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

GENERIC EVALUATION CRITERIA20010-2015

Fourth 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

Fourth 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.

20010-2015Fourth 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 CRITERIAFourth Grade Mathematics

Fourth grade objectives emphasize critical thinking skills to create independent problem solvers who possess a personalized set of skills and strategies to solve problems in everyday life. Concepts which are stressed include: quick recall of multiplication and corresponding division facts, multiplication and division of two-and three-digit numbers, construction and description of objects from different perspectives, plotting points in quadrant one of a coordinate plane, estimation, reading temperatures, description of possible outcomes in a given situation, use of calculators and computers, and describing mathematical relationships and patterns in other content areas and the real-world. Additional concepts targeted include adding and subtracting like fractions, and adding and subtracting decimals. 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 provide students with the opportunity to

A. Number and Operations

1. read, write, order, and compare whole numbers to the millions place and decimals to thousandths place using a variety of strategies (e.g. symbols, manipulatives, number line, pictorial representations).

2. demonstrate an understanding of the place value of each digit utilizing standard and expanded form through 1,000,000 with multiples of 10 [(5 X 10,000) + (3 X 1,000) + (4 X 10) + 2].

3. estimate solutions to problems including rounding, benchmarks, compatible numbers and evaluate the reasonableness of the solution, justify results.

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4. using concrete models, benchmark fractions, number line compare and order fractions with like and unlike

denominators add and subtract fractions with like and unlike

denominators model equivalent fractions

model addition and subtraction of mixed numbers with and without regrouping.

5. analyze the relationship of fractions to decimals using concrete objects and pictorial representations.

6. round decimals to the nearest whole, 10th, or 100th place.

7. add and subtract whole numbers(up to five –digit number) and decimals to the 1000th place, multiply (up to three digits by two-digits, and divide(up to a three digit number with a one and two-digit number).

8. solve multi-digit whole number multiplication problems using a variety of strategies, including the standard algorithm, justify methods used.

9. quick recall of basic multiplication facts and corresponding division facts.

10.create grade-level real-world appropriate story problems using multiple strategies including simple ratios, justify the reason for choosing a particular strategy and present results.

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B. Algebra

1. determine the rule and explain how change in one variable relates to the change in the second variable, given an input/output model using two operations.

2. recognize and describe relationships in which quantities change proportionally.

3. represent the idea of a variable as an unknown quantity using a letter, write an expression using a variable to describe a real-world situation.

4. solve real-world problems involving order of operations including grouping symbols and the four operations,

C. Geometry

1. identify, classify, compare and contrast two-dimensional (including quadrilateral shapes) and three-dimensional geometric figures according to attributes.

2. recognize and describe three-dimensional objects from different perspectives.

3. identify, draw, label, compare and contrast, and classify lines (intersecting, parallel, and perpendicular) angles (acute, right, obtuse, and straight)

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4. identify and create a two-dimensional design with one line of symmetry.

5. graph/plot ordered pairs on a first-quadrant grid and use the coordinate system to specify location and describe path.

6. draw and identify parts of a circle: center point, diameter, and radius.

7. select, analyze and justify appropriate use of transformations (translations, rotations, flips) to solve geometric problems including congruency and tiling (tessellations).

D. Measurement

1. select appropriate measuring tools, apply and convert standard units within a system to estimate, measure, compare and order real-world measurements including:

lengths using customary (to the nearest one-fourth inch) and metric units,

weight, capacity, temperature, and

justify and present results.

2. Quantify area by finding the total number of same sized units that cover a shape, develop a rule and justify the formula for the area of a rectangle using the area model representing multiplication.

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3. read time to the minute, calculate elapsed time in hours/minutes within a 24-hour period.

4. given real-world situations, count coins and bills and determine correct change.

E. Data Analysis and Probability

1. read and interpret information represented on a circle graph.

2. pose a grade-appropriate question that can be addressed with data, collect, organize, display, and analyze data in order to answer the question.

3. design and conduct a simple probability experiment using concrete objects, examine and list all possible combinations using a tree diagram, represent the outcomes as a ratio and present the results.

4. solve real world problems using mean, median and mode.

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