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# West Virginia Standards Ninth Grade Mathematics resources

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Mathematics: Algebra I

M.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.

M.O.A1.2.1. Students will formulate algebraic expressions for use in equations and inequalities that require planning to accurately model real-world problems.

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

M.O.A1.2.10. Students will simplify and evaluate algebraic expressions

M.O.A1.2.10.a. Add and subtract polynomials

Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

M.O.A1.2.10.b. Multiply and divide binomials by binomials or monomials

Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

M.O.A1.2.11. Students will create polynomials to represent and solve problems from real-world situations while focusing on symbolic and graphical patterns.

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

M.O.A1.2.17. Students will perform a linear regression (with and without technology),

M.O.A1.2.17.a. Compare and evaluate methods of fitting lines to data.

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships

M.O.A1.2.2. Students will 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.

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

M.O.A1.2.20. Students will design experiments to model and solve problems using the concepts of sample space and probability distribution.

Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability

M.O.A1.2.3. Students will evaluate data provided, given a real-world situation, select an appropriate literal equation and solve for a needed variable.

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

M.O.A1.2.4. Students will develop and test hypotheses to derive the laws of exponents and use them to perform operations on expressions with integral exponents.

Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

M.O.A1.2.5. Students will 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.

Flip Charts Arithmetic & Sequences

Flip Charts Circle Around

Flip Charts Math Grade 8

Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences

M.O.A1.2.6. Students will determine the slope of a line through a variety of strategies (e.g. given an equation or graph).

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

M.O.A1.2.8. Students will 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).

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships

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

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

Mathematics: Algebra II

M.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.

M.O.A2.2.11. Students will solve practical problems involving direct, inverse and joint variation.

Quiz, Flash Cards, Worksheet, Game & Study Guide Functions

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships

Mathematics: Algebra III

M.S.A3.2. 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.

M.O.A3.2.1. Students will use properties of analytic geometry to justify and use the distance and midpoint formulas and negative reciprocal criterion for non-vertical perpendicular lines.

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures

M.O.A3.2.11. Students will determine the average rate of change of a function between any two points on its graph and use this rate to find the equation of a secant line; interpret the average rate of change to solve real world problems; relate signs of average rate of change to the function increasing or decreasing; and demonstrate a geometrical and conceptual understanding of the difference quotient.

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

M.O.A3.2.22. Students will build on the skills of solving linear equations in two variables using elimination, substitution, or matrix methods to solve systems with three or more unknowns involving real world applications. Categorize systems of equations as zero, one, or infinitely many solutions, by both geometric and algebraic methods.

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

M.O.A3.2.3. Students will relate analytical attributes such as characteristics of zeros, x- and y- intercepts, symmetry, asymptotes, end behavior, maximum and minimum points, and domain and range, to graphical and algebraic representations of polynomials and rational functions.

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

M.O.A3.2.8. Students will differentiate between functions and relations; evaluate, add, subtract, multiply, divide, rationalize, simplify, and compose functions (including rational, radical and those with fractional exponents); express domain and range of functions.

Quiz, Flash Cards, Worksheet, Game & Study Guide Functions

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

Mathematics: Calculus

M.S.C.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.

M.O.C.2.1. Students will use abstract notation to apply properties of algebraic, trigonometric, exponential, logarithmic and composite functions, as well as their inverses, represented graphically, numerically, analytically, and verbally; and demonstrate an understanding of the connections among these representations.

Quiz, Flash Cards, Worksheet, Game & Study Guide Functions

M.S.C.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.

M.O.C.5.1. Students will identify a real life situation that involves quantities that change 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; 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 calculus.

Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data

Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability

Mathematics: Conceptual Mathematics

M.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.

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

Flip Charts Applying Percents

Flip Charts Math Grade 8

Quiz, Flash Cards, Worksheet, Game & Study Guide Applications of percent

M.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.

M.O.CM.3.1. Students will apply concepts of geometry including the Pythagorean Theorem, similar triangles, and right triangle trigonometry.

Flip Charts Math Grade 8

Flip Charts Ratios, Rates & Proportions

M.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.

M.O.CM.5.3. Students will 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.

Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting

M.O.CM.5.4. Students will design and conduct probability investigations and then determine, analyze, and communicate the results.

Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability

M.O.CM.5.7. Students will apply the measures of central tendency and the measures of dispersion to workplace situations.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data

Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

Mathematics: Geometry and Applied Geometry

M.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.

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

Flip Charts Math Grade 8

Flip Charts Plane Geometry

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures

M.O.G.3.11. Students will 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.

Flip Charts Math Grade 8

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

M.O.G.3.15. Students will develop properties of tessellating figures and use those properties to tessellate the plane.

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

M.O.G.3.17. Students will 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.

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures

M.O.G.3.19. Students will create and apply concepts using transformational geometry and laws of symmetry, of a

M.O.G.3.19.e. Dilation of a figure, and

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

M.O.G.3.5. Students will construct formal and informal proofs by applying definitions, theorems, and postulates related to such topics as

M.O.G.3.5.d. Angles formed by perpendicular lines, and

Flip Charts Math Grade 8

Flip Charts Plane Geometry

M.O.G.3.6. Students will 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.

Flip Charts Math Grade 8

Flip Charts Plane Geometry

M.O.G.3.7. Students will make conjectures and justify congruence relationships with an emphasis on triangles and employ these relationships to solve problems.

Flip Charts Math Grade 8

Flip Charts Plane Geometry

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

M.O.G.3.9. Students will 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).

Flip Charts Math Grade 8

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

Mathematics: Pre-Calculus

M.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.

M.O.PC.2.9. Students will apply the method of mathematical induction to prove formulas and statements.

Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

Mathematics: Probability and Statistics

M.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.

M.O.PS.5.13. Students will 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.

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships

M.O.PS.5.14. Students will perform an analysis of variance (ANOVA) and interpret the results.

Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data

M.O.PS.5.2. Students will 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.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

M.O.PS.5.3. Students will determine possible outcomes using tree diagrams and the counting principles of permutations and combinations.

Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting

M.O.PS.5.4. Students will express the chances of events occurring either in terms of a probability or odds.

Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability

Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting

M.O.PS.5.6. Students will 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.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data

Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

M.O.PS.5.7. Students will 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.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

M.O.PS.5.9. Students will analyze the role of sampling, randomness, bias, and sample size in data collection and interpretation.

Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data

Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability