PUBLISHER:
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GENERIC EVALUATION CRITERIA
20010-2015
Third 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
Third 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
Third 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
Third Grade Mathematics
Third grade objectives extend the students’ mathematical skills and concepts through concrete experiences and appropriate
technology. These concepts and operations include: whole number operations; comparing and ordering numbers to hundredths and ten
thousands; fractions and decimals; recall of multiplication facts with corresponding division facts. Additional concepts include gathering
and organizing data, estimating and performing measurements. 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 and write numbers to 10,000.
2. order and compare numbers to 10,000 using a variety of
strategies (e.g., symbols, manipulatives, number line).
3. read and write decimals to hundredths, with
manipulatives.
4. order, and compare decimals to hundredths, with
manipulatives.
5. identify place value of each digit utilizing standard and
expanded form to 10,000.
6. apply estimation skills (rounding, benchmarks, compatible
numbers) to solve and evaluate reasonableness of an
answer.
12
7. demonstrate an understanding of fractions as part of a
whole/one and as part of a set/group using models and
pictorial representations.
8. create concrete models and pictorial representations to
compare and order fractions with like and unlike
denominators.
9. create concrete models and pictorial representations to
add and subtract fractions with like denominators, and
verify results.
10. use concrete models and pictorial representations to
demonstrate an understanding of equivalent fractions.
11. use concrete models and pictorial representations to
demonstrate an understanding of proper and improper
fractions and mixed numbers.
12. add 2- and 3-digit whole numbers and money with and
without regrouping.
13. subtract 2- and 3-digit whole numbers and money with
and without regrouping.
14. demonstrate and model multiplication (repeated addition,
arrays).
15. demonstrate and model division (repeated subtraction,
partitioning).
13
16. use and explain the operations of multiplication and
division including the properties (e.g., identity element of
multiplication, commutative property, property of zero,
associative property, inverse operations).
17. recall basic multiplication facts and the corresponding
division facts.
18. model the distributive property in multiplication of 2- and
3-digit numbers by a 1-digit number.
19. use models to demonstrate division of 2- and 3-digit
numbers by a 1-digit number.
20. create grade-appropriate real-world problems involving
any of the four operations using multiple strategies,
explain the reasoning used, and justify the procedures
selected when presenting solutions.
B. Algebra
1. analyze and extend geometric patterns.
2. analyze and extend numeric patterns.
3. create an input/output model using addition, subtraction,
multiplication or division.
4. analyze a given pattern and write the rule.
14
5. write equivalent numerical expressions and justify
equivalency.
6. use symbol and letter variables to represent an unknown
quantity and determine the value of the variable.
C. Geometry
1. identify and create new polygons by transforming
polygons.
2. identify and create new polygons by combining and
decomposing polygons.
3. identify, describe, and classify the following geometric
solids according to the number of faces, edges, and
vertices:
 cube
 rectangular solid
 cylinder
 cone
 pyramid
4. identify a solid figure from a plane drawing.
5. construct a solid figure from a plane drawing.
6. identify, describe and draw lines of symmetry in twodimensional shapes.
15
7. model, describe, and draw lines and rays.
8. model, describe, and draw angles including right, obtuse,
and acute angles.
9. draw an example of a flip, slide and turn (reflection,
translation, and rotation) given a model.
10. name the location of a point on a first-quadrant grid,
represent using ordered pairs.
D. Measurement
1. Within a project based investigation, identify a real life
situation, consider a number of variables and use
appropriate measurement tools, overtime, make a
hypothesis as to the change over time; with more
precision than whole units;
 length in centimeters and inches,
 temperature in Celsius and Fahrenheit
 weight/mass in pounds and kilograms, and
design and implement a method to collect, organize, and
analyze data; analyze results to make a conclusion;
evaluate the validity of the hypothesis based upon
collected data; design a mode of presentation (with and
without technology).
2. estimate and find the perimeter and area of familiar
geometric shapes, using manipulatives, grids, or
appropriate measuring tools.
16
3. determine the formula for the area of a rectangle and
explain reasoning through modeling.
4. read time to 5-minute intervals (am and pm) using analog
and digital clocks.
5. compute elapsed time to the quarter-hour using a clock.
6. identify, count and organize coins and bills to display a
variety of price values from real-life examples with a total
value of $100 or less.
7. model making change using manipulatives.
E. Data Analysis and Probability
1. collect and organize grade-appropriate real-world data
from observation, surveys, and experiments, and identify
and construct appropriate ways to display data.
2. develop and conduct grade-appropriate experiments
using concrete objects (e.g. counters, number cubes,
spinners) to determine the likeliness of events and list all
outcomes.
3. analyze real-world data represented on a graph using
grade-appropriate questions.
17