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

GENERIC EVALUATION CRITERIA20010-2015

Sixth Grade Mathematics

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 CRITERIA20010-2015

Sixth 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 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.

20010-2015Sixth 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.

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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 CRITERIASixth Grade Mathematics

Sixth grade objectives place continued emphasis on the study of whole numbers, decimals and fractions (primary focus on multiplication and division of fractions and mixed numbers). Introductory work with integers includes understanding why the rules for adding, subtracting, multiplying and dividing integers work. Opportunities to apply these skills to real world situations help to make sense of the mathematics. Calculators, computers and manipulatives may be used to solve problems. Probability, Statistics, Geometry, and Pre-Algebra will be stressed. Concepts of using ratios to compare data sets, making geometric constructions of three-dimensional figures and solving problems involving circles, volume and surface area are emphasized. 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 OperationsThrough 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: 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 4: MeasurementThrough 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 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…

A. Number and Operations

1. provide a variety of examples and exercises to demonstrate an understanding of large numbers by converting and comparing numbers in scientific notation and standard notation (with and without technology).

2. provide a variety of examples and exercises to determine the greatest common factor and least common multiple using multiple strategies to solve real-world problems; find prime factorization of a number.

3. provide a variety of examples and exercises to compare and order integers using multiple strategies (e.g., symbols, manipulatives, number line).

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4. provide a variety of examples and exercises to analyze and solve real-world problems involving addition, subtraction , multiplication and division of

whole numbers, fractions, mixed numbers, decimals integers

and justify the reasonableness by estimation.

5. provide a variety of examples and exercises to apply the distributive, commutative, associative and identity properties to numeric expressions and use to prove equivalency.

6. provide a variety of examples and exercises to convert between fractions/ratios, mixed numbers, decimals and percents in appropriate real-world problems.

7. provide a variety of examples and exercises to compute the percent of a number to solve application problems and justify the reasonableness by estimation.

8. provide a variety of examples and exercises to demonstrate an understanding of the effect of multiplying and dividing, whole numbers, fractions and decimals by numbers  including 0, 1 and values between 0 and 1.

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9. provide a variety of examples and exercises to develop and test hypotheses to derive the rules for addition, subtraction, multiplication and division of integers, justify by using real-world examples and use them to solve problems.

B. Algebra

1. provide examples and exercises to simplify numerical expressions and evaluate algebraic expressions using order of operations.

2. provide opportunities to use inductive reasoning to extend patterns to predict the nth term (e.g., powers and triangular numbers).

3. provide opportunities to create algebraic expressions that correspond to real-world situations; use the expressions to solve problems.

4. provide examples and exercises to determine the rule, output or input; given an input/output model using one operation, write an algebraic expression for the rule and use to identify other input/output values.

5. provide examples and exercises to solve real-world proportion problems involving rates, probability and measurements using multiple strategies, justify selection of strategies.

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6. provide examples and exercises to write and solve one-step equations using number sense, properties of operations and the idea of maintaining equality to represent and solve real-world problems.

C. Geometry

1. provide opportunities to analyze characteristics using defining properties of lines, angles, polygons, triangles, and

compare these geometric figures.

2. provide examples and exercises to use inductive reasoning with the measures of interior angles in polygons and derive the formula to determine the sum of the measures of the interior angles.

3. provide examples and exercises to apply the concepts of parallel, perpendicular, intersecting, and skew lines to real-world situations (i.e. roads and routes).

4. provide examples and exercises to create designs using line and rotational symmetry.

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5. provide examples and exercises to predict, describe, and perform transformations on two-dimensional shapes

translations rotations reflections

6. provide examples and exercises to use geometric representations to solve real-world problems.

7. provide examples and exercises to plot polygons on coordinate grids, determine lengths and areas from the graph.

D. Measurement

1. provide opportunities to determine an approximation for pi using actual measurements.

2. provide examples and exercises to develop and test hypotheses to determine formulas for

perimeter of polygons, including composite figures area of parallelograms area of triangles area of composite figures made of parallelograms

and triangles circumference of a circle area of a circle volume of a rectangular prism

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3. provide opportunities to investigate, model and describe surface area of rectangular prisms and cylinders; develop strategies to determine the surface area of rectangular prisms.

4. provide opportunities to develop strategies to determine volume of cylinders; solve real-world problems involving volume of cylinders, justify the results.

5. provide opportunities to construct a scale drawing given the scale factor of a two-dimensional polygon.

E. Data Analysis and Probability

1. provide examples and exercises to collect, organize, display, read, interpret and analyze real-world data using appropriate graphs and tables (with and without technology).

2. provide opportunities to identify a real life situation using statistical measures (mean, median, mode, range, outliers) overtime, make a hypothesis as to the outcome; design and implement a method to collect, organize and analyze data; analyze the results to make a conclusion; evaluate the validity of the hypothesis based upon collected data, design a mode of presentation using words, graphs, models, and/or tables (with and without technology).

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3. provide opportunities to perform simple probability events using manipulatives; predict the outcome given events using experimental and theoretical probability; express experimental and theoretical probability as a ratio, decimal or percent.

4. provide opportunities to determine combinations and permutations of given real-world situations by multiple strategies, including creating lists.

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