PUBLISHER:SUBJECT:SPECIFIC GRADE:COURSE:TITLE:COPYRIGHT DATE:SE ISBN:TE ISBN:

GENERIC EVALUATION CRITERIA20010-2015Mathematics

Pre-Calculus

R-E-S-P-O-N-S-ECRITERIA NOTESYes No N/A

I. INTER-ETHNICThe 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 OPPORTUNITYThe 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).

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INSTRUCTIONAL MATERIALS ADOPTION: 21st CENTURY LEARNING EVALUATION CRITERIA

GENERAL EVALUATION CRITERIA20010-2015Mathematics

Pre-Calculus

(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 ContentContent 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 UnderstandingLearning 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

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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)

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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.

20010-2015Mathematics

Pre-Calculus

(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.

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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.

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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).

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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.

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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.

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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.

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SPECIFIC EVALUATION CRITERIAMathematics

Pre-Calculus

Pre-Calculus objectives extend students' knowledge of functions and equations (e.g., higher-order functions, exponential, and logarithmic) as well as provide preparation for a calculus course. Available technology will be used by students and teachers to enhance learning. Graphing utilities are powerful tools for solving and verifying equations and inequalities. They also aid in investigating functions, and their inverses.

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: AlgebraThrough 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.

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Standard 3: GeometryThrough 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 5: Data Analysis and ProbabilityThrough 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.

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(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. Algebra

1. Provide various opportunities to investigate and sketch the graphs of functions by analyzing and using the characteristics of zeros, y-intercepts, symmetry, and domain and range.

2. Provide various opportunities to investigate and sketch the graphs of polynomials by analyzing and using the characteristics of upper and lower bounds, end behavior, maximum and minimum points.

3. Provide various opportunities to investigate and sketch the graphs of rational functions by analyzing and using the characteristics of asymptotes and end behavior,

4. Provide examples and exercises to solve higher order polynomial equations utilizing techniques such as Descartes' Rule of Signs, upper and lower bounds, and the Rational Root Theorem.

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5. Provide opportunities to investigate and apply the relationships between Pascal’s Triangle and the Binomial Theorem; use both to expand binomials with positive integral exponents.

6. Provide various opportunities to investigate the inverse relationship between exponential and logarithmic functions; graph related functions and include their domain and range using interval notation, solve practical problems with exponential and logarithmic functions.

7. Provide opportunities to investigate and compare laws of exponents to properties of logarithms; solve equations and practical problems involving exponential and logarithmic expressions, including natural and common logarithms; confirm solutions graphically and numerically.

8. Provide examples and exercises to solve problems involving the sum of finite and infinite sequences and series, including Sigma notation.

9. Provide examples and exercises to use tables of values, graphs, conjectures, algebraic methods, and numerical substitution to find or estimate the limit of a function, a sequence or a series.

10.Provide examples and exercises to analyze and describe the geometry of vectors, perform mathematical operations with vectors and use vectors to solve practical problems.

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11.Provide opportunities to investigate and apply the method of mathematical induction to prove formulas and statements.

B. Geometry

1. Provide examples and exercises to graph functions and conic sections using transformations.

2. Provide opportunities to investigate, analyze and describe properties of conic sections; explain the interrelationship among the properties; solve practical problems involving conic sections.

C. Data Analysis and Probability

1. Provide resources that identify real life situations that exhibit characteristics of exponential or logistic growth or decay for students to investigate, analyze, and draw conclusions.

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