mathematics content standards...

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GENERIC EVALUATION CRITERIA20010-2015Mathematics

College Transition

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).

INSTRUCTIONAL MATERIALS ADOPTION: 21st CENTURY LEARNING EVALUATION CRITERIA

GENERAL EVALUATION CRITERIA20010-2015Mathematics

College Transition

(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

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)

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

20010-2015Mathematics

College Transition





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.

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.

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).

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.

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.

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.

SPECIFIC EVALUATION CRITERIA

MathematicsCollege Transition

The WVDE has recognized the need to identify students prior to high school graduation, who will be unprepared for college and/or who will be enrolled in remedial mathematics courses, in order to provide additional instruction for these students. Students in grade 11 who are either in the professional pathway, or are college bound in the skilled pathway and are not achieving the state assessment college readiness benchmark in mathematics, will be required in grade 12 to take the college mathematics transition course. Since high school students are allowed to choose the sequence of the mathematics courses in which they enroll, there is no specific mathematics course required of all grade 11 students. Students in grade 11 can take Algebra I, Geometry, Algebra II, Trigonometry and/or higher level mathematics courses. Specific objectives were identified as aligning to the West Virginia Higher Education Mathematics College Readiness Standards.

For mathematics, there is a 100% alignment between the West Virginia Higher Education Mathematics College Readiness Standards and the identified mathematics objectives. Following are the number and percent of objectives identified by course: Algebra I 12 objectives 32% Algebra II 7 objectives 18% Geometry 17 objectives 45% Trigonometry 2 objectives 05%. The college transition mathematics course may be counted as a required mathematics credit for high school graduation. Rigorous benchmarks (cut scores) to determine college readiness will be determined; it is important to note that mastery on the Grade 11 Mathematics WESTEST 2 may be different from the benchmark for college readiness.

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.

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.





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 create and solve multi-step linear equations, absolute value equations, and linear inequalities in one variable, (with and without technology); apply skills toward solving practical problems such as distance, mixtures or motion and judge the reasonableness of solutions.(A1.2.2)

2. Provide opportunities to investigate and develop and test hypotheses to derive the laws of exponents and use them to perform operations on expressions with integral exponents. (A1.2.4)

3. Provide opportunities to investigate and analyze a given set of data and prove the existence of a pattern numerically, algebraically and graphically, write equations from the patterns and make inferences and predictions based on observing the pattern. (A1.2.5)

4. Provide opportunities to investigate and 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.(A1.2.7)

5. Provide various opportunities to extrapolate data represented by graphs, tables and formulas to make inferences and predictions on rate of change (slope) and justify when communicating results within a project based investigation. (A1.2.8)

6. Provide examples and exercises to create and solve systems of linear equations graphically and numerically using the elimination method and the substitution method, given a real-world situation. (A1.2.9)

7. Provide examples and exercises to simplify and evaluate algebraic expressions, add and subtract polynomials, multiply and divide binomials by binomials or monomials (A1.2.10)

8. Provide examples and exercises to simplify radical expressions through adding, subtracting, multiplying and dividing exact and approximate forms (A1.2.13)

9. Provide various opportunities to solve quadratic equations by graphing (with and without technology), factoring, quadratic formula, and draw reasonable conclusions about a situation being modeled. (A1.2.14)

10.Provide examples and exercises to simplify and evaluate rational expressions, add, subtract, multiply and divide determine when an expression is undefined. (A1.2.16)

11.Provide opportunities to investigate and gather data to create histograms, box plots, scatter plots and normal distribution curves and use them to draw and support conclusions about the data. (A1.2.19)

12.Provide opportunities to design experiments to model and solve problems using the concepts of sample space and probability distribution. (A1.2.20)

13.Provide various opportunities to factor higher order polynomials by applying various methods including factoring by grouping and the sum and difference of two cubes; analyze and describe the relationship between the factored form and the graphical representation. (A2.2.2)

14.Provide opportunities to investigate properties of complex numbers, simplify powers of ‘i’, perform basic operations with complex numbers, and give answers as complex numbers in simplest form. (A2.2.3)

15.Provide examples and exercises to simplify expressions involving radicals and fractional exponents, convert between the two forms, and solve equations containing radicals and exponents. (A2.2.4)

16.Provide various opportunities to solve quadratic equations over the set of complex numbers: apply the techniques of factoring, completing the square, and the quadratic formula; use the discriminate to determine the number and nature of the roots; identify the maxima and minima; use words, graphs, tables, and equations to generate and analyze solutions to practical problems.(A2.2.5)

17.Provide various opportunities to define a function and find its zeros; express the domain and range using interval notation; find the inverse of a function; find the value of a function for a given element in its domain; and perform basic operations on functions including composition of functions.(A2.2.7)

18.Provide opportunities to investigate and analyze families of functions and their transformations; recognize linear, quadratic, radical, absolute value, step, piece-wise, and exponential functions; analyze connections among words, graphs, tables and equations when solving practical problems with and without technology.(A2.2.8)

19.Provide examples and exercises to solve absolute value inequalities graphically, numerically and algebraically and express the solution set in interval notation. (A2.2.13)

B. Geometry

1. Provide opportunities to investigate and apply differentiate and apply inductive and deductive reasoning, justify conclusions in real-world settings.(G.3.2)

2. Provide various opportunities to validate conclusions by constructing logical arguments using both formal and informal methods with direct and indirect reasoning. (G.3.4)

3. Provide various opportunities to construct formal and informal proofs by applying definitions, theorems, and postulates related to such topics as complementary, supplementary, vertical angles, angles formed by perpendicular lines, and justify the steps. (G.3.5)

4. Provide opportunities to investigate and compare and contrast the relationships between angles formed by two lines cut by a transversal when lines are parallel and when they are not parallel, and use the results to develop concepts that will justify parallelism. (G.3.6)

5. Provide opportunities to investigate and make conjectures and justify congruence relationships with an emphasis on triangles and employ these relationships to solve problems. (G.3.7)

6. Provide opportunities to investigate and apply the general properties of and compare and contrast the properties of convex and concave quadrilaterals, parallelograms, rectangles, rhombuses, squares and trapezoids (G.3.8)

7. Provide opportunities to investigate and draw conclusions in problem solving situations that include two and three dimensions of figures based on the properties of similarity. (G.3.9)

8. Provide opportunities to investigate measures of angles and lengths of segments to determine the existence of a triangle (triangle inequality) and to establish the relationship between the measures of the angles and the length of the sides (with and without technology). (G.3.10)

9. Provide opportunities to investigate, verify and justify the basis for the trigonometric ratios by applying properties of similar triangles and use the results to find inaccessible heights and distances. Using the ratios of similar triangles to find unknown side lengths and angle measures, construct a physical model that illustrates the use of a scale drawing in a real-world situation. (G.3.11)

10.Provide opportunities to investigate and apply the Pythagorean Theorem and its converse to solve real-world problems and derive the special right triangle relationships (i.e. 30-60-90, 45-45-90). (G.3.12)

11. Provide opportunities to investigate and apply measures of angles formed by chords, tangents, and secants of a circle and draw conclusions for the relationship to its arcs. (G.3.13)

12.Provide examples and exercises to find angle measures of interior and exterior angles; given a polygon, find the length of sides from given data; and use properties of regular polygons to find any unknown measurements of sides or angles.(G.3.14)

13.Provide opportunities to investigate and develop properties of tessellating figures and use those properties to tessellate the plane. (G.3.15)

14.Provide opportunities to investigate, derive and justify formulas for area, perimeter, surface area, and volume using nets and apply them to solve real-world problems. (G.3.16)

15.Provide opportunities to investigate and apply concepts of analytical geometry such as formulas for distance, slope, and midpoint and apply these to finding dimensions of polygons on the coordinate plane.(G.3.17)

16.Provide opportunities to investigate and construct a triangle’s medians, altitudes, angle and perpendicular bisectors using various methods; and develop their relationships to be used in solving real-world problems. (G.3.18)

17.Provide various opportunities to create and apply concepts using transformational geometry and laws of symmetry, of a reflection, translation, rotation, glide reflection, dilation of a figure, and develop logical arguments for congruency and similarity. (G.3.19)

18.Provide opportunities to investigate and apply the right triangle definition of the six trigonometric functions of an angle to determine the values of the function values of an angle in standard position given a point on the terminal side of the angle. determine the value of the other trigonometric functions given the value of one of the trigonometric functions and verify these values with technology.using geometric principles and the Pythagorean Theorem, determine the six function values for the special angles and the quadrantal angles and use them in real-world problems.(T.3.1)

19.Provide opportunities to investigate and compare circular functions and the trigonometric function values to draw inferences about coterminal angles and co-functions.(T.3.1)

20.Provide resources that identify real-world problems within a project based investigation involving triangles using the trigonometric functions, the law of sines and the law of cosines,. (T.3.8)

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