PUBLISHER:
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GENERIC EVALUATION CRITERIA
20010-2015
Fourth 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
Fourth 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
Fourth 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
Fourth Grade Mathematics
Fourth grade objectives emphasize critical thinking skills to create independent problem solvers who possess a personalized set
of skills and strategies to solve problems in everyday life. Concepts which are stressed include: quick recall of multiplication and
corresponding division facts, multiplication and division of two-and three-digit numbers, construction and description of objects from
different perspectives, plotting points in quadrant one of a coordinate plane, estimation, reading temperatures, description of possible
outcomes in a given situation, use of calculators and computers, and describing mathematical relationships and patterns in other
content areas and the real-world. Additional concepts targeted include adding and subtracting like fractions, and adding and subtracting
decimals. 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 provide students with the opportunity to
A. Number and Operations
1. read, write, order, and compare whole numbers to the
millions place and decimals to thousandths place using a
variety of strategies (e.g. symbols, manipulatives, number
line, pictorial representations).
2. demonstrate an understanding of the place value of each
digit utilizing standard and expanded form through
1,000,000 with multiples of 10 [(5 X 10,000) + (3 X 1,000)
+ (4 X 10) + 2].
3. estimate solutions to problems including rounding,
benchmarks, compatible numbers and evaluate the
reasonableness of the solution, justify results.
12
4. using concrete models, benchmark fractions, number line
 compare and order fractions with like and unlike
denominators
 add and subtract fractions with like and unlike
denominators
 model equivalent fractions
model addition and subtraction of mixed numbers with
and without regrouping.
5. analyze the relationship of fractions to decimals using
concrete objects and pictorial representations.
6. round decimals to the nearest whole, 10th, or 100th place.
7. add and subtract whole numbers(up to five –digit number)
and decimals to the 1000th place, multiply (up to three
digits by two-digits, and divide(up to a three digit number
with a one and two-digit number).
8. solve multi-digit whole number multiplication problems
using a variety of strategies, including the standard
algorithm, justify methods used.
9. quick recall of basic multiplication facts and corresponding
division facts.
10. create grade-level real-world appropriate story problems
using multiple strategies including simple ratios, justify the
reason for choosing a particular strategy and present
results.
13
B. Algebra
1. determine the rule and explain how change in one
variable relates to the change in the second variable,
given an input/output model using two operations.
2. recognize and describe relationships in which quantities
change proportionally.
3. represent the idea of a variable as an unknown quantity
using a letter, write an expression using a variable to
describe a real-world situation.
4. solve real-world problems involving order of operations
including grouping symbols and the four operations,
C. Geometry
1. identify, classify, compare and contrast two-dimensional
(including quadrilateral shapes) and three-dimensional
geometric figures according to attributes.
2. recognize and describe three-dimensional objects from
different perspectives.
3. identify, draw, label, compare and contrast, and classify
 lines (intersecting, parallel, and perpendicular)
 angles (acute, right, obtuse, and straight)
14
4. identify and create a two-dimensional design with one line
of symmetry.
5. graph/plot ordered pairs on a first-quadrant grid and use
the coordinate system to specify location and describe
path.
6. draw and identify parts of a circle: center point, diameter,
and radius.
7. select, analyze and justify appropriate use of
transformations (translations, rotations, flips) to solve
geometric problems including congruency and tiling
(tessellations).
D. Measurement
1. select appropriate measuring tools, apply and convert
standard units within a system to estimate, measure,
compare and order real-world measurements including:
 lengths using customary (to the nearest one-fourth
inch) and metric units,
 weight,
 capacity,
 temperature, and
justify and present results.
2. Quantify area by finding the total number of same sized
units that cover a shape, develop a rule and justify the
formula for the area of a rectangle using the area model
representing multiplication.
15
3. read time to the minute, calculate elapsed time in
hours/minutes within a 24-hour period.
4. given real-world situations, count coins and bills and
determine correct change.
E. Data Analysis and Probability
1. read and interpret information represented on a circle
graph.
2. pose a grade-appropriate question that can be addressed
with data, collect, organize, display, and analyze data in
order to answer the question.
3. design and conduct a simple probability experiment using
concrete objects, examine and list all possible
combinations using a tree diagram, represent the
outcomes as a ratio and present the results.
4. solve real world problems using mean, median and mode.
16