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GENERIC EVALUATION CRITERIA
20010-2015
Fifth 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
Fifth 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
Fifth 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
Fifth Grade Mathematics
Fifth grade objectives place emphasis on developing proficiency in using whole numbers, fractions (primary focus on adding and
subtracting fractions with like and unlike denominators and mixed numbers), and decimals to solve problems. Additional concepts
include collecting, displaying and analyzing data in a variety of ways and solving probability problems. Other problems involve area and
perimeter, classifing polygons, plotting points on a coordinate plane, and writing a number sentence using a variable to solve problems.
The use of the standard algorithm to solve multi-digit whole number division should be preceded by work with understanding and
justifying why the algorithm works. Continued work with concrete materials and appropriate technologies such as calculators and
computers is emphasized. Problem solving should be integrated throughout all the strands. The development of a variety of problemsolving strategies should be a major goal of mathematics at this grade-level. 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 all whole numbers using
multiple strategies (e.g., symbols, manipulatives, number
line).
2. read, write, order and compare all fractions and mixed
numbers using multiple strategies (e.g., symbols,
manipulatives, number line).
3. read, write, order and compare all decimals using multiple
strategies (e.g., symbols, manipulatives, number line).
4. demonstrate an understanding of place value of each digit
utilizing standard and expanded form in any whole
number using powers of 10 [(3 X 105) + (4 X 103) + 7 X
102) + (1 X 101) + 6].
12
5. estimate solutions to problems involving
 whole numbers
 decimals
 fractions
 and percents
to determine reasonableness using benchmarks.
6. use inductive reasoning to identify the divisibility rules of
2, 3, 5, 9 and 10 and apply the rules to solve application
problems.
7. determine and apply greatest common factor to write
equivalent fractions and to real-world problem situations.
8. determine and apply lowest common multiple to write
equivalent fractions and to real-world problem situations.
9. model and write equivalencies of
 fractions
 decimals,
 percents,
 and ratios.
10. analyze and solve application problems and justify
reasonableness of solution in problems involving addition
and subtraction of fractions and mixed numbers.
11. analyze and solve application problems and justify
reasonableness of solution in problems involving addition
and subtraction of decimals.
13
12. apply the distributive property as it relates to multiplication
over addition.
13. solve multi-digit whole number division problems using a
variety of strategies, including the standard algorithm and
justify the solutions.
14. demonstrate fluency in addition, subtraction, multiplication
and division of whole numbers.
15. solve real-world problems involving whole numbers,
decimals and fractions using multiple strategies and justify
the reasonableness by estimation.
B. Algebra
1. use inductive reasoning to find missing elements in a
variety of patterns (e.g., square numbers, arithmetic
sequences).
2. given an input/output model using two operations,
determine the rule, output or input.
3. solve simple equations and inequalities using patterns
and models of real-world situations,
4. create graphs on number lines of the equations and
interpret the results.
14
5. Model, identify and describe square, prime and composite
numbers.
C. Geometry
1. classify and compare triangles by sides and angles.
2. measure the angles of a triangle using a protractor.
3. construct and analyze three-dimensional shapes using
properties (i.e. edges, faces or vertices).
4. create a design with more than one line of symmetry.
5. construct a circle with a given radius or diameter.
6. draw a similar figure using a scale, given a real-world
situation.
D. Measurement
1. estimate, measure, compare, order and draw lengths of
real objects in parts of an inch up to 1/8 of an inch and
millimeters.
2. model, calculate and compare area of triangles and
parallelograms using multiples strategies (including, but
not limited to, formulas).
15
3. develop strategies (i.e. finding number of same sized units
of volume)to determine the volume of a rectangular prism;
solve application problems involving estimating or
measuring volume of rectangular prisms.
4. describe the effects on the measurements of a twodimensional shape (such as its perimeter and area) when
the shape is changed in some way, justify changes.
5. solve real-world problems requiring conversions within a
system of measurement.
6. estimate and/or measure the weight/mass of real objects
in ounces, pounds, grams, and kilograms.
7. collect, record, estimate and calculate elapsed times from
real-world situations (with and without technology)
8. determine the actual measurements of a figure from a
scale drawing, using multiple strategies.
E. Data Analysis and Probability
1. construct a sample space and make a hypothesis as to
the probability of a real life situation overtime, test the
prediction with experimentation, and present conclusions
(with and without technology).
16
2. construct, read, and interpret tables, charts, and graphs
including stem and leaf plots to draw reasonable
inferences or verify predictions.
3. collect and organize real-world data to construct a circle
graph (with and without technology), present data and
draw conclusions.
4. collect and analyze data using mean, median and mode
to determine the best statistical measure.
17