities to analyze, describe and compare
the characteristics of rational and irrational numbers.
2. provide examples and opportunities to analyze and solve
application problems with
 powers,
 squares,
 square roots,
 scientific notation, and
verify solutions using estimation techniques.
3. provide examples and opportunities to analyze and solve
grade-appropriate real-world problems with
 whole numbers,
 decimals,
 fractions,
 percents, percent increase and decrease,
 integers, and
including, but not limited to, rates, tips, discounts, sales
tax and interest and verify solutions using estimation
techniques.
12
B. Algebra
1. provide opportunities to use a variety of strategies to solve
one and two-step linear equations and inequalities with
rational solutions; to defend the selection of the strategy;
to graph the solutions and justify the reasonableness of
the solution.
2. provide examples and opportunities to identify
proportional relationships in real-world situations, then to
find and select an appropriate method to determine the
solution; to justify the reasonableness of the solution.
3. provide examples and opportunities to add and subtract
polynomials limited to two variables and positive
exponents.
4. provide examples and opportunities to use systems of
linear equations to analyze situations and solve problems.
5. provide examples and opportunities to apply inductive and
deductive reasoning to write a rule from data in an
input/output table, to analyze the table and the rule to
determine if a functional relationship exists.
6. provide opportunities to graph linear equations and
inequalities within the Cartesian coordinate plane by
generating a table of values (with and without
technology).
13
7. provide examples and opportunities to formulate and
apply a rule to generate an arithmetic, geometric and
algebraic pattern.
8. provide examples and opportunities to determine the
slope of a line using a variety of methods including
 graphing
 change in y over change in x
 equation
9. provide examples and opportunities to represent and
solve real-world grade-appropriate problems using
multiple strategies and justify solutions.
10. provide opportunities to identify a real life problem
involving change over time; make a hypothesis as to the
outcome; develop, justify, and implement a method to
collect, organize, and analyze data; generalize the results
to make a conclusion; compare the hypothesis and the
results of the investigation; present the project using
words, graphs, drawings, models, or tables.
C. Geometry
1. provide opportunities to justify the relationships among
corresponding, alternate interior, alternate exterior and
vertical angles when parallel lines are cut by a transversal
using models, pencil/paper, graphing calculator, and
technology.
14
2. provide opportunities to classify polyhedrons according to
the number and shape of faces; use inductive reasoning
to determine the relationship between vertices, faces and
edges (edges + 2 = faces + vertices).
3. provide examples and opportunities to identify, apply, and
construct perpendicular and angle bisectors with and
without technology ) given a real-world situation.
4. provide opportunities to create geometric patterns
including tiling, art design, tessellations and scaling using
transformations (rotations, reflections, translations) and
predict results of combining, subdividing, and changing
shapes of plane figures and solids.
5. provide examples and opportunities to create scale
models of similar figures using ratio, proportion with
pencil/paper and technology and determine scale factor.
6. provide examples and opportunities to make and test a
conjecture concerning
 regular polygons,
 the cross section of a solid such as a cylinder,
cone, and pyramid,
 the intersection of two or more geometric figures in
the plane (e.g., intersection of a circle and a line),
and justify the results.
15
D. Measurement
1. provide examples and opportunities to select and apply an
appropriate method to solve; justify the method and the
reasonableness of the solution of problems involving
volume of
 prisms
 cylinders
 cones
 pyramids
 spheres
given real-world problem solving situations.
2. provide examples and opportunities to solve problems
involving missing measurements in plane and solid
geometric figures using formulas and drawings including
irregular figures, models or definitions.
3. provide examples and opportunities to solve right triangle
problems where the existence of triangles is not obvious
using the Pythagorean Theorem and indirect
measurement in real-world problem solving situations.
16
E. Data Analysis and Probability
1. provide examples and opportunities to determine and
explain whether a real-world situation involves
permutations or combinations, then use appropriate
technology to solve the problem.
2. provide examples and opportunities to compare the
experimental and theoretical probability of a given
situation (including compound probability of a dependent
and independent event).
3. provide examples and opportunities to create and
extrapolate information from multiple-bar graphs, box and
whisker plots, and other data displays using appropriate
technology.
4. provide examples and opportunities to analyze problem
situations, games of chance, and consumer applications
using random and non-random samplings to determine
probability, make predictions, and identify sources of bias.
5. provide examples and opportunities to draw inferences,
make conjectures and construct convincing arguments
involving different effects that changes in data values
have on measures of central tendency misuses of
statistical or numeric information, based on data analysis
of same and different sets of data.
17