West Virginia State Standards for Mathematics:

WV.MA.S.K.1. Number and Operations: Through 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.

MA.O.K.1.1. Count forward to 20 and backward from 10 with and without manipulatives.

MA.O.K.1.2. Read, write, order, and compare numbers to 20 using multiple strategies (e.g. manipulatives, number line).

MA.O.K.1.3. Group and count manipulatives by ones, fives, and tens.

MA.O.K.1.4. Model and identify place value of each digit utilizing standard and expanded form through 20.

MA.O.K.1.5 Use ordinal numbers 1st - 10th to identify position in a sequence.

MA.O.K.1.6. Estimate the number of objects in a group of 20 or less and count to evaluate reasonableness of estimation.

MA.O.K.1.7. Identify and name halves and wholes using concrete models.

MA.O.K.1.8. Use concrete objects to model addition and subtraction of whole numbers related to sums of 10 or less and write corresponding number sentence.

MA.O.K.1.9. Model meanings of operations and the relationship between addition and subtraction (e.g., identity element of addition, commutative property) using manipulatives.

MA.O.K.1.10. Create grade-appropriate picture and story problems, solve using a variety of strategies, present solutions and justify results.

WV.MA.S.K.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.

MA.O.K.2.1. Justify the classification of self-selected objects based on attributes.

MA.O.K.2.2. Create, describe, and extend a repeating pattern using common objects, sound, and movement.

MA.O.K.2.3. Model and identify patterns of counting by 5's and 10's.

WV.MA.S.K.3. Geometry: Through 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.

MA.O.K.3.1. Use physical materials to construct, identify, and classify basic geometric plane shapes: circles, ellipses (oval), rectangles including squares, triangles

MA.O.K.3.2. Recognize and describe basic geometric shapes in the environment.

MA.O.K.3.3. Model and describe spatial relationships: inside/outside, top/bottom, before/after

MA.O.K.3.4. Identify the separate parts used to make a whole object.

WV.MA.S.K.4. Measurement: Through 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.

MA.O.K.4.1. Estimate the size of an object and compare and order objects with respect to a given attribute.

MA.O.K.4.2. Use standard and nonstandard units of measure to find the length of an object.

MA.O.K.4.3. Compare two objects in nonstandard units of measure, according to one or more of the following attributes: length, height, weight

MA.O.K.4.4. Use calendar to identify date and the sequence of days of the week.

MA.O.K.4.5. Read time to the hour using analog and digital clocks.

MA.O.K.4.6. Identify the name and value of coins and explain the relationships between: penny, nickel, dime.

WV.MA.S.K.5. Data Analysis and Probability: Through 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.

MA.O.K.5.1. Collect, organize, display, and interpret data using a pictograph and bar graph (with and without technology).

MA.O.K.5.2. Conduct a simple probability experiment and use tallies to record results in a table, make predictions based on results.

WV.MA.S.1.1. Number and Operations: Through 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.

MA.O.1.1.1. Count forward to 100 and backward from 20 with and without manipulatives.

MA.O.1.1.2. Read, write, order, and compare numbers to 100 using multiple strategies (e.g. manipulatives, number line, symbols).

MA.O.1.1.3. Identify odd and even numbers to 20 and determine if a set of objects has an odd or even number of elements.

MA.O.1.1.4. Group and count manipulatives by ones, fives, and tens to 100.

MA.O.1.1.5. Model and identify place value of each digit utilizing standard and expanded form to 100.

MA.O.1.1.6. Round any two-digit number to the nearest 10.

MA.O.1.1.7. Use ordinal numbers 1st - 20th to identify position in a sequence.

MA.O.1.1.8. Estimate the number of objects in a group of 100 or less and count to evaluate reasonableness of estimate.

MA.O.1.1.9. Identify, name, and explain why a given part is a half, third or fourth of a whole or part of a group, using concrete models.

MA.O.1.1.10. Use concrete objects to model the addition of two or three addends and subtraction of whole numbers related to sums less than 18 and write the corresponding number sentence.

MA.O.1.1.11. Model operations, addition and subtraction, and the relationship between addition and subtraction (e.g., identity element of addition, commutative property, fact families, inverse operations) using concrete objects.

MA.O.1.1.12. Quick recall of basic addition facts with sums to 10 and corresponding subtraction facts.

MA.O.1.1.13. Model and solve 2-digit addition and subtraction without regrouping.

MA.O.1.1.14. Create grade-appropriate picture and story problems using a variety of strategies (with and without technology), present solutions and justify results.

WV.MA.S.1.2. 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.

MA.O.1.2.1. Sort and classify objects by more than one attribute, using various strategies, including Venn Diagrams.

MA.O.1.2.2. Determine the rule or give the output given an input/output model using addition or subtraction.

MA.O.1.2.3. Identify and write number patterns by 2's, 5's, and 10's.

MA.O.1.2.4. Create and analyze number patterns based on real-life situations using words, AB form, and T-charts and present results.

MA.O.1.2.5. Use concrete materials to demonstrate that the quantities on both sides of a grade-appropriate number sentence are equivalent.

WV.MA.S.1.3. Geometry: Through 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.

MA.O.1.3.1. Draw, label, and sort circle, rectangles including squares, triangles, and according to sides and vertices

MA.O.1.3.2. Use physical materials to construct, identify, and classify three-dimensional figures: cube, cone, sphere, rectangular solid, pyramid, cylinder

MA.O.1.3.3. Recognize three-dimensional shapes in the environment.

MA.O.1.3.4. Draw and identify: open and closed figures, congruent plane shapes

MA.O.1.3.5. Create and describe simple symmetrical designs.

MA.O.1.3.6. Describe spatial relationships: over/under, left/right.

MA.O.1.3.7. Find and name locations on a first-quadrant grid.

MA.O.1.3.8. Predict the result of combining or decomposing two or more two-dimensional/three-dimensional shapes.

WV.MA.S.1.4. Measurement: Through 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.

MA.O.1.4.1. Estimate, measure, compare and order using customary, metric, and nonstandard units to determine length to nearer whole unit.

MA.O.1.4.2. Select appropriate units and tools to measure and compare two objects or events according to one or more of the following attributes: length, height, weight, temperature, volume justify selection of units and tools used to measure the attributes and present results.

MA.O.1.4.3. Use calendar to identify date, sequence of days of the week, and months of the year.

MA.O.1.4.4. Explain time concept in context of personal experience.

MA.O.1.4.5. Read time to the half hour using an analog and digital clock.

MA.O.1.4.6. Identify, count, trade and organize the following coins and bill to display a variety of price values from real-life examples with a total value of 100 cents or less: penny, nickel, dime, quarter, dollar bill.

WV.MA.S.1.5. Data Analysis and Probability: Through 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.

MA.O.1.5.1. Identify a real life situation to gather data over time; make a hypothesis as to the outcome; design and implement a method to collect, organize, and analyze the results to make a conclusion; evaluate the validity of the hypothesis based upon collected data; design a mode of presentation using a pictograph and a bar graph (with and without technology).

MA.O.1.5.2. Conduct simple experiments, record data on a tally chart or table and use the data to predict which of the events is more likely or less likely to occur if the experiment is repeated.

WV.MA.S.2.1. Number and Operations: Through 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.

MA.O.2.1.1. Read, write, order, and compare numbers to 1,000 using multiple strategies (e.g. symbols, manipulatives, number line).

MA.O.2.1.2. Justify any number as odd or even and determine if a set has and odd or even number of elements.

MA.O.2.1.3. Count and group concrete manipulatives by ones, tens, and hundreds to 1,000.

MA.O.2.1.4. Model and identify place value of each digit utilizing standard and expanded form through 1000.

MA.O.2.1.5. Identify and read any ordinal number to identify position in a sequence.

MA.O.2.1.6. Round any 3-digit number to both the nearer 10 and 100.

MA.O.2.1.7. Identify and explain fractions as part of a whole and as part of a set/group using models.

MA.O.2.1.8. Model and justify the relationship between addition and subtraction (e.g., identity element of addition, associative property, commutative property, inverse operations, fact families).

MA.O.2.1.9. Demonstrate quick recall of basic addition facts with sums to 18 and corresponding subtraction facts.

MA.O.2.1.10. Model 2- and 3-digit addition and subtraction with regrouping using multiple strategies.

MA.O.2.1.11. Add and subtract 2- and 3-digit numbers without regrouping.

MA.O.2.1.12. Use rounding to analyze the reasonableness of a sum or a difference.

MA.O.2.1.13. Create story problems that require one or two-step procedures, using a variety of strategies explain the reasoning used, justify the procedures selected and present the results.

WV.MA.S.2.2. 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.

MA.O.2.2.1. Analyze, describe, extend and create a growing pattern using objects or numbers.

MA.O.2.2.2. Explain how one variable produces a change in another variable.

MA.O.2.2.3. Describe, complete and extend a variety of counting patterns, according to a given rule.

MA.O.2.2.4. Create physical models to demonstrate equivalency of two numerical expressions written as a grade-appropriate number sentence.

WV.MA.S.2.3. Geometry: Through 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.

MA.O.2.3.1. Identify and describe the following geometric solids according to the number of faces and edges: rectangular solid, cube, cylinder, cone, pyramid

MA.O.2.3.2. Compare and contrast plane and solid geometric shapes.

MA.O.2.3.3. Identify and draw congruent shapes that have been rotated or reflected.

MA.O.2.3.4. Model and draw line segments and angles.

MA.O.2.3.5. Plot and describe the path between locations on a grid.

MA.O.2.3.6. Identify similar shapes.

WV.MA.S.2.4. Measurement: Through 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.

MA.O.2.4.1. Identify a real life situation to use appropriate measurement tools; over time make a hypothesis as to the change overtime using whole units: length in centimeters and inches, temperature in Celsius and Fahrenheit, weight/mass in pounds and kilograms, and 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 (with and without technology).

MA.O.2.4.2. Estimate and determine the perimeter of squares, rectangles and triangles.

MA.O.2.4.3. Estimate and count the number of square units needed to cover a given area using manipulatives.

MA.O.2.4.4. Order events in relation to time.

MA.O.2.4.5. Determine past and future days of the week and identify specific dates, given a calendar.

MA.O.2.4.6. Read time to the quarter hour using an analog and digital clock.

MA.O.2.4.7. Identify, count and organize coins and bills to display a variety of price values from real-life examples with a total value of one dollar or less and model making change using manipulatives.

WV.MA.S.2.5. Data Analysis and Probability: Through 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.

MA.O.2.5.1. Create, read, and interpret a pictograph with each picture representing greater than or equal to a single unit.

MA.O.2.5.2. Conduct simple experiments with more than two outcomes and use the data to predict which event is more, less, or equally likely to occur if the experiment is repeated.

MA.O.2.5.3. Analyze data represented on a graph using grade-appropriate questions.

MA.O.2.5.4. Formulate questions, collect data, organize and display as a chart, table or bar graph.

WV.MA.S.3.1. Number and Operations: Through 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.

MA.O.3.1.1. Read, write, order, and compare numbers to 10,000 using a variety of strategies (e.g., symbols, manipulatives, number line).

MA.O.3.1.2. Read, write, order, and compare decimals to hundredths, with manipulatives.

MA.O.3.1.3. Identify place value of each digit utilizing standard and expanded form to 10,000.

MA.O.3.1.4. Apply estimation skills (rounding, benchmarks, compatible numbers) to solve and evaluate reasonableness of an answer.

MA.O.3.1.5. Demonstrate an understanding of fractions as part of a whole/one and as part of a set/group using models and pictorial representations.

MA.O.3.1.6. Create concrete models and pictorial representations to compare and order fractions with like and unlike denominators, add and subtract fractions with like denominators, and verify results.

MA.O.3.1.7. Use concrete models and pictorial representations to demonstrate an understanding of equivalent fractions, proper and improper fractions, and mixed numbers.

MA.O.3.1.8. Add and subtract 2- and 3-digit whole numbers and money with and without regrouping.

MA.O.3.1.9. Demonstrate and model multiplication (repeated addition, arrays) and division (repeated subtraction, partitioning).

MA.O.3.1.10. Use and explain the operations of multiplication and division including the properties (e.g., identity element of multiplication, commutative property, property of zero, associative property, inverse operations).

MA.O.3.1.11. Recall basic multiplication facts and the corresponding division facts.

MA.O.3.1.12. Model the distributive property in multiplication of 2- and 3-digit numbers by a 1-digit number.

MA.O.3.1.13. Use models to demonstrate division of 2- and 3-digit numbers by a 1-digit number.

MA.O.3.1.14. Create grade-appropriate real-world problems involving any of the four operations using multiple strategies, explain the reasoning used, and justify the procedures selected when presenting solutions.

WV.MA.S.3.2. 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.

MA.O.3.2.1. Analyze and extend geometric and numeric patterns.

MA.O.3.2.2. Create an input/output model using addition, subtraction, multiplication or division.

MA.O.3.2.3. Analyze a given pattern and write the rule.

MA.O.3.2.4. Write equivalent numerical expressions and justify equivalency.

MA.O.3.2.5. Use symbol and letter variables to represent an unknown quantity and determine the value of the variable.

WV.MA.S.3.3. Geometry: Through 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.

MA.O.3.3.1. Identify and create new polygons by transforming, combining and decomposing polygons.

MA.O.3.3.2. Identify, describe, and classify the following geometric solids according to the number of faces, edges, and vertices: cube, rectangular solid, cylinder, cone, pyramid

MA.O.3.3.3. Construct and identify a solid figure from a plane drawing.

MA.O.3.3.4. Identify, describe and draw lines of symmetry in two-dimensional shapes.

MA.O.3.3.5. Model, describe, and draw: lines, rays, angles including right, obtuse, and acute angles.

MA.O.3.3.6. Draw an example of a flip, slide and turn (reflection, translation, and rotation) given a model.

MA.O.3.3.7. Name the location of a point on a first-quadrant grid, represent using ordered pairs.

WV.MA.S.3.4. Measurement: Through 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.

MA.O.3.4.1. Within a project based investigation, identify a real life situation, consider a number of variables and use appropriate measurement tools, overtime, make a hypothesis as to the change overtime; with more precision than whole units; length in centimeters and inches, temperature in Celsius and Fahrenheit, weight/mass in pounds and kilograms, and design and implement a method to collect, organize, and analyze data; analyze results to make a conclusion; evaluate the validity of the hypothesis upon collected data; design a mode of presentation (with and without technology)

MA.O.3.4.2. Estimate and find the perimeter and area of familiar geometric shapes, using manipulatives, grids, or appropriate measuring tools.

MA.O.3.4.3. Determine the formula the area of a rectangle and explain reasoning through modeling.

MA.O.3.4.4. Read time to 5-minute intervals using (am and pm) analog and digital clocks, compute elapsed time to the quarter-hour using a clock.

MA.O.3.4.5. Identify, count and organize coins and bills to display a variety of price values from real-life examples with a total value of $100 or less and model making change using manipulatives.

WV.MA.S.3.5. Data Analysis and Probability: Through 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.

MA.O.3.5.1. Collect and organize grade-appropriate real-world data from observation, surveys, and experiments, and identify and construct appropriate ways to display data.

MA.O.3.5.2. Develop and conduct grade-appropriate experiments using concrete objects (e.g. counters, number cubes, spinners) to determine the likeliness of events and list all outcomes.

MA.O.3.5.3. Analyze real-world data represented on a graph using grade-appropriate questions.

WV.MA.S.4.1. Number and Operations: Through 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.

MA.O.4.1.1. 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).

MA.O.4.1.2. 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].

MA.O.4.1.3. Estimate solutions to problems including rounding, benchmarks, compatible numbers and evaluate the reasonableness of the solution, justify results.

MA.O.4.1.4. 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.

MA.O.4.1.5. Analyze the relationship of fractions to decimals using concrete objects and pictorial representations.

MA.O.4.1.6. Round decimals to the nearest whole, 10th, or 100th place.

MA.O.4.1.7. 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).

MA.O.4.1.8. Solve multi-digit whole number multiplication problems using a variety of strategies, including the standard algorithm, justify methods used.

MA.O.4.1.9. Quick recall of basic multiplication facts and corresponding division facts.

MA.O.4.1.10. 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.

WV.MA.S.4.2. 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.

MA.O.4.2.1. 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.

MA.O.4.2.2. Recognize and describe relationships in which quantities change proportionally.

MA.O.4.2.3. 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.

MA.O.4.2.4. Solve real-world problems involving order of operations including grouping symbols and the four operations.

WV.MA.S.4.3. Geometry: Through 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.

MA.O.4.3.1. Identify, classify, compare and contrast two-dimensional (including quadrilateral shapes) and three-dimensional geometric figures according to attributes.

MA.O.4.3.2. Recognize and describe three-dimensional objects from different perspectives.

MA.O.4.3.3. Identify, draw, label, compare and contrast, and classify lines (intersecting, parallel, and perpendicular) angles (acute, right, obtuse, and straight)

MA.O.4.3.4. Identify and create a two-dimensional design with one line of symmetry.

MA.O.4.3.5. Graph/plot ordered pairs on a first-quadrant grid and use the coordinate system to specify location and describe path.

MA.O.4.3.6. Draw and identify parts of a circle: center point, diameter, and radius.

MA.O.4.3.7. Select, analyze and justify appropriate use of transformations (translations, rotations, flips) to solve geometric problems including congruency and tiling (tessellations).

WV.MA.S.4.4. Measurement: Through 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 unites, systems, and processes of measurement, and apply appropriate techniques, tools and formulas to determine measurements.

MA.O.4.4.1. 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.

MA.O.4.4.2. 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.

MA.O.4.4.3. Read time to the minute, calculate elapsed time in hours/minutes within a 24-hour period.

MA.O.4.4.4. Given real-world situations, count coins and bills and determine correct change.

WV.MA.S.4.5. Data Analysis and Probability: Through 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.

MA.O.4.5.1. Read and interpret information represented on a circle graph.

MA.O.4.5.2. Pose a grade-appropriate question that can be addressed with data, collect, organize, display, and analyze data in order to answer the question.

MA.O.4.5.3. 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.

MA.O.4.5.4. Solve real world problems using mean, median and mode.

WV.MA.S.5.1. Number and Operations: Through 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.

MA.O.5.1.1. Read, write, order and compare all whole numbers, fractions, mixed numbers and decimals using multiple strategies (e.g., symbols, manipulatives, number line).

MA.O.5.1.2. Demonstrate an understanding of place value of each digit utilizing standard and expanded form in any whole number using powers of 10 [(3 X 10 to the 5th) + (4 X 10 to the 3rd) + 7 X 10 to the 2nd) + (1 X 10 to the 1st) + 6].

MA.O.5.1.3. Estimate solutions to problems involving whole numbers, decimals, fractions, and percents to determine reasonableness using benchmarks.

MA.O.5.1.4. Use inductive reasoning to identify the divisibility rules of 2, 3, 5, 9 and 10 and apply the rules to solve application problems.

MA.O.5.1.5. Determine and apply greatest common factor and lowest common multiple to write equivalent fractions and to real-world problem situations.

MA.O.5.1.6. Model and write equivalencies of fractions decimals, percents, and ratios.

MA.O.5.1.7. Analyze and solve application problems and justify reasonableness of solution in problems involving addition and subtraction of: fractions and mixed numbers, decimals.

MA.O.5.1.8. Apply the distributive property as it relates to multiplication over addition.

MA.O.5.1.9. Solve multi-digit whole number division problems using a variety of strategies, including the standard algorithm and justify the solutions.

MA.O.5.1.10. Demonstrate fluency in addition, subtraction, multiplication and division of whole numbers.

MA.O.5.1.11. Solve real-world problems involving whole numbers, decimals and fractions using multiple strategies and justify the reasonableness by estimation.

WV.MA.S.5.2. 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.

MA.O.5.2.1. Use inductive reasoning to find missing elements in a variety of patterns (e.g., square numbers, arithmetic sequences).

MA.O.5.2.2. Given an input/output model using two operations, determine the rule, output or input.

MA.O.5.2.3. Solve simple equations and inequalities using patterns and models of real-world situations, create graphs on number lines of the equations and interpret the results.

MA.O.5.2.4. Model identify and describe square, prime and composite numbers.

WV.MA.S.5.3. Geometry: Through 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.

MA.O.5.3.1. Classify and compare triangles by sides and angles; measure the angles of a triangle using a protractor.

MA.O.5.3.2. Construct and analyze three-dimensional shapes using properties (i.e. edges, faces or vertices).

MA.O.5.3.3. Create a design with more than one line of symmetry.

MA.O.5.3.4. Construct a circle with a given radius or diameter.

MA.O.5.3.5. Draw a similar figure using a scale, given a real-world situation.

WV.MA.S.5.4. Measurement: Through 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.

MA.O.5.4.1. Estimate, measure, compare, order and draw lengths of real objects in parts of an inch up to 1/8 of an inch and millimeters.

MA.O.5.4.2. Model, calculate and compare area of triangles and parallelograms using multiples strategies (including, but not limited to, formulas).

MA.O.5.4.3. Develop strategies (i.e. finding number of same sized units of volume)to determine the volume of a rectangular prism; solve application problems involving estimating or measuring volume of rectangular prisms.

MA.O.5.4.4. Describe the effects on the measurements of a two-dimensional shape (such as its perimeter and area) when the shape is changed in some way, justify changes.

MA.O.5.4.5. Solve real-world problems requiring conversions within a system of measurement.

MA.O.5.4.6. Estimate and/or measure the weight/mass of real objects in ounces, pounds, grams, and kilograms.

MA.O.5.4.7. Collect, record, estimate and calculate elapsed times from real-world situations (with and without technology).

MA.O.5.4.8. Determine the actual measurements of a figure from a scale drawing, using multiple strategies.

WV.MA.S.5.5. Data Analysis and Probability: Through 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.

MA.O.5.5.1. Construct a sample space and make a hypothesis as to the probability of a real life situation overtime, test the prediction with experimentation, and present conclusions (with and without technology).

MA.O.5.5.2. Construct, read, and interpret tables, charts, and graphs including stem and leaf plots to draw reasonable inferences or verify predictions.

MA.O.5.5.3. Collect and organize real-world data to construct a circle graph (with and without technology), present data and draw conclusions.

MA.O.5.5.4. Collect and analyze data using mean, median and mode to determine the best statistical measure.

WV.MA.S.6.1. Number and Operations: Through 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.

MA.O.6.1.1. Demonstrate an understanding of large numbers by converting and comparing numbers in scientific notation and standard notation (with and without technology).

MA.O.6.1.2. Determine the greatest common factor and least common multiple using multiple strategies to solve real-world problems; find prime factorization of a number.

MA.O.6.1.3. Compare and order integers using multiple strategies (e.g., symbols, manipulatives, number line).

MA.O.6.1.4. 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.

MA.O.6.1.5. Apply the distributive, commutative, associative and identity properties to numeric expressions and use to prove equivalency.

MA.O.6.1.6. Convert between fractions/ratios, mixed numbers, decimals and percents in appropriate real-world problems.

MA.O.6.1.7. Compute the percent of a number to solve application problems and justify the reasonableness by estimation.

MA.O.6.1.8. 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.

MA.O.6.1.9. 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.

WV.MA.S.6.2. 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.

MA.O.6.2.1. Simplify numerical expressions and evaluate algebraic expressions using order of operations.

MA.O.6.2.2. Use inductive reasoning to extend patterns to predict the nth term (e.g., powers and triangular numbers).

MA.O.6.2.3. Create algebraic expressions that correspond to real-world situations; use the expressions to solve problems.

MA.O.6.2.4. 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.

MA.O.6.2.5. Solve real-world proportion problems involving rates, probability and measurements using multiple strategies, justify selection of strategies.

MA.O.6.2.6. 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.

WV.MA.S.6.3. Geometry: Through 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.

MA.O.6.3.1. Analyze characteristics using defining properties of lines, angles, polygons, triangles, and compare these geometric figures.

MA.O.6.3.2. 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.

MA.O.6.3.3. Apply the concepts of parallel, perpendicular, intersecting, and skew lines to real-world situations (i.e. roads and routes).

MA.O.6.3.4. Create designs using line and rotational symmetry.

MA.O.6.3.5. Predict, describe, and perform transformations on two-dimensional shapes: translations, rotations, reflections

MA.O.6.3.6. Use geometric representations to solve real-world problems.

MA.O.6.3.7. Plot polygons on coordinate grids, determine lengths and areas from the graph.

WV.MA.S.6.4. Measurement: Through 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.

MA.O.6.4.1. Determine an approximation for pi using actual measurements.

MA.O.6.4.2. 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

MA.O.6.4.3. Investigate, model and describe surface area of rectangular prisms and cylinders; develop strategies to determine the surface area of rectangular prisms.

MA.O.6.4.4. Develop strategies to determine volume of cylinders; solve real-world problems involving volume of cylinders, justify the results.

MA.O.6.4.5. Given a two-dimensional polygon, construct a scale drawing given the scale factor.

WV.MA.S.6.5. Data Analysis and Probability: Through 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.

MA.O.6.5.1. Collect, organize, display, read, interpret and analyze real-world data using appropriate graphs and tables (with and without technology).

MA.O.6.5.2. 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).

MA.O.6.5.3. 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.

MA.O.6.5.4. Determine combinations and permutations of given real-world situations by multiple strategies, including creating lists.

WV.MA.S.7.1. Number and Operations: Through 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.

MA.O.7.1.1. Compare, order, and differentiate among integers, decimals, fractions, and irrational numbers using multiple representations (e.g., symbols, manipulatives, graphing on a number line).

MA.O.7.1.2. Model the relationship between perfect squares and square roots using physical representations; estimate square root and evaluate using technology.

MA.O.7.1.3. Using simple computation and problem-solving situations, demonstrate fluency and justify solutions in performing operations with rational numbers including negative numbers for adding, subtracting, multiplying, dividing

MA.O.7.1.4. Justify the use of the commutative, associative, distributive, identity and inverse properties to simplify numeric expressions.

MA.O.7.1.5. Analyze and solve grade-appropriate real-world problems with whole numbers, integers, decimals, fractions and percents including problems involving discounts, interest, taxes, tips, percent increase or decrease, and justify solutions including using estimation and reasonableness.

MA.O.7.1.6. Use inductive reasoning to find and justify the laws of exponents with numeric bases.

MA.O.7.1.7. Solve problems using numbers in scientific notation (positive and negative exponents) with and without technology, and interpret from real life contexts.

WV.MA.S.7.2. 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 contents.

MA.O.7.2.1. Use inductive reasoning to find missing elements in a variety of arithmetic and geometric patterns including algebraic sequences and series.

MA.O.7.2.2. Evaluate algebraic expressions with whole numbers, integers, absolute value and exponents using the order of operations.

MA.O.7.2.3. Solve problems by creating an input/output function table(including, but not limited to, spreadsheets) to predict future values, given a real-world situation involving rational numbers.

MA.O.7.2.4. Analyze proportional relationships in real-world situations, select an appropriate method to determine the solution and justify reasoning for choice of method to solve.

MA.O.7.2.5. Solve one-step linear equations and inequalities using a variety of strategies containing rational numbers with integer solutions; graph solutions, and justify the selection of the strategy and the reasonableness of the solution.

MA.O.7.2.6. Plot lines within the Cartesian coordinate plane from a table of values to solve mathematical real-world problems.

MA.O.7.2.7. Determine the slope of a line from its graphical representation.

MA.O.7.2.8. Represent algebraically and solve real-world application problems and justify solutions.

MA.O.7.2.9. Identify a real life problem involving proportionality; make a hypothesis as to the outcome; develop, justify, and implement a method to collect, organize, and analyze data; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project using words, graphs, drawings, models, or tables.

WV.MA.S.7.3. Geometry: Through 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.

MA.O.7.3.1. Identify and construct: angle-pairs adjacent, complementary, supplementary, vertical; congruent segments and angles; perpendicular bisectors of segments; angle-bisectors

MA.O.7.3.2. Apply line symmetry to classify plane figures.

MA.O.7.3.3. Apply rotations, reflections, translations to plane figures and determine the coordinates of its transformation and compare and contrast the new figure with the original.

MA.O.7.3.4. Pose and solve ratio and proportion problems including scale drawings and similar polygons.

MA.O.7.3.5. Solve problems and explain the relationships among scale factor and area and volume including: square of a scale factor, cube of a scale factor

MA.O.7.3.6. Solve mathematical real-world problems using compound geometric figures.

WV.MA.S.7.4. Measurement: Through 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 measurements, and apply appropriate techniques, tools and formulas to determine measurements.

MA.O.7.4.1. Select and apply an appropriate method to solve (including, but not limited to, formulas) justify the method and the reasonableness of the solution, given a real-world problem solving situation involving: perimeter, circumference, area, surface area of prisms (rectangular and triangular), volume of prisms and cylinders, distance and temperature (Celsius, Fahrenheit)

MA.O.7.4.2. Use the Pythagorean Theorem to find the length of any side of a right triangle and apply to problem solving situations.

MA.O.7.4.3. Convert units of measurement, linear, area and volume, within customary and metric systems.

WV.MA.S.7.5. Data Analysis and Probability: Through 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.

MA.O.7.5.1. Determine theoretical probability of an event, make and test predictions through experimentation.

MA.O.7.5.2. Determine combinations and permutations by constructing sample spaces (e.g., listing, tree diagrams, frequency distribution tables).

MA.O.7.5.3. Collect, organize, graphically represent, and interpret data displays including frequency distributions, line-plots, scatter plots, box and whiskers, and multiple-line graphs.

MA.O.7.5.4. Analyze and solve application problems involving measures of central tendency (mean, median, mode) and dispersion (range) from data, graphs, tables, and experiments using appropriate technology to compare two sets of data.

WV.MA.S.8.1. Number and Operations: Through 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.

MA.O.8.1.1. Analyze, describe and compare the characteristics of rational and irrational numbers.

MA.O.8.1.2. Analyze and solve application problems with powers, squares, square roots, scientific notation, and verify solutions using estimation techniques.

MA.O.8.1.3. Analyze and solve grade-appropriate real-world problems with whole numbers, decimals, fractions, percents, percent increase and decrease, integers, and including, but not limited to, rates, tips, discounts, sales tax and interest and verify solutions using estimation techniques.

WV.MA.S.8.2. 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.

MA.O.8.2.1. Use a variety of strategies to solve one and two-step linear equations and inequalities with rational solutions; defend the selection of the strategy; graph the solutions and justify the reasonableness of the solution.

MA.O.8.2.2. Identify proportional relationships in real-world situations, then find and select an appropriate method to determine the solution; justify the reasonableness of the solution.

MA.O.8.2.3. Add and subtract polynomials limited to two variables and positive exponents.

MA.O.8.2.4. Use systems of linear equations to analyze situations and solve problems.

MA.O.8.2.5. Apply inductive and deductive reasoning to write a rule from data in an input/output table, analyze the table and the rule to determine if a functional relationship exists.

MA.O.8.2.6. Graph linear equations and inequalities within the Cartesian coordinate plane by generating a table of values (with and without technology).

MA.O.8.2.7. Formulate and apply a rule to generate an arithmetic, geometric and algebraic pattern.

MA.O.8.2.8. Determine the slope of a line using a variety of methods including graphing, change in y over change in x, equation

MA.O.8.2.9. Represent and solve real-world grade-appropriate problems using multiple strategies and justify solutions.

MA.O.8.2.10. Identify a real life problem involving change over time; make a hypothesis as to the outcome; develop, justify, and implement a method to collect, organize, and analyze data; generalize the results to make a conclusion; compare the hypothesis and the results of the investigation; present the project using words, graphs, drawings, models, or tables.

WV.MA.S.8.3. Geometry: Through 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 transformation and use symmetry to analyze mathematical situations, and solve problems using visualization, spatial reasoning, and geometric modeling.

MA.O.8.3.1. Justify the relationships among corresponding, alternate interior, alternate exterior and vertical angles when parallel lines are cut by a transversal using models, pencil/paper, graphing calculator, and technology.

MA.O.8.3.2. Classify polyhedrons according to the number and shape of faces; use inductive reasoning to determine the relationship between vertices, faces and edges (edges + 2 = faces + vertices).

MA.O.8.3.3. Identify, apply, and construct perpendicular and angle bisectors with and without technology ) given a real-world situation.

MA.O.8.3.4. Create geometric patterns including tiling, art design, tessellations and scaling using transformations (rotations, reflections, translations) and predict results of combining, subdividing, and changing shapes of plane figures and solids.

MA.O.8.3.5. Create scale models of similar figures using ratio, proportion with pencil/paper and technology and determine scale factor.

MA.O.8.3.6. Make and test a conjecture concerning regular polygons, the cross section of a solid such as a cylinder, cone, and pyramid, the intersection of two or more geometric figures in the plane (e.g., intersection of a circle and a line), and justify the results.

WV.MA.S.8.4. Measurement: Through 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 measurements, and apply appropriate techniques, tools, and formulas to determine measurements.

MA.O.8.4.1. Select and apply an appropriate method to solve; justify the method and the reasonableness of the solution of problems involving volume of prisms, cylinders, cones, pyramids, spheres, given real-world problem solving situations.

MA.O.8.4.2. Solve problems involving missing measurements in plane and solid geometric figures using formulas and drawings including irregular figures, models or definitions.

MA.O.8.4.3. Solve right triangle problems where the existence of triangles is not obvious using the Pythagorean Theorem and indirect measurement in real-world problem solving situations.

WV.MA.S.8.5. Data Analysis and Probability: Through 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.

MA.O.8.5.1. Determine and explain whether a real-world situation involves permutations or combinations, then use appropriate technology to solve the problem.

MA.O.8.5.2. Compare the experimental and theoretical probability of a given situation (including compound probability of a dependent and independent event).

MA.O.8.5.3. Create and extrapolate information from multiple-bar graphs, box and whisker plots, and other data displays using appropriate technology.

MA.O.8.5.4. Analyze problem situations, games of chance, and consumer applications using random and non-random samplings to determine probability, make predictions, and identify sources of bias.

MA.O.8.5.5. Draw inferences, make conjectures and construct convincing arguments involving different effects that changes in data values have on measures of central tendency; misuses of statistical or numeric information, based on data analysis of same and different sets of data.

WV.MA.S.A1. Algebra I Mathematics

MA.S.A1.2. 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.

MA.O.A1.2.1. Formulate algebraic expressions for use in equations and inequalities that require planning to accurately model real-world problems.

MA.O.A1.2.2. 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.

MA.O.A1.2.3. Evaluate data provided, given a real-world situation, select an appropriate literal equation and solve for a needed variable.

MA.O.A1.2.4. Develop and test hypotheses to derive the laws of exponents and use them to perform operations on expressions with integral exponents.

MA.O.A1.2.5. 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.

MA.O.A1.2.6. Determine the slope of a line through a variety of strategies (e.g. given an equation or graph).

MA.O.A1.2.7. 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.

MA.O.A1.2.8. Identify a real life situation 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 technology).

MA.O.A1.2.9. Create and solve systems of linear equations graphically and numerically using the elimination method and the substitution method, given a real-world situation.

MA.O.A1.2.10. Simplify and evaluate algebraic expressions add and subtract polynomials multiply and divide binomials by binomials or monomials.

MA.O.A1.2.11. Create polynomials to represent and solve problems from real-world situations while focusing on symbolic and graphical patterns.

MA.O.A1.2.12. Use area models and graphical representations to develop and explain appropriate methods of factoring.

MA.O.A1.2.13. Simplify radical expressions through: adding, subtracting, multiplying and dividing; exact and approximate forms.

MA.O.A1.2.14. Choose the most efficient method to solve quadratic equations by graphing (with and without technology), factoring quadratic formula and draw reasonable conclusions about a situation being modeled.

MA.O.A1.2.15. Describe real life situations involving exponential growth and decay equations including y=2 to the x and y=(1/2) to the x; compare the equation with attributes of an associated table and graph to demonstrate an understanding of their interrelationship.

MA.O.A1.2.16. Simplify and evaluate rational expressions add, subtract, multiply and divide determine when an expression is undefined.

MA.O.A1.2.17. Perform a linear regression (with and without technology): 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.

MA.O.A1.2.18. Compute and interpret the expected value of random variables in simple cases using simulations and rules of probability (with and without technology).

MA.O.A1.2.19. Gather data to create histograms, box plots, scatter plots and normal distribution curves and use them to draw and support conclusions about the data.

MA.O.A1.2.20. Design experiments to model and solve problems using the concepts of sample space and probability distribution.

MA.O.A1.2.21. Use multiple representations, such as words, graphs, tables of values and equations, to solve practical problems; describe advantages and disadvantages of the use of each representation.

WV.MA.S.G. Geometry Mathematics

MA.S.G.3. Geometry: Through 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.

MA.O.G.3.1. Represent geometric figures, such as points, lines, planes, segments, rays, and angles pictorially with proper identification and distinguish between undefined and defined terms.

MA.O.G.3.2. Differentiate and apply inductive and deductive reasoning, justify conclusions in real-world settings.

MA.O.G.3.3. Use the basic concepts of symbolic logic including identifying the converse, inverse, and contrapositive of a conditional statement and test the validity of conclusions with methods that include Venn Diagrams.

MA.O.G.3.4. Validate conclusions by constructing logical arguments using both formal and informal methods with direct and indirect reasoning.

MA.O.G.3.5. 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.

MA.O.G.3.6. 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.

MA.O.G.3.7. Make conjectures and justify congruence relationships with an emphasis on triangles and employ these relationships to solve problems.

MA.O.G.3.8. Identify general properties of and compare and contrast the properties of convex and concave quadrilaterals: parallelograms, rectangles, rhombuses, squares, trapezoids

MA.O.G.3.9. Identify a real life situation that involves similarity in two or three dimensions; pose a question; make a hypothesis as to the answer, develop, justify, and implement a method to collect, organize, and analyze related data; 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 and geometry (with and without technology).

MA.O.G.3.10. 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).

MA.O.G.3.11. 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.

MA.O.G.3.12. 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).

MA.O.G.3.13. Investigate measures of angles formed by chords, tangents, and secants of a circle and draw conclusions for the relationship to its arcs.

MA.O.G.3.14. 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.

MA.O.G.3.15. Develop properties of tessellating figures and use those properties to tessellate the plane.

MA.O.G.3.16. Derive and justify formulas for area, perimeter, surface area, and volume using nets and apply them to solve real-world problems.

MA.O.G.3.17. 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.

MA.O.G.3.18. Construct a triangle's medians, altitudes, angle and perpendicular bisectors using various methods; and develop logical concepts about their relationships to be used in solving real-world problems.

MA.O.G.3.19. 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.

MA.O.G.3.20. Compare and contrast Euclidean geometry to other geometries (i.e. spherical, elliptic) using various forms of communication such as development of physical models, oral or written reports.

MA.O.G.3.21. Approximate the area of irregularly shaped regions based on the approximations and the attributes of the related region, develop a formula for finding the area of irregularly shaped regions. Plan, organize and present results by justifying conclusions.

WV.MA.S.A2. Algebra II Mathematics

MA.S.A2.2. 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.

MA.O.A2.2.1. Determine equations of lines including parallel, perpendicular, vertical and horizontal lines, and compare and contrast the properties of these equations.

MA.O.A2.2.2. 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.

MA.O.A2.2.3. Define complex numbers, simplify powers of ''i', perform basic operations with complex numbers, and give answers as complex numbers in simplest form.

MA.O.A2.2.4. Simplify expressions involving radicals and fractional exponents, convert between the two forms, and solve equations containing radicals and exponents.

MA.O.A2.2.5. 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.

MA.O.A2.2.6. Develop and use the appropriate field properties of matrices by adding, subtracting, and multiplying; solve a system of linear equations using matrices; and apply skills toward solving practical problems.

MA.O.A2.2.7. 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.

MA.O.A2.2.8. 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.

MA.O.A2.2.9. Solve quadratic inequalities, graph their solution sets, and express solutions using interval notation.

MA.O.A2.2.10. Solve and graph the solution set of systems of linear inequalities in two variables by finding the maximum or minimum values of a function over the feasible region using linear programming techniques.

MA.O.A2.2.11. Solve practical problems involving direct, inverse and joint variation.

MA.O.A2.2.12. Analyze the conic sections; identify and sketch the graphs of a parabola, circle, ellipse, and hyperbola and convert between graphs and equations.

MA.O.A2.2.13. Solve absolute value inequalities graphically, numerically and algebraically and express the solution set in interval notation.

MA.O.A2.2.14. Define a logarithmic function, transform between exponential and logarithmic forms, and apply the basic properties of logarithms to simplify or expand an expression.

MA.O.A2.2.15. Identify a real life situation that exhibits characteristics of change that can be modeled by a quadratic equations; pose a questions; 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 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 technology).

MA.O.A2.2.16. Describe and illustrate how patterns and sequences are used to develop recursive and closed form equations; analyze and describe characteristics of each form.

WV.MA.S.CM. Conceptual Mathematics

MA.S.CM.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.

MA.O.CM.2.1. Use a variety of problem solving strategies (e.g., draw a diagram, look for a pattern, work backwards) to solve real-world problems.

MA.O.CM.2.2. Interpret graphs of functions including linear, quadratic, and exponential.

MA.O.CM.2.3. Solve application problems using linear, quadratic and exponential functions with emphasis on data collection and analysis.

MA.O.CM.2.4. Choose the appropriate formulas to solve workplace problems and judge the reasonableness of the solutions.

MA.O.CM.2.5. Describe and illustrate how calculating costs, simple and compound interest, finance charge, loan payment and tax functions are used to solve real-world problems.

MA.O.CM.2.6. Identify a real life situation that involves investing money over time; pose a question; make a hypothesis as to the answer; develop, justify, and implement a method to collect, organize, and analyze related data; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project numerically, analytically, graphically and verbally using words, graphs, models, or tables (with and without technology).

MA.S.CM.3. Geometry: Through 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.

MA.O.CM.3.1. Apply concepts of geometry including the Pythagorean Theorem, similar triangles, and right triangle trigonometry.

MA.O.CM.3.2. Compute measures to solve real-world problems, using relationships involving perimeter, area, surface area and volume of geometric figures.

MA.O.CM.3.3. Analyze the connections of various geometric shapes and patterns to art, architecture, and nature.

MA.S.CM.5. Data Analysis and Probability: Through 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.

MA.O.CM.5.1. Relate mathematical content to its historical development.

MA.O.CM.5.2. Integrate other disciplines into the study of mathematics through simulations, research, and projects.

MA.O.CM.5.3. Determine possible outcomes using tree diagrams and the counting principles of permutations and combinations, develop conclusions and offer solutions for new situations, using real-world data.

MA.O.CM.5.4. Design and conduct probability investigations and then determine, analyze, and communicate the results.

MA.O.CM.5.5. Collect and interpret data using various methods of displaying numerical data, including frequency distributions, graphs, histograms, stem-and-leaf plots, and box-and-whiskers plots, using technology when appropriate.

MA.O.CM.5.6. Relate the measures of central tendency and the measures of dispersion to a normal distribution.

MA.O.CM.5.7. Apply the measures of central tendency and the measures of dispersion to workplace situations.

MA.O.CM.5.8. Use statistical tools for workplace applications such as quality control, marketing and predicting trends.

WV.MA.S.T. Trigonometry Mathematics

MA.S.T.3. Geometry: Through 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.

MA.O.T.3.1. 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.

MA.O.T.3.1.1. Determine the value of the other trigonometric functions given the value of one of the trigonometric functions and verify these values with technology.

MA.O.T.3.1.2. 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.

MA.O.T.3.1.3. Compare circular functions and the trigonometric function values to draw inferences about coterminal angles and co-functions.

MA.O.T.3.2. Convert angle measures from degrees to radians (and vice versa) and apply this concept to

MA.O.T.3.2.1. Create a data set, analyze, and formulate a hypothesis to test and develop formulas for the arc length, area of a sector, and angular velocity and use the formula for application in the real-world.

MA.O.T.3.2.2. Compare and contrast the concepts of angular velocity and linear velocity and demonstrate by graphical or algebraic means relationship between them and apply to real-world problems.

MA.O.T.3.3. Using various methods, basic identities and graphical representation

MA.O.T.3.3.1. Verify trigonometric identities

MA.O.T.3.3.2. Prove the sum and difference to two angles, double-angles, and half-angle identities

MA.O.T.3.4. Justify and present the solutions of trigonometric equations that include both infinite and finite (over a restricted domain) solutions.

MA.O.T.3.5. Find the value of the inverse trigonometric functions using special angle trigonometric function values and technology.

MA.O.T.3.5.1. Draw inferences of restricted domain to recognize and produce a graph of the inverse trigonometric functions.

MA.O.T.3.5.2. Prove conjectures made about the solution of the equations such as x = sin (arcsin y), x = sin (arcos y) being sure to consider restrictions of the domain.

MA.O.T.3.6. Identify a real life problem utilizing graphs of trigonometric functions and/or the inverse functions; make a hypothesis as to the outcome; develop, justify, and implement a method to collect, organize, and analyze data; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project using words, graphs, drawings, models, or tables.

MA.O.T.3.7. Model periodic data sets using graphs, tables, and equations and use them to analyze real-world problems such as electricity and harmonic motion.

MA.O.T.3.8. Investigate real-world problems within a project based investigation involving triangles using the trigonometric functions, the law of sines and the law of cosines, justify and present results.

MA.O.T.3.9. Develop and test a hypothesis to find the area of a triangle given the measures of two sides and the included angle or the measures of three sides (Heron's formula) and use these formulas to find total area of figures constructed of multiple shapes.

MA.O.T.3.10. Express complex numbers in polar form:

MA.O.T.3.10.1. Perform operations including adding, subtracting, multiplying, and dividing;

MA.O.T.3.10.2. Evaluate powers and roots of complex numbers using De Moivre's Theorem; and graph complex numbers.

MA.O.T.3.10.3. Graph complex numbers in the polar coordinate plane and make conjectures about some polar graphs and real-world situations such as the paths that the planets travel.

MA.O.T.3.11. Create graphical and algebraic representations for performing vector operations and analyze these to solve real-world problems such as force analysis and navigation.

WV.MA.S.PS. Probability and Statistics Mathematics

MA.S.PS.5. Data Analysis and Probability: Through 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.

MA.O.PS.5.1. Distinguish between experimental and theoretical probability.

MA.O.PS.5.2. Using a real-world problem solving investigation, create and interpret data using various methods of displaying circle graphs, histograms, and frequency curves, make predictions, include information concerning outliers, present and justify results.

MA.O.PS.5.3. Determine possible outcomes using tree diagrams and the counting principles of permutations and combinations.

MA.O.PS.5.4. Express the chances of events occurring either in terms of a probability or odds.

MA.O.PS.5.5. Use the normal distribution and the binomial distribution including Pascal's triangle, to determine probability of events.

MA.O.PS.5.6. Analyze measures of central tendency (mean, median, and mode) from data presented in a variety of forms such as charts, tables, and graphs or from data created through experimentation.

MA.O.PS.5.7. Interpret and calculate measures of dispersions (range and standard deviation) from data presented in a variety of forms such as charts, tables and graphs or from data created through experimentation.

MA.O.PS.5.8. Analyze individual performances in terms of percentiles, z-scores, and t- scores.

MA.O.PS.5.9. Analyze the role of sampling, randomness, bias, and sample size in data collection and interpretation.

MA.O.PS.5.10. Identify a real life situation that involves statistical concepts including a t-test, make a hypothesis as to the outcome; develop, justify, and implement a method to collect, organize and analyze data; generalize the results to make a conclusion, compare the hypothesis and the conclusion; present the project using predictive and analytic tools (with and without technology).

MA.O.PS.5.11. Determine the correlation values for given data or for data generated by students and use the results to describe the association of the variables within the given data. Identify whether this association is systematic or predictable.

MA.O.PS.5.12. Calculate the Chi-Square values for a given population.

MA.O.PS.5.13. Perform a regression analysis on a set of data, either given or created through experimentation, and use the results to predict specific values of a variable. Identify the regression equation.

MA.O.PS.5.14. Perform an analysis of variance (ANOVA) and interpret the results.

WV.MA.S.PC. Pre-Calculus Mathematics

MA.S.PC.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.

MA.O.PC.2.1. Investigate and sketch the graphs of polynomials and rational functions by analyzing and using the characteristics of zeros, upper and lower bounds, y-intercepts, symmetry, asymptotes and end behavior, maximum and minimum points, and domain and range.

MA.O.PC.2.2. Solve higher order polynomial equations utilizing techniques such as Descartes' Rule of Signs, upper and lower bounds, and the Rational Root Theorem.

MA.O.PC.2.3. Relate Pascal's Triangle and the Binomial Theorem; use both to expand binomials with positive integral exponents.

MA.O.PC.2.4. Establish and explain the inverse relationship between exponential and logarithmic functions; graph related functions and include their domain and range using interval notation.

MA.O.PC.2.5. 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.

MA.O.PC.2.6. Solve problems involving the sum of finite and infinite sequences and series, including Sigma notation.

MA.O.PC.2.7. 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.

MA.O.PC.2.8. Analyze and describe the geometry of vectors, perform mathematical operations with vectors and use vectors to solve practical problems.

MA.O.PC.2.9. Apply the method of mathematical induction to prove formulas and statements.

MA.O.PC.2.10. Apply parametric methods to represent motion of objects.

MA.O.PC.2.11. Use multiple representations, such as words, graphs, tables, and equations, to solve practical problems involving logarithmic, exponential, polynomial, rational, and radical functions; explain how the representations are related to each other, as well as to the problem.

MA.S.PC.3. Geometry: Through 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.

MA.O.PC.3.1. Graph functions and conic sections using transformations.

MA.O.PC.3.2. Analyze and describe properties of conic sections; explain the interrelationship among the properties; solve practical problems involving conic sections.

MA.S.PC.5. Data Analysis and Probability: Through 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.

MA.O.PC.5.1. Identify a real life situation that exhibits characteristics of exponential or logistic growth or decay; 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 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 pre-calculus (with and without technology).

WV.MA.S.A1. Algebra I Mathematics

MA.S.A1.2. 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.

MA.O.A1.2.1. Formulate algebraic expressions for use in equations and inequalities that require planning to accurately model real-world problems.

MA.O.A1.2.2. 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.

MA.O.A1.2.3. Evaluate data provided, given a real-world situation, select an appropriate literal equation and solve for a needed variable.

MA.O.A1.2.4. Develop and test hypotheses to derive the laws of exponents and use them to perform operations on expressions with integral exponents.

MA.O.A1.2.5. 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.

MA.O.A1.2.6. Determine the slope of a line through a variety of strategies (e.g. given an equation or graph).

MA.O.A1.2.7. 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.

MA.O.A1.2.8. Identify a real life situation 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 technology).

MA.O.A1.2.9. Create and solve systems of linear equations graphically and numerically using the elimination method and the substitution method, given a real-world situation.

MA.O.A1.2.10. Simplify and evaluate algebraic expressions add and subtract polynomials multiply and divide binomials by binomials or monomials.

MA.O.A1.2.11. Create polynomials to represent and solve problems from real-world situations while focusing on symbolic and graphical patterns.

MA.O.A1.2.12. Use area models and graphical representations to develop and explain appropriate methods of factoring.

MA.O.A1.2.13. Simplify radical expressions through: adding, subtracting, multiplying and dividing; exact and approximate forms.

MA.O.A1.2.14. Choose the most efficient method to solve quadratic equations by graphing (with and without technology), factoring quadratic formula and draw reasonable conclusions about a situation being modeled.

MA.O.A1.2.15. Describe real life situations involving exponential growth and decay equations including y=2 to the x and y=(1/2) to the x; compare the equation with attributes of an associated table and graph to demonstrate an understanding of their interrelationship.

MA.O.A1.2.16. Simplify and evaluate rational expressions add, subtract, multiply and divide determine when an expression is undefined.

MA.O.A1.2.17. Perform a linear regression (with and without technology): 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.

MA.O.A1.2.18. Compute and interpret the expected value of random variables in simple cases using simulations and rules of probability (with and without technology).

MA.O.A1.2.19. Gather data to create histograms, box plots, scatter plots and normal distribution curves and use them to draw and support conclusions about the data.

MA.O.A1.2.20. Design experiments to model and solve problems using the concepts of sample space and probability distribution.

MA.O.A1.2.21. Use multiple representations, such as words, graphs, tables of values and equations, to solve practical problems; describe advantages and disadvantages of the use of each representation.

WV.MA.S.G. Geometry Mathematics

MA.S.G.3. Geometry: Through 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.

MA.O.G.3.1. Represent geometric figures, such as points, lines, planes, segments, rays, and angles pictorially with proper identification and distinguish between undefined and defined terms.

MA.O.G.3.2. Differentiate and apply inductive and deductive reasoning, justify conclusions in real-world settings.

MA.O.G.3.3. Use the basic concepts of symbolic logic including identifying the converse, inverse, and contrapositive of a conditional statement and test the validity of conclusions with methods that include Venn Diagrams.

MA.O.G.3.4. Validate conclusions by constructing logical arguments using both formal and informal methods with direct and indirect reasoning.

MA.O.G.3.5. 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.

MA.O.G.3.6. 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.

MA.O.G.3.7. Make conjectures and justify congruence relationships with an emphasis on triangles and employ these relationships to solve problems.

MA.O.G.3.8. Identify general properties of and compare and contrast the properties of convex and concave quadrilaterals: parallelograms, rectangles, rhombuses, squares, trapezoids

MA.O.G.3.9. Identify a real life situation that involves similarity in two or three dimensions; pose a question; make a hypothesis as to the answer, develop, justify, and implement a method to collect, organize, and analyze related data; 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 and geometry (with and without technology).

MA.O.G.3.10. 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).

MA.O.G.3.11. 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.

MA.O.G.3.12. 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).

MA.O.G.3.13. Investigate measures of angles formed by chords, tangents, and secants of a circle and draw conclusions for the relationship to its arcs.

MA.O.G.3.14. 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.

MA.O.G.3.15. Develop properties of tessellating figures and use those properties to tessellate the plane.

MA.O.G.3.16. Derive and justify formulas for area, perimeter, surface area, and volume using nets and apply them to solve real-world problems.

MA.O.G.3.17. 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.

MA.O.G.3.18. Construct a triangle's medians, altitudes, angle and perpendicular bisectors using various methods; and develop logical concepts about their relationships to be used in solving real-world problems.

MA.O.G.3.19. 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.

MA.O.G.3.20. Compare and contrast Euclidean geometry to other geometries (i.e. spherical, elliptic) using various forms of communication such as development of physical models, oral or written reports.

MA.O.G.3.21. Approximate the area of irregularly shaped regions based on the approximations and the attributes of the related region, develop a formula for finding the area of irregularly shaped regions. Plan, organize and present results by justifying conclusions.

WV.MA.S.A2. Algebra II Mathematics

MA.S.A2.2. 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.

MA.O.A2.2.1. Determine equations of lines including parallel, perpendicular, vertical and horizontal lines, and compare and contrast the properties of these equations.

MA.O.A2.2.2. 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.

MA.O.A2.2.3. Define complex numbers, simplify powers of ''i', perform basic operations with complex numbers, and give answers as complex numbers in simplest form.

MA.O.A2.2.4. Simplify expressions involving radicals and fractional exponents, convert between the two forms, and solve equations containing radicals and exponents.

MA.O.A2.2.5. 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.

MA.O.A2.2.6. Develop and use the appropriate field properties of matrices by adding, subtracting, and multiplying; solve a system of linear equations using matrices; and apply skills toward solving practical problems.

MA.O.A2.2.7. 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.

MA.O.A2.2.8. 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.

MA.O.A2.2.9. Solve quadratic inequalities, graph their solution sets, and express solutions using interval notation.

MA.O.A2.2.10. Solve and graph the solution set of systems of linear inequalities in two variables by finding the maximum or minimum values of a function over the feasible region using linear programming techniques.

MA.O.A2.2.11. Solve practical problems involving direct, inverse and joint variation.

MA.O.A2.2.12. Analyze the conic sections; identify and sketch the graphs of a parabola, circle, ellipse, and hyperbola and convert between graphs and equations.

MA.O.A2.2.13. Solve absolute value inequalities graphically, numerically and algebraically and express the solution set in interval notation.

MA.O.A2.2.14. Define a logarithmic function, transform between exponential and logarithmic forms, and apply the basic properties of logarithms to simplify or expand an expression.

MA.O.A2.2.15. Identify a real life situation that exhibits characteristics of change that can be modeled by a quadratic equations; pose a questions; 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 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 technology).

MA.O.A2.2.16. Describe and illustrate how patterns and sequences are used to develop recursive and closed form equations; analyze and describe characteristics of each form.

WV.MA.S.CM. Conceptual Mathematics

MA.S.CM.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.

MA.O.CM.2.1. Use a variety of problem solving strategies (e.g., draw a diagram, look for a pattern, work backwards) to solve real-world problems.

MA.O.CM.2.2. Interpret graphs of functions including linear, quadratic, and exponential.

MA.O.CM.2.3. Solve application problems using linear, quadratic and exponential functions with emphasis on data collection and analysis.

MA.O.CM.2.4. Choose the appropriate formulas to solve workplace problems and judge the reasonableness of the solutions.

MA.O.CM.2.5. Describe and illustrate how calculating costs, simple and compound interest, finance charge, loan payment and tax functions are used to solve real-world problems.

MA.O.CM.2.6. Identify a real life situation that involves investing money over time; pose a question; make a hypothesis as to the answer; develop, justify, and implement a method to collect, organize, and analyze related data; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project numerically, analytically, graphically and verbally using words, graphs, models, or tables (with and without technology).

MA.S.CM.3. Geometry: Through 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.

MA.O.CM.3.1. Apply concepts of geometry including the Pythagorean Theorem, similar triangles, and right triangle trigonometry.

MA.O.CM.3.2. Compute measures to solve real-world problems, using relationships involving perimeter, area, surface area and volume of geometric figures.

MA.O.CM.3.3. Analyze the connections of various geometric shapes and patterns to art, architecture, and nature.

MA.S.CM.5. Data Analysis and Probability: Through 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.

MA.O.CM.5.1. Relate mathematical content to its historical development.

MA.O.CM.5.2. Integrate other disciplines into the study of mathematics through simulations, research, and projects.

MA.O.CM.5.3. Determine possible outcomes using tree diagrams and the counting principles of permutations and combinations, develop conclusions and offer solutions for new situations, using real-world data.

MA.O.CM.5.4. Design and conduct probability investigations and then determine, analyze, and communicate the results.

MA.O.CM.5.5. Collect and interpret data using various methods of displaying numerical data, including frequency distributions, graphs, histograms, stem-and-leaf plots, and box-and-whiskers plots, using technology when appropriate.

MA.O.CM.5.6. Relate the measures of central tendency and the measures of dispersion to a normal distribution.

MA.O.CM.5.7. Apply the measures of central tendency and the measures of dispersion to workplace situations.

MA.O.CM.5.8. Use statistical tools for workplace applications such as quality control, marketing and predicting trends.

WV.MA.S.T. Trigonometry Mathematics

MA.S.T.3. Geometry: Through 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.

MA.O.T.3.1. 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.

MA.O.T.3.1.1. Determine the value of the other trigonometric functions given the value of one of the trigonometric functions and verify these values with technology.

MA.O.T.3.1.2. 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.

MA.O.T.3.1.3. Compare circular functions and the trigonometric function values to draw inferences about coterminal angles and co-functions.

MA.O.T.3.2. Convert angle measures from degrees to radians (and vice versa) and apply this concept to

MA.O.T.3.2.1. Create a data set, analyze, and formulate a hypothesis to test and develop formulas for the arc length, area of a sector, and angular velocity and use the formula for application in the real-world.

MA.O.T.3.2.2. Compare and contrast the concepts of angular velocity and linear velocity and demonstrate by graphical or algebraic means relationship between them and apply to real-world problems.

MA.O.T.3.3. Using various methods, basic identities and graphical representation

MA.O.T.3.3.1. Verify trigonometric identities

MA.O.T.3.3.2. Prove the sum and difference to two angles, double-angles, and half-angle identities

MA.O.T.3.4. Justify and present the solutions of trigonometric equations that include both infinite and finite (over a restricted domain) solutions.

MA.O.T.3.5. Find the value of the inverse trigonometric functions using special angle trigonometric function values and technology.

MA.O.T.3.5.1. Draw inferences of restricted domain to recognize and produce a graph of the inverse trigonometric functions.

MA.O.T.3.5.2. Prove conjectures made about the solution of the equations such as x = sin (arcsin y), x = sin (arcos y) being sure to consider restrictions of the domain.

MA.O.T.3.6. Identify a real life problem utilizing graphs of trigonometric functions and/or the inverse functions; make a hypothesis as to the outcome; develop, justify, and implement a method to collect, organize, and analyze data; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project using words, graphs, drawings, models, or tables.

MA.O.T.3.7. Model periodic data sets using graphs, tables, and equations and use them to analyze real-world problems such as electricity and harmonic motion.

MA.O.T.3.8. Investigate real-world problems within a project based investigation involving triangles using the trigonometric functions, the law of sines and the law of cosines, justify and present results.

MA.O.T.3.9. Develop and test a hypothesis to find the area of a triangle given the measures of two sides and the included angle or the measures of three sides (Heron's formula) and use these formulas to find total area of figures constructed of multiple shapes.

MA.O.T.3.10. Express complex numbers in polar form:

MA.O.T.3.10.1. Perform operations including adding, subtracting, multiplying, and dividing;

MA.O.T.3.10.2. Evaluate powers and roots of complex numbers using De Moivre's Theorem; and graph complex numbers.

MA.O.T.3.10.3. Graph complex numbers in the polar coordinate plane and make conjectures about some polar graphs and real-world situations such as the paths that the planets travel.

MA.O.T.3.11. Create graphical and algebraic representations for performing vector operations and analyze these to solve real-world problems such as force analysis and navigation.

WV.MA.S.PS. Probability and Statistics Mathematics

MA.S.PS.5. Data Analysis and Probability: Through 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.

MA.O.PS.5.1. Distinguish between experimental and theoretical probability.

MA.O.PS.5.2. Using a real-world problem solving investigation, create and interpret data using various methods of displaying circle graphs, histograms, and frequency curves, make predictions, include information concerning outliers, present and justify results.

MA.O.PS.5.3. Determine possible outcomes using tree diagrams and the counting principles of permutations and combinations.

MA.O.PS.5.4. Express the chances of events occurring either in terms of a probability or odds.

MA.O.PS.5.5. Use the normal distribution and the binomial distribution including Pascal's triangle, to determine probability of events.

MA.O.PS.5.6. Analyze measures of central tendency (mean, median, and mode) from data presented in a variety of forms such as charts, tables, and graphs or from data created through experimentation.

MA.O.PS.5.7. Interpret and calculate measures of dispersions (range and standard deviation) from data presented in a variety of forms such as charts, tables and graphs or from data created through experimentation.

MA.O.PS.5.8. Analyze individual performances in terms of percentiles, z-scores, and t- scores.

MA.O.PS.5.9. Analyze the role of sampling, randomness, bias, and sample size in data collection and interpretation.

MA.O.PS.5.10. Identify a real life situation that involves statistical concepts including a t-test, make a hypothesis as to the outcome; develop, justify, and implement a method to collect, organize and analyze data; generalize the results to make a conclusion, compare the hypothesis and the conclusion; present the project using predictive and analytic tools (with and without technology).

MA.O.PS.5.11. Determine the correlation values for given data or for data generated by students and use the results to describe the association of the variables within the given data. Identify whether this association is systematic or predictable.

MA.O.PS.5.12. Calculate the Chi-Square values for a given population.

MA.O.PS.5.13. Perform a regression analysis on a set of data, either given or created through experimentation, and use the results to predict specific values of a variable. Identify the regression equation.

MA.O.PS.5.14. Perform an analysis of variance (ANOVA) and interpret the results.

WV.MA.S.PC. Pre-Calculus Mathematics

MA.S.PC.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.

MA.O.PC.2.1. Investigate and sketch the graphs of polynomials and rational functions by analyzing and using the characteristics of zeros, upper and lower bounds, y-intercepts, symmetry, asymptotes and end behavior, maximum and minimum points, and domain and range.

MA.O.PC.2.2. Solve higher order polynomial equations utilizing techniques such as Descartes' Rule of Signs, upper and lower bounds, and the Rational Root Theorem.

MA.O.PC.2.3. Relate Pascal's Triangle and the Binomial Theorem; use both to expand binomials with positive integral exponents.

MA.O.PC.2.4. Establish and explain the inverse relationship between exponential and logarithmic functions; graph related functions and include their domain and range using interval notation.

MA.O.PC.2.5. 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.

MA.O.PC.2.6. Solve problems involving the sum of finite and infinite sequences and series, including Sigma notation.

MA.O.PC.2.7. 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.

MA.O.PC.2.8. Analyze and describe the geometry of vectors, perform mathematical operations with vectors and use vectors to solve practical problems.

MA.O.PC.2.9. Apply the method of mathematical induction to prove formulas and statements.

MA.O.PC.2.10. Apply parametric methods to represent motion of objects.

MA.O.PC.2.11. Use multiple representations, such as words, graphs, tables, and equations, to solve practical problems involving logarithmic, exponential, polynomial, rational, and radical functions; explain how the representations are related to each other, as well as to the problem.

MA.S.PC.3. Geometry: Through 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.

MA.O.PC.3.1. Graph functions and conic sections using transformations.

MA.O.PC.3.2. Analyze and describe properties of conic sections; explain the interrelationship among the properties; solve practical problems involving conic sections.

MA.S.PC.5. Data Analysis and Probability: Through 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.

MA.O.PC.5.1. Identify a real life situation that exhibits characteristics of exponential or logistic growth or decay; 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 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 pre-calculus (with and without technology).

WV.MA.S.A1. Algebra I Mathematics

MA.S.A1.2. 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.

MA.O.A1.2.1. Formulate algebraic expressions for use in equations and inequalities that require planning to accurately model real-world problems.

MA.O.A1.2.2. 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.

MA.O.A1.2.3. Evaluate data provided, given a real-world situation, select an appropriate literal equation and solve for a needed variable.

MA.O.A1.2.4. Develop and test hypotheses to derive the laws of exponents and use them to perform operations on expressions with integral exponents.

MA.O.A1.2.5. 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.

MA.O.A1.2.6. Determine the slope of a line through a variety of strategies (e.g. given an equation or graph).

MA.O.A1.2.7. 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.

MA.O.A1.2.8. Identify a real life situation 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 technology).

MA.O.A1.2.9. Create and solve systems of linear equations graphically and numerically using the elimination method and the substitution method, given a real-world situation.

MA.O.A1.2.10. Simplify and evaluate algebraic expressions add and subtract polynomials multiply and divide binomials by binomials or monomials.

MA.O.A1.2.11. Create polynomials to represent and solve problems from real-world situations while focusing on symbolic and graphical patterns.

MA.O.A1.2.12. Use area models and graphical representations to develop and explain appropriate methods of factoring.

MA.O.A1.2.13. Simplify radical expressions through: adding, subtracting, multiplying and dividing; exact and approximate forms.

MA.O.A1.2.14. Choose the most efficient method to solve quadratic equations by graphing (with and without technology), factoring quadratic formula and draw reasonable conclusions about a situation being modeled.

MA.O.A1.2.15. Describe real life situations involving exponential growth and decay equations including y=2 to the x and y=(1/2) to the x; compare the equation with attributes of an associated table and graph to demonstrate an understanding of their interrelationship.

MA.O.A1.2.16. Simplify and evaluate rational expressions add, subtract, multiply and divide determine when an expression is undefined.

MA.O.A1.2.17. Perform a linear regression (with and without technology): 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.

MA.O.A1.2.18. Compute and interpret the expected value of random variables in simple cases using simulations and rules of probability (with and without technology).

MA.O.A1.2.19. Gather data to create histograms, box plots, scatter plots and normal distribution curves and use them to draw and support conclusions about the data.

MA.O.A1.2.20. Design experiments to model and solve problems using the concepts of sample space and probability distribution.

MA.O.A1.2.21. Use multiple representations, such as words, graphs, tables of values and equations, to solve practical problems; describe advantages and disadvantages of the use of each representation.

WV.MA.S.G. Geometry Mathematics

MA.S.G.3. Geometry: Through 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.

MA.O.G.3.1. Represent geometric figures, such as points, lines, planes, segments, rays, and angles pictorially with proper identification and distinguish between undefined and defined terms.

MA.O.G.3.2. Differentiate and apply inductive and deductive reasoning, justify conclusions in real-world settings.

MA.O.G.3.3. Use the basic concepts of symbolic logic including identifying the converse, inverse, and contrapositive of a conditional statement and test the validity of conclusions with methods that include Venn Diagrams.

MA.O.G.3.4. Validate conclusions by constructing logical arguments using both formal and informal methods with direct and indirect reasoning.

MA.O.G.3.5. 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.

MA.O.G.3.6. 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.

MA.O.G.3.7. Make conjectures and justify congruence relationships with an emphasis on triangles and employ these relationships to solve problems.

MA.O.G.3.8. Identify general properties of and compare and contrast the properties of convex and concave quadrilaterals: parallelograms, rectangles, rhombuses, squares, trapezoids

MA.O.G.3.9. Identify a real life situation that involves similarity in two or three dimensions; pose a question; make a hypothesis as to the answer, develop, justify, and implement a method to collect, organize, and analyze related data; 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 and geometry (with and without technology).

MA.O.G.3.10. 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).

MA.O.G.3.11. 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.

MA.O.G.3.12. 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).

MA.O.G.3.13. Investigate measures of angles formed by chords, tangents, and secants of a circle and draw conclusions for the relationship to its arcs.

MA.O.G.3.14. 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.

MA.O.G.3.15. Develop properties of tessellating figures and use those properties to tessellate the plane.

MA.O.G.3.16. Derive and justify formulas for area, perimeter, surface area, and volume using nets and apply them to solve real-world problems.

MA.O.G.3.17. 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.

MA.O.G.3.18. Construct a triangle's medians, altitudes, angle and perpendicular bisectors using various methods; and develop logical concepts about their relationships to be used in solving real-world problems.

MA.O.G.3.19. 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.

MA.O.G.3.20. Compare and contrast Euclidean geometry to other geometries (i.e. spherical, elliptic) using various forms of communication such as development of physical models, oral or written reports.

MA.O.G.3.21. Approximate the area of irregularly shaped regions based on the approximations and the attributes of the related region, develop a formula for finding the area of irregularly shaped regions. Plan, organize and present results by justifying conclusions.

WV.MA.S.A2. Algebra II Mathematics

MA.S.A2.2. 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.

MA.O.A2.2.1. Determine equations of lines including parallel, perpendicular, vertical and horizontal lines, and compare and contrast the properties of these equations.

MA.O.A2.2.2. 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.

MA.O.A2.2.3. Define complex numbers, simplify powers of ''i', perform basic operations with complex numbers, and give answers as complex numbers in simplest form.

MA.O.A2.2.4. Simplify expressions involving radicals and fractional exponents, convert between the two forms, and solve equations containing radicals and exponents.

MA.O.A2.2.5. 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.

MA.O.A2.2.6. Develop and use the appropriate field properties of matrices by adding, subtracting, and multiplying; solve a system of linear equations using matrices; and apply skills toward solving practical problems.

MA.O.A2.2.7. 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.

MA.O.A2.2.8. 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.

MA.O.A2.2.9. Solve quadratic inequalities, graph their solution sets, and express solutions using interval notation.

MA.O.A2.2.10. Solve and graph the solution set of systems of linear inequalities in two variables by finding the maximum or minimum values of a function over the feasible region using linear programming techniques.

MA.O.A2.2.11. Solve practical problems involving direct, inverse and joint variation.

MA.O.A2.2.12. Analyze the conic sections; identify and sketch the graphs of a parabola, circle, ellipse, and hyperbola and convert between graphs and equations.

MA.O.A2.2.13. Solve absolute value inequalities graphically, numerically and algebraically and express the solution set in interval notation.

MA.O.A2.2.14. Define a logarithmic function, transform between exponential and logarithmic forms, and apply the basic properties of logarithms to simplify or expand an expression.

MA.O.A2.2.15. Identify a real life situation that exhibits characteristics of change that can be modeled by a quadratic equations; pose a questions; 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 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 technology).

MA.O.A2.2.16. Describe and illustrate how patterns and sequences are used to develop recursive and closed form equations; analyze and describe characteristics of each form.

WV.MA.S.CM. Conceptual Mathematics

MA.S.CM.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.

MA.O.CM.2.1. Use a variety of problem solving strategies (e.g., draw a diagram, look for a pattern, work backwards) to solve real-world problems.

MA.O.CM.2.2. Interpret graphs of functions including linear, quadratic, and exponential.

MA.O.CM.2.3. Solve application problems using linear, quadratic and exponential functions with emphasis on data collection and analysis.

MA.O.CM.2.4. Choose the appropriate formulas to solve workplace problems and judge the reasonableness of the solutions.

MA.O.CM.2.5. Describe and illustrate how calculating costs, simple and compound interest, finance charge, loan payment and tax functions are used to solve real-world problems.

MA.O.CM.2.6. Identify a real life situation that involves investing money over time; pose a question; make a hypothesis as to the answer; develop, justify, and implement a method to collect, organize, and analyze related data; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project numerically, analytically, graphically and verbally using words, graphs, models, or tables (with and without technology).

MA.S.CM.3. Geometry: Through 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.

MA.O.CM.3.1. Apply concepts of geometry including the Pythagorean Theorem, similar triangles, and right triangle trigonometry.

MA.O.CM.3.2. Compute measures to solve real-world problems, using relationships involving perimeter, area, surface area and volume of geometric figures.

MA.O.CM.3.3. Analyze the connections of various geometric shapes and patterns to art, architecture, and nature.

MA.S.CM.5. Data Analysis and Probability: Through 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.

MA.O.CM.5.1. Relate mathematical content to its historical development.

MA.O.CM.5.2. Integrate other disciplines into the study of mathematics through simulations, research, and projects.

MA.O.CM.5.3. Determine possible outcomes using tree diagrams and the counting principles of permutations and combinations, develop conclusions and offer solutions for new situations, using real-world data.

MA.O.CM.5.4. Design and conduct probability investigations and then determine, analyze, and communicate the results.

MA.O.CM.5.5. Collect and interpret data using various methods of displaying numerical data, including frequency distributions, graphs, histograms, stem-and-leaf plots, and box-and-whiskers plots, using technology when appropriate.

MA.O.CM.5.6. Relate the measures of central tendency and the measures of dispersion to a normal distribution.

MA.O.CM.5.7. Apply the measures of central tendency and the measures of dispersion to workplace situations.

MA.O.CM.5.8. Use statistical tools for workplace applications such as quality control, marketing and predicting trends.

WV.MA.S.T. Trigonometry Mathematics

MA.S.T.3. Geometry: Through 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.

MA.O.T.3.1. 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.

MA.O.T.3.1.1. Determine the value of the other trigonometric functions given the value of one of the trigonometric functions and verify these values with technology.

MA.O.T.3.1.2. 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.

MA.O.T.3.1.3. Compare circular functions and the trigonometric function values to draw inferences about coterminal angles and co-functions.

MA.O.T.3.2. Convert angle measures from degrees to radians (and vice versa) and apply this concept to

MA.O.T.3.2.1. Create a data set, analyze, and formulate a hypothesis to test and develop formulas for the arc length, area of a sector, and angular velocity and use the formula for application in the real-world.

MA.O.T.3.2.2. Compare and contrast the concepts of angular velocity and linear velocity and demonstrate by graphical or algebraic means relationship between them and apply to real-world problems.

MA.O.T.3.3. Using various methods, basic identities and graphical representation

MA.O.T.3.3.1. Verify trigonometric identities

MA.O.T.3.3.2. Prove the sum and difference to two angles, double-angles, and half-angle identities

MA.O.T.3.4. Justify and present the solutions of trigonometric equations that include both infinite and finite (over a restricted domain) solutions.

MA.O.T.3.5. Find the value of the inverse trigonometric functions using special angle trigonometric function values and technology.

MA.O.T.3.5.1. Draw inferences of restricted domain to recognize and produce a graph of the inverse trigonometric functions.

MA.O.T.3.5.2. Prove conjectures made about the solution of the equations such as x = sin (arcsin y), x = sin (arcos y) being sure to consider restrictions of the domain.

MA.O.T.3.6. Identify a real life problem utilizing graphs of trigonometric functions and/or the inverse functions; make a hypothesis as to the outcome; develop, justify, and implement a method to collect, organize, and analyze data; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project using words, graphs, drawings, models, or tables.

MA.O.T.3.7. Model periodic data sets using graphs, tables, and equations and use them to analyze real-world problems such as electricity and harmonic motion.

MA.O.T.3.8. Investigate real-world problems within a project based investigation involving triangles using the trigonometric functions, the law of sines and the law of cosines, justify and present results.

MA.O.T.3.9. Develop and test a hypothesis to find the area of a triangle given the measures of two sides and the included angle or the measures of three sides (Heron's formula) and use these formulas to find total area of figures constructed of multiple shapes.

MA.O.T.3.10. Express complex numbers in polar form:

MA.O.T.3.10.1. Perform operations including adding, subtracting, multiplying, and dividing;

MA.O.T.3.10.2. Evaluate powers and roots of complex numbers using De Moivre's Theorem; and graph complex numbers.

MA.O.T.3.10.3. Graph complex numbers in the polar coordinate plane and make conjectures about some polar graphs and real-world situations such as the paths that the planets travel.

MA.O.T.3.11. Create graphical and algebraic representations for performing vector operations and analyze these to solve real-world problems such as force analysis and navigation.

WV.MA.S.PS. Probability and Statistics Mathematics

MA.S.PS.5. Data Analysis and Probability: Through 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.

MA.O.PS.5.1. Distinguish between experimental and theoretical probability.

MA.O.PS.5.2. Using a real-world problem solving investigation, create and interpret data using various methods of displaying circle graphs, histograms, and frequency curves, make predictions, include information concerning outliers, present and justify results.

MA.O.PS.5.3. Determine possible outcomes using tree diagrams and the counting principles of permutations and combinations.

MA.O.PS.5.4. Express the chances of events occurring either in terms of a probability or odds.

MA.O.PS.5.5. Use the normal distribution and the binomial distribution including Pascal's triangle, to determine probability of events.

MA.O.PS.5.6. Analyze measures of central tendency (mean, median, and mode) from data presented in a variety of forms such as charts, tables, and graphs or from data created through experimentation.

MA.O.PS.5.7. Interpret and calculate measures of dispersions (range and standard deviation) from data presented in a variety of forms such as charts, tables and graphs or from data created through experimentation.

MA.O.PS.5.8. Analyze individual performances in terms of percentiles, z-scores, and t- scores.

MA.O.PS.5.9. Analyze the role of sampling, randomness, bias, and sample size in data collection and interpretation.

MA.O.PS.5.10. Identify a real life situation that involves statistical concepts including a t-test, make a hypothesis as to the outcome; develop, justify, and implement a method to collect, organize and analyze data; generalize the results to make a conclusion, compare the hypothesis and the conclusion; present the project using predictive and analytic tools (with and without technology).

MA.O.PS.5.11. Determine the correlation values for given data or for data generated by students and use the results to describe the association of the variables within the given data. Identify whether this association is systematic or predictable.

MA.O.PS.5.12. Calculate the Chi-Square values for a given population.

MA.O.PS.5.13. Perform a regression analysis on a set of data, either given or created through experimentation, and use the results to predict specific values of a variable. Identify the regression equation.

MA.O.PS.5.14. Perform an analysis of variance (ANOVA) and interpret the results.

WV.MA.S.PC. Pre-Calculus Mathematics

MA.S.PC.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.

MA.O.PC.2.1. Investigate and sketch the graphs of polynomials and rational functions by analyzing and using the characteristics of zeros, upper and lower bounds, y-intercepts, symmetry, asymptotes and end behavior, maximum and minimum points, and domain and range.

MA.O.PC.2.2. Solve higher order polynomial equations utilizing techniques such as Descartes' Rule of Signs, upper and lower bounds, and the Rational Root Theorem.

MA.O.PC.2.3. Relate Pascal's Triangle and the Binomial Theorem; use both to expand binomials with positive integral exponents.

MA.O.PC.2.4. Establish and explain the inverse relationship between exponential and logarithmic functions; graph related functions and include their domain and range using interval notation.

MA.O.PC.2.5. 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.

MA.O.PC.2.6. Solve problems involving the sum of finite and infinite sequences and series, including Sigma notation.

MA.O.PC.2.7. 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.

MA.O.PC.2.8. Analyze and describe the geometry of vectors, perform mathematical operations with vectors and use vectors to solve practical problems.

MA.O.PC.2.9. Apply the method of mathematical induction to prove formulas and statements.

MA.O.PC.2.10. Apply parametric methods to represent motion of objects.

MA.O.PC.2.11. Use multiple representations, such as words, graphs, tables, and equations, to solve practical problems involving logarithmic, exponential, polynomial, rational, and radical functions; explain how the representations are related to each other, as well as to the problem.

MA.S.PC.3. Geometry: Through 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.

MA.O.PC.3.1. Graph functions and conic sections using transformations.

MA.O.PC.3.2. Analyze and describe properties of conic sections; explain the interrelationship among the properties; solve practical problems involving conic sections.

MA.S.PC.5. Data Analysis and Probability: Through 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.

MA.O.PC.5.1. Identify a real life situation that exhibits characteristics of exponential or logistic growth or decay; 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 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 pre-calculus (with and without technology).

WV.MA.S.A1. Algebra I Mathematics

MA.S.A1.2. 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.

MA.O.A1.2.1. Formulate algebraic expressions for use in equations and inequalities that require planning to accurately model real-world problems.

MA.O.A1.2.2. 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.

MA.O.A1.2.3. Evaluate data provided, given a real-world situation, select an appropriate literal equation and solve for a needed variable.

MA.O.A1.2.4. Develop and test hypotheses to derive the laws of exponents and use them to perform operations on expressions with integral exponents.

MA.O.A1.2.5. 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.

MA.O.A1.2.6. Determine the slope of a line through a variety of strategies (e.g. given an equation or graph).

MA.O.A1.2.7. 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.

MA.O.A1.2.8. Identify a real life situation 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 technology).

MA.O.A1.2.9. Create and solve systems of linear equations graphically and numerically using the elimination method and the substitution method, given a real-world situation.

MA.O.A1.2.10. Simplify and evaluate algebraic expressions add and subtract polynomials multiply and divide binomials by binomials or monomials.

MA.O.A1.2.11. Create polynomials to represent and solve problems from real-world situations while focusing on symbolic and graphical patterns.

MA.O.A1.2.12. Use area models and graphical representations to develop and explain appropriate methods of factoring.

MA.O.A1.2.13. Simplify radical expressions through: adding, subtracting, multiplying and dividing; exact and approximate forms.

MA.O.A1.2.14. Choose the most efficient method to solve quadratic equations by graphing (with and without technology), factoring quadratic formula and draw reasonable conclusions about a situation being modeled.

MA.O.A1.2.15. Describe real life situations involving exponential growth and decay equations including y=2 to the x and y=(1/2) to the x; compare the equation with attributes of an associated table and graph to demonstrate an understanding of their interrelationship.

MA.O.A1.2.16. Simplify and evaluate rational expressions add, subtract, multiply and divide determine when an expression is undefined.

MA.O.A1.2.17. Perform a linear regression (with and without technology): 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.

MA.O.A1.2.18. Compute and interpret the expected value of random variables in simple cases using simulations and rules of probability (with and without technology).

MA.O.A1.2.19. Gather data to create histograms, box plots, scatter plots and normal distribution curves and use them to draw and support conclusions about the data.

MA.O.A1.2.20. Design experiments to model and solve problems using the concepts of sample space and probability distribution.

MA.O.A1.2.21. Use multiple representations, such as words, graphs, tables of values and equations, to solve practical problems; describe advantages and disadvantages of the use of each representation.

WV.MA.S.G. Geometry Mathematics

MA.S.G.3. Geometry: Through 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.

MA.O.G.3.1. Represent geometric figures, such as points, lines, planes, segments, rays, and angles pictorially with proper identification and distinguish between undefined and defined terms.

MA.O.G.3.2. Differentiate and apply inductive and deductive reasoning, justify conclusions in real-world settings.

MA.O.G.3.3. Use the basic concepts of symbolic logic including identifying the converse, inverse, and contrapositive of a conditional statement and test the validity of conclusions with methods that include Venn Diagrams.

MA.O.G.3.4. Validate conclusions by constructing logical arguments using both formal and informal methods with direct and indirect reasoning.

MA.O.G.3.5. 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.

MA.O.G.3.6. 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.

MA.O.G.3.7. Make conjectures and justify congruence relationships with an emphasis on triangles and employ these relationships to solve problems.

MA.O.G.3.8. Identify general properties of and compare and contrast the properties of convex and concave quadrilaterals: parallelograms, rectangles, rhombuses, squares, trapezoids

MA.O.G.3.9. Identify a real life situation that involves similarity in two or three dimensions; pose a question; make a hypothesis as to the answer, develop, justify, and implement a method to collect, organize, and analyze related data; 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 and geometry (with and without technology).

MA.O.G.3.10. 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).

MA.O.G.3.11. 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.

MA.O.G.3.12. 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).

MA.O.G.3.13. Investigate measures of angles formed by chords, tangents, and secants of a circle and draw conclusions for the relationship to its arcs.

MA.O.G.3.14. 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.

MA.O.G.3.15. Develop properties of tessellating figures and use those properties to tessellate the plane.

MA.O.G.3.16. Derive and justify formulas for area, perimeter, surface area, and volume using nets and apply them to solve real-world problems.

MA.O.G.3.17. 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.

MA.O.G.3.18. Construct a triangle's medians, altitudes, angle and perpendicular bisectors using various methods; and develop logical concepts about their relationships to be used in solving real-world problems.

MA.O.G.3.19. 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.

MA.O.G.3.20. Compare and contrast Euclidean geometry to other geometries (i.e. spherical, elliptic) using various forms of communication such as development of physical models, oral or written reports.

MA.O.G.3.21. Approximate the area of irregularly shaped regions based on the approximations and the attributes of the related region, develop a formula for finding the area of irregularly shaped regions. Plan, organize and present results by justifying conclusions.

WV.MA.S.A2. Algebra II Mathematics

MA.S.A2.2. 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.

MA.O.A2.2.1. Determine equations of lines including parallel, perpendicular, vertical and horizontal lines, and compare and contrast the properties of these equations.

MA.O.A2.2.2. 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.

MA.O.A2.2.3. Define complex numbers, simplify powers of ''i', perform basic operations with complex numbers, and give answers as complex numbers in simplest form.

MA.O.A2.2.4. Simplify expressions involving radicals and fractional exponents, convert between the two forms, and solve equations containing radicals and exponents.

MA.O.A2.2.5. 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.

MA.O.A2.2.6. Develop and use the appropriate field properties of matrices by adding, subtracting, and multiplying; solve a system of linear equations using matrices; and apply skills toward solving practical problems.

MA.O.A2.2.7. 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.

MA.O.A2.2.8. 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.

MA.O.A2.2.9. Solve quadratic inequalities, graph their solution sets, and express solutions using interval notation.

MA.O.A2.2.10. Solve and graph the solution set of systems of linear inequalities in two variables by finding the maximum or minimum values of a function over the feasible region using linear programming techniques.

MA.O.A2.2.11. Solve practical problems involving direct, inverse and joint variation.

MA.O.A2.2.12. Analyze the conic sections; identify and sketch the graphs of a parabola, circle, ellipse, and hyperbola and convert between graphs and equations.

MA.O.A2.2.13. Solve absolute value inequalities graphically, numerically and algebraically and express the solution set in interval notation.

MA.O.A2.2.14. Define a logarithmic function, transform between exponential and logarithmic forms, and apply the basic properties of logarithms to simplify or expand an expression.

MA.O.A2.2.15. Identify a real life situation that exhibits characteristics of change that can be modeled by a quadratic equations; pose a questions; 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 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 technology).

MA.O.A2.2.16. Describe and illustrate how patterns and sequences are used to develop recursive and closed form equations; analyze and describe characteristics of each form.

WV.MA.S.CM. Conceptual Mathematics

MA.S.CM.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.

MA.O.CM.2.1. Use a variety of problem solving strategies (e.g., draw a diagram, look for a pattern, work backwards) to solve real-world problems.

MA.O.CM.2.2. Interpret graphs of functions including linear, quadratic, and exponential.

MA.O.CM.2.3. Solve application problems using linear, quadratic and exponential functions with emphasis on data collection and analysis.

MA.O.CM.2.4. Choose the appropriate formulas to solve workplace problems and judge the reasonableness of the solutions.

MA.O.CM.2.5. Describe and illustrate how calculating costs, simple and compound interest, finance charge, loan payment and tax functions are used to solve real-world problems.

MA.O.CM.2.6. Identify a real life situation that involves investing money over time; pose a question; make a hypothesis as to the answer; develop, justify, and implement a method to collect, organize, and analyze related data; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project numerically, analytically, graphically and verbally using words, graphs, models, or tables (with and without technology).

MA.S.CM.3. Geometry: Through 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.

MA.O.CM.3.1. Apply concepts of geometry including the Pythagorean Theorem, similar triangles, and right triangle trigonometry.

MA.O.CM.3.2. Compute measures to solve real-world problems, using relationships involving perimeter, area, surface area and volume of geometric figures.

MA.O.CM.3.3. Analyze the connections of various geometric shapes and patterns to art, architecture, and nature.

MA.S.CM.5. Data Analysis and Probability: Through 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.

MA.O.CM.5.1. Relate mathematical content to its historical development.

MA.O.CM.5.2. Integrate other disciplines into the study of mathematics through simulations, research, and projects.

MA.O.CM.5.3. Determine possible outcomes using tree diagrams and the counting principles of permutations and combinations, develop conclusions and offer solutions for new situations, using real-world data.

MA.O.CM.5.4. Design and conduct probability investigations and then determine, analyze, and communicate the results.

MA.O.CM.5.5. Collect and interpret data using various methods of displaying numerical data, including frequency distributions, graphs, histograms, stem-and-leaf plots, and box-and-whiskers plots, using technology when appropriate.

MA.O.CM.5.6. Relate the measures of central tendency and the measures of dispersion to a normal distribution.

MA.O.CM.5.7. Apply the measures of central tendency and the measures of dispersion to workplace situations.

MA.O.CM.5.8. Use statistical tools for workplace applications such as quality control, marketing and predicting trends.

WV.MA.S.T. Trigonometry Mathematics

MA.S.T.3. Geometry: Through 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.

MA.O.T.3.1. 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.

MA.O.T.3.1.1. Determine the value of the other trigonometric functions given the value of one of the trigonometric functions and verify these values with technology.

MA.O.T.3.1.2. 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.

MA.O.T.3.1.3. Compare circular functions and the trigonometric function values to draw inferences about coterminal angles and co-functions.

MA.O.T.3.2. Convert angle measures from degrees to radians (and vice versa) and apply this concept to

MA.O.T.3.2.1. Create a data set, analyze, and formulate a hypothesis to test and develop formulas for the arc length, area of a sector, and angular velocity and use the formula for application in the real-world.

MA.O.T.3.2.2. Compare and contrast the concepts of angular velocity and linear velocity and demonstrate by graphical or algebraic means relationship between them and apply to real-world problems.

MA.O.T.3.3. Using various methods, basic identities and graphical representation

MA.O.T.3.3.1. Verify trigonometric identities

MA.O.T.3.3.2. Prove the sum and difference to two angles, double-angles, and half-angle identities

MA.O.T.3.4. Justify and present the solutions of trigonometric equations that include both infinite and finite (over a restricted domain) solutions.

MA.O.T.3.5. Find the value of the inverse trigonometric functions using special angle trigonometric function values and technology.

MA.O.T.3.5.1. Draw inferences of restricted domain to recognize and produce a graph of the inverse trigonometric functions.

MA.O.T.3.5.2. Prove conjectures made about the solution of the equations such as x = sin (arcsin y), x = sin (arcos y) being sure to consider restrictions of the domain.

MA.O.T.3.6. Identify a real life problem utilizing graphs of trigonometric functions and/or the inverse functions; make a hypothesis as to the outcome; develop, justify, and implement a method to collect, organize, and analyze data; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project using words, graphs, drawings, models, or tables.

MA.O.T.3.7. Model periodic data sets using graphs, tables, and equations and use them to analyze real-world problems such as electricity and harmonic motion.

MA.O.T.3.8. Investigate real-world problems within a project based investigation involving triangles using the trigonometric functions, the law of sines and the law of cosines, justify and present results.

MA.O.T.3.9. Develop and test a hypothesis to find the area of a triangle given the measures of two sides and the included angle or the measures of three sides (Heron's formula) and use these formulas to find total area of figures constructed of multiple shapes.

MA.O.T.3.10. Express complex numbers in polar form:

MA.O.T.3.10.1. Perform operations including adding, subtracting, multiplying, and dividing;

MA.O.T.3.10.2. Evaluate powers and roots of complex numbers using De Moivre's Theorem; and graph complex numbers.

MA.O.T.3.10.3. Graph complex numbers in the polar coordinate plane and make conjectures about some polar graphs and real-world situations such as the paths that the planets travel.

MA.O.T.3.11. Create graphical and algebraic representations for performing vector operations and analyze these to solve real-world problems such as force analysis and navigation.

WV.MA.S.PS. Probability and Statistics Mathematics

MA.S.PS.5. Data Analysis and Probability: Through 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.

MA.O.PS.5.1. Distinguish between experimental and theoretical probability.

MA.O.PS.5.2. Using a real-world problem solving investigation, create and interpret data using various methods of displaying circle graphs, histograms, and frequency curves, make predictions, include information concerning outliers, present and justify results.

MA.O.PS.5.3. Determine possible outcomes using tree diagrams and the counting principles of permutations and combinations.

MA.O.PS.5.4. Express the chances of events occurring either in terms of a probability or odds.

MA.O.PS.5.5. Use the normal distribution and the binomial distribution including Pascal's triangle, to determine probability of events.

MA.O.PS.5.6. Analyze measures of central tendency (mean, median, and mode) from data presented in a variety of forms such as charts, tables, and graphs or from data created through experimentation.

MA.O.PS.5.7. Interpret and calculate measures of dispersions (range and standard deviation) from data presented in a variety of forms such as charts, tables and graphs or from data created through experimentation.

MA.O.PS.5.8. Analyze individual performances in terms of percentiles, z-scores, and t- scores.

MA.O.PS.5.9. Analyze the role of sampling, randomness, bias, and sample size in data collection and interpretation.

MA.O.PS.5.10. Identify a real life situation that involves statistical concepts including a t-test, make a hypothesis as to the outcome; develop, justify, and implement a method to collect, organize and analyze data; generalize the results to make a conclusion, compare the hypothesis and the conclusion; present the project using predictive and analytic tools (with and without technology).

MA.O.PS.5.11. Determine the correlation values for given data or for data generated by students and use the results to describe the association of the variables within the given data. Identify whether this association is systematic or predictable.

MA.O.PS.5.12. Calculate the Chi-Square values for a given population.

MA.O.PS.5.13. Perform a regression analysis on a set of data, either given or created through experimentation, and use the results to predict specific values of a variable. Identify the regression equation.

MA.O.PS.5.14. Perform an analysis of variance (ANOVA) and interpret the results.

WV.MA.S.PC. Pre-Calculus Mathematics

MA.S.PC.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.

MA.O.PC.2.1. Investigate and sketch the graphs of polynomials and rational functions by analyzing and using the characteristics of zeros, upper and lower bounds, y-intercepts, symmetry, asymptotes and end behavior, maximum and minimum points, and domain and range.

MA.O.PC.2.2. Solve higher order polynomial equations utilizing techniques such as Descartes' Rule of Signs, upper and lower bounds, and the Rational Root Theorem.

MA.O.PC.2.3. Relate Pascal's Triangle and the Binomial Theorem; use both to expand binomials with positive integral exponents.

MA.O.PC.2.4. Establish and explain the inverse relationship between exponential and logarithmic functions; graph related functions and include their domain and range using interval notation.

MA.O.PC.2.5. 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.

MA.O.PC.2.6. Solve problems involving the sum of finite and infinite sequences and series, including Sigma notation.

MA.O.PC.2.7. 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.

MA.O.PC.2.8. Analyze and describe the geometry of vectors, perform mathematical operations with vectors and use vectors to solve practical problems.

MA.O.PC.2.9. Apply the method of mathematical induction to prove formulas and statements.

MA.O.PC.2.10. Apply parametric methods to represent motion of objects.

MA.O.PC.2.11. Use multiple representations, such as words, graphs, tables, and equations, to solve practical problems involving logarithmic, exponential, polynomial, rational, and radical functions; explain how the representations are related to each other, as well as to the problem.

MA.S.PC.3. Geometry: Through 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.

MA.O.PC.3.1. Graph functions and conic sections using transformations.

MA.O.PC.3.2. Analyze and describe properties of conic sections; explain the interrelationship among the properties; solve practical problems involving conic sections.

MA.S.PC.5. Data Analysis and Probability: Through 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.

MA.O.PC.5.1. Identify a real life situation that exhibits characteristics of exponential or logistic growth or decay; 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 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 pre-calculus (with and without technology).