PUBLISHER:
SUBJECT:
SPECIFIC GRADE:
COURSE:
TITLE:
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SE ISBN:
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Yes
R-E-S-P-O-N-S-E
No N/A
20010-2015
Mathematics
CRITERIA
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).
NOTES
1

INSTRUCTIONAL MATERIALS ADOPTION: 21 st CENTURY LEARNING EVALUATION CRITERIA
20010-2015
Mathematics
(Vendor/Publisher)
SPECIFIC LOCATION OF
CONTENT WITHIN PRODUCT
I=In-depth
A=Adequate
(IMR Committee) Responses
M=Minimal N=Nonexistent
I A M
In addition to alignment of Content Standards and Objectives (CSOs), materials must also clearly connect to
Learning for the 21 st Century which includes opportunities for students to develop
N
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. 21 st 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: 21 st 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
Mathematics
(Vendor/Publisher)
SPECIFIC LOCATION OF
CONTENT WITHIN PRODUCT
I=In-depth A=Adequate
(IMR Committee) Responses
M=Minimal N=Nonexistent
I A M
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.
N
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.
D. Life Skills
3. Present real world application that is current, engaging, integrated throughout the instruction, and promotes and develops critical thinking.
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

Mathematics
Algebra I objectives provide the gateway to all higher mathematics courses. An emphasis on conceptual development and multiple representations will be used to draw generalizations and to serve as a tool for solving real-world problems. Algeblocks may be used to bridge the gap from the concrete to the abstract. Available technology such as calculators, computers, and interactive utilities are to be used as tools to enhance learning. 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 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

(Vendor/Publisher)
SPECIFIC LOCATION OF
CONTENT WITHIN PRODUCT
I=In-depth A=Adequate
(IMR Committee) Responses
M=Minimal N=Nonexistent
I A M
N
A. Algebra
1. Provide opportunities to formulate algebraic expressions for use in equations and inequalities that require planning to accurately model real-world problems with multiple solution paths.
2. Engage in opportunities to create and solve multi-step linear equations, absolute value equations, and linear inequalities in one variable, (with and without technologies)
3. apply skills toward solving practical problems such as distance, mixtures or motion and judge the reasonableness of solutions both individually and collaboratively.
11

4. Provide opportunities to evaluate data provided, given a real-world situation, select an appropriate literal equation and solve for a needed variable.
5. Provide opportunities to explore and develop and test hypotheses to derive the laws of exponents and use them to perform operations on expressions with integral exponents.
6. Create and investigate given sets of data and prove the existence of a pattern numerically, algebraically and graphically, write equations from the patterns and connect inferences and predictions based on observing the pattern.
7. Provide opportunities to explore and develop the concept of the slope of a line through a variety of strategies (e.g. given an equation or graph).
8. Provide multiple examples and exercises to analyze situations and solve problems by determining the equation of a line given a graph of a line, two points on the line, the slope and a point, or the slope and y intercept.
12

9. Appropriately introduce and reinforce the necessary experience that identify a real life experience that involves:

a constant rate of change;

pose a question;

make a hypothesis as to the answer;

develop, justify, and implement a method to collect, organize, and analyze related data;

extend the nature of collected, discrete data to that of a continuous linear function that describes the known data set;

generalize the results to make a conclusion;

compare the hypothesis and the conclusion; present the project numerically, analytically, graphically and verbally using the predictive and analytic tools of algebra
(with and without technologies).
10. investigate and solve systems of linear equations graphically and numerically using the elimination method and the substitution method, given a real-world situation.
11. simplify and evaluate algebraic expressions using technology and manipulatives to

add and subtract polynomials

multiply and divide binomials by binomials or monomials
12. Challenge learners to develop an understanding of polynomials to represent and solve problems from realworld situations while focusing on symbolic and graphical patterns.
13

13. Implement and justify the use area models and graphical representations to develop and explain appropriate methods of factoring.
14. Provide multiple opportunities and examples to simplify radical expressions

through adding, subtracting, multiplying and dividing

exact and approximate forms
14

15. Choose and justify the most efficient method to solve quadratic equations by

graphing (with and without technology),

factoring

quadratic formula and draw reasonable mathematical arguments and conclusions about a situation being modeled.
16. Explore and investigate real life situations involving exponential growth and decay equations including y=2 x and y=(½) x ; compare the equation with attributes of an associated table and graph to demonstrate an understanding of their interrelationship using multiple representations.
17. Provide multiple opportunities and examples to simplify and evaluate rational expressions

add, subtract, multiply and divide

determine when an expression is undefined.
18. Provide opportunities for students to perform a linear regression (with and without technology), and develop connections to

compare and evaluate methods of fitting lines to data.

identify the equation for the line of regression,

examine the correlation coefficient to determine how well the line fits the data use the equation to predict specific values of a variable.
15

19. Explore, develop, compute and interpret the expected value of random variables in simple cases using simulations and rules of probability (with and without technologies).
20. gather data to create histograms, box plots, scatter plots and normal distribution curves and use them to draw and support conclusions about the data using precise mathematical language.
21. design worthwhile experiments to model and solve problems using the concepts of sample space and probability distribution.
22. use multiple mathematical representations, such as words, graphs, tables of values and equations, to solve practical problems; communicate advantages and disadvantages of the use of each representation.
16