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GENERIC EVALUATION CRITERIA
20010-2015
Sixth 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
Sixth 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
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
Sixth 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
Sixth Grade Mathematics
Sixth grade objectives place continued emphasis on the study of whole numbers, decimals and fractions (primary focus on
multiplication and division of fractions and mixed numbers). Introductory work with integers includes understanding why the rules for
adding, subtracting, multiplying and dividing integers work. Opportunities to apply these skills to real world situations help to make
sense of the mathematics. Calculators, computers and manipulatives may be used to solve problems. Probability, Statistics, Geometry,
and Pre-Algebra will be stressed. Concepts of using ratios to compare data sets, making geometric constructions of three-dimensional
figures and solving problems involving circles, volume and surface area are emphasized. 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 a variety of examples and exercises to
demonstrate an understanding of large numbers by
converting and comparing numbers in scientific notation
and standard notation (with and without technology).
2. provide a variety of examples and exercises to determine
the greatest common factor and least common multiple
using multiple strategies to solve real-world problems; find
prime factorization of a number.
3. provide a variety of examples and exercises to compare
and order integers using multiple strategies (e.g.,
symbols, manipulatives, number line).
12
4. provide a variety of examples and exercises to analyze
and solve real-world problems involving addition,
subtraction , multiplication and division of
 whole numbers,
 fractions, mixed numbers,
 decimals
 integers
and justify the reasonableness by estimation.
5. provide a variety of examples and exercises to apply the
distributive, commutative, associative and identity
properties to numeric expressions and use to prove
equivalency.
6. provide a variety of examples and exercises to convert
between fractions/ratios, mixed numbers, decimals and
percents in appropriate real-world problems.
7. provide a variety of examples and exercises to compute
the percent of a number to solve application problems and
justify the reasonableness by estimation.
8. provide a variety of examples and exercises to
demonstrate an understanding of the effect of multiplying
and dividing, whole numbers, fractions and decimals by
numbers including 0, 1 and values between 0 and 1.
13
9. provide a variety of examples and exercises to develop
and test hypotheses to derive the rules for addition,
subtraction, multiplication and division of integers, justify
by using real-world examples and use them to solve
problems.
B. Algebra
1. provide examples and exercises to simplify numerical
expressions and evaluate algebraic expressions using
order of operations.
2. provide opportunities to use inductive reasoning to extend
patterns to predict the nth term (e.g., powers and
triangular numbers).
3. provide opportunities to create algebraic expressions that
correspond to real-world situations; use the expressions
to solve problems.
4. provide examples and exercises to determine the rule,
output or input; given an input/output model using one
operation, write an algebraic expression for the rule and
use to identify other input/output values.
5. provide examples and exercises to solve real-world
proportion problems involving rates, probability and
measurements using multiple strategies, justify selection
of strategies.
14
6. provide examples and exercises to write and solve onestep equations using number sense, properties of
operations and the idea of maintaining equality to
represent and solve real-world problems.
C. Geometry
1. provide opportunities to analyze characteristics using
defining properties of
 lines,
 angles,
 polygons,
 triangles, and
compare these geometric figures.
2. provide examples and exercises to use inductive
reasoning with the measures of interior angles in polygons
and derive the formula to determine the sum of the
measures of the interior angles.
3. provide examples and exercises to apply the concepts of
parallel, perpendicular, intersecting, and skew lines to
real-world situations (i.e. roads and routes).
4. provide examples and exercises to create designs using
line and rotational symmetry.
15
5. provide examples and exercises to predict, describe, and
perform transformations on two-dimensional shapes
 translations
 rotations
 reflections
6. provide examples and exercises to use geometric
representations to solve real-world problems.
7. provide examples and exercises to plot polygons on
coordinate grids, determine lengths and areas from the
graph.
D. Measurement
1. provide opportunities to determine an approximation for pi
using actual measurements.
2. provide examples and exercises to develop and test
hypotheses to determine formulas for
 perimeter of polygons, including composite figures
 area of parallelograms
 area of triangles
 area of composite figures made of parallelograms
and triangles
 circumference of a circle
 area of a circle
 volume of a rectangular prism
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3. provide opportunities to investigate, model and describe
surface area of rectangular prisms and cylinders; develop
strategies to determine the surface area of rectangular
prisms.
4. provide opportunities to develop strategies to determine
volume of cylinders; solve real-world problems involving
volume of cylinders, justify the results.
5. provide opportunities to construct a scale drawing given
the scale factor of a two-dimensional polygon.
E. Data Analysis and Probability
1. provide examples and exercises to collect, organize,
display, read, interpret and analyze real-world data using
appropriate graphs and tables (with and without
technology).
2. provide opportunities to identify a real life situation using
statistical measures (mean, median, mode, range,
outliers) overtime, make a hypothesis as to the outcome;
design and implement a method to collect, organize and
analyze data; analyze the results to make a conclusion;
evaluate the validity of the hypothesis based upon
collected data, design a mode of presentation using
words, graphs, models, and/or tables (with and without
technology).
17
3. provide opportunities to perform simple probability events
using manipulatives; predict the outcome given events
using experimental and theoretical probability; express
experimental and theoretical probability as a ratio, decimal
or percent.
4. provide opportunities to determine combinations and
permutations of given real-world situations by multiple
strategies, including creating lists.
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