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# Virginia Standards Ninth Grade Mathematics resources

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Algebra I

Statistics

A.11. The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve real-world problems, using mathematical models. Mathematical models will include linear and quadratic functions.

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

Quiz, Flash Cards, Worksheet, Game & Study Guide Displaying data

Functions

A.7. The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including

A.7.a) determining whether a relation is a function.

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

A.8. The student, given a situation in a real-world context, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically.

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

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

Equations and Inequalities

A.4. The student will solve multistep linear and quadratic equations in two variables, including

A.4.a) solving literal equations (formulas) for a given variable.

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

A.4.d) solving multistep linear equations algebraically and graphically.

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

A.4.e) solving systems of two linear equations in two variables algebraically and graphically.

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

A.5. The student will solve multistep linear inequalities in two variables, including

A.5.a) solving multistep linear inequalities algebraically and graphically.

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

A.6. The student will graph linear equations and linear inequalities in two variables, including

A.6.a) determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined.

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

Expressions and Operations

A.1. The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables.

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

A.2. The student will perform operations on polynomials, including

A.2.a) applying the laws of exponents to perform operations on expressions.

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

A.2.b) adding, subtracting, multiplying, and dividing polynomials.

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

Algebra, Functions, and Data Analysis

Data Analysis

AFDA.6. The student will calculate probabilities. Key concepts include

AFDA.6.b) dependent and independent events.

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

AFDA.6.d) counting techniques (permutations and combinations).

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

AFDA.8. The student will design and conduct an experiment/survey. Key concepts include

AFDA.8.b) sampling technique.

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

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

AFDA.8.d) data collection.

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

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

AFDA.8.e) data analysis and reporting.

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

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

Algebra and Functions

AFDA.1. The student will investigate and analyze function (linear, quadratic, exponential, and logarithmic) families and their characteristics. Key concepts include

Algebra II

Statistics

AII.10. The student will identify, create, and solve real-world problems involving inverse variation, joint variation, and a combination of direct and inverse variations.

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

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

AII.12. The student will compute and distinguish between permutations and combinations and use technology for applications.

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

Functions

AII.7. The student will investigate and analyze functions algebraically and graphically. Key concepts include

Expressions and Operations

AII.2. The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve real-world problems, including writing the first n terms, finding the nth term, and evaluating summation formulas.

Flip Charts Arithmetic & Sequences

Flip Charts Circle Around

Flip Charts Math Grade 8

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

Algebra II and Trigonometry

Statistics

AII/T.10. The student will identify, create, and solve real-world problems involving inverse variation, joint variation, and a combination of direct and inverse variations.

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

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

AII/T.12. The student will compute and distinguish between permutations and combinations and use technology for applications.

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

Functions

AII/T.7. The student will investigate and analyze functions algebraically and graphically. Key concepts include

Expressions and Operations

AII/T.2. The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve real-world problems, including writing the first n terms, finding the nth term, and evaluating summation formulas.

Flip Charts Arithmetic & Sequences

Flip Charts Circle Around

Flip Charts Math Grade 8

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

Discrete Mathematics

DM.13. The student will apply the formulas of combinatorics in the areas of

DM.13a). the Fundamental (Basic) Counting Principle;

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

DM.13c). permutations and combinations; and

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

Geometry

Three-Dimensional Figures

G.14. The student will use similar geometric objects in two- or three-dimensions to

G.14.a) compare ratios between side lengths, perimeters, areas, and volumes.

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

G.14.d) solve real-world problems about similar geometric objects.

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

Reasoning, Lines, and Transformations

G.2. The student will use the relationships between angles formed by two lines cut by a transversal to

G.2.a) determine whether two lines are parallel.

Flip Charts Math Grade 8

Flip Charts Plane Geometry

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

G.2.b) verify the parallelism, using algebraic and coordinate methods as well as deductive proofs.

Flip Charts Math Grade 8

Flip Charts Plane Geometry

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

G.2.c) solve real-world problems involving angles formed when parallel lines are cut by a transversal.

Flip Charts Math Grade 8

Flip Charts Plane Geometry

G.3. The student will use pictorial representations, including computer software, constructions, and coordinate methods, to solve problems involving symmetry and transformation. This will include

G.3.a) investigating and using formulas for finding distance, midpoint, and slope.

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

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

G.3.b) applying slope to verify and determine whether lines are parallel or perpendicular.

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

G.3.c) investigating symmetry and determining whether a figure is symmetric with respect to a line or a point.

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

Polygons and Circles

G.11. The student will use angles, arcs, chords, tangents, and secants to

G.11.b) solve real-world problems involving properties of circles.

Flip Charts Dot to Dot

Flip Charts Math Grade 8

Flip Charts Perimeter & Area

Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area

Mathematical Analysis

MA.6. The student will use mathematical induction to prove formulas and mathematical statements.

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

MA.9. The student will investigate and identify the characteristics of exponential and logarithmic functions in order to graph these functions and solve equations and real-world problems. This will include the role of e, natural and common logarithms, laws of exponents and logarithms, and the solution of logarithmic and exponential equations.

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

Probability and Statistics

PS.1. The student will analyze graphical displays of univariate data, including dotplots, stemplots, and histograms, to identify and describe patterns and departures from patterns, using central tendency, spread, clusters, gaps, and outliers. Appropriate technology will be used to create graphical displays.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

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

PS.11. The student will identify and describe two or more events as complementary, dependent, independent, and/or mutually exclusive.

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

PS.12. The student will find probabilities (relative frequency and theoretical), including conditional probabilities for events that are either dependent or independent, by applying the Law of Large Numbers concept, the addition rule, and the multiplication rule.

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

PS.15. The student will identify random variables as independent or dependent and find the mean and standard deviations for sums and differences of independent random variables.

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

PS.2. The student will analyze numerical characteristics of univariate data sets to describe patterns and departures from patterns, using mean, median, mode, variance, standard deviation, interquartile range, range, and outliers.

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

PS.3. The student will compare distributions of two or more univariate data sets, analyzing center and spread (within group and between group variations), clusters and gaps, shapes, outliers, or other unusual features.

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

PS.4. The student will analyze scatterplots to identify and describe the relationship between two variables, using shape; strength of relationship; clusters; positive, negative, or no association; outliers; and influential points.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Displaying data

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

PS.5. The student will find and interpret linear correlation, use the method of least squares regression to model the linear relationship between two variables, and use the residual plots to assess linearity.

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

PS.8. The student will describe the methods of data collection in a census, sample survey, experiment, and observational study and identify an appropriate method of solution for a given problem setting.

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

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

PS.9. The student will plan and conduct a survey. The plan will address sampling techniques (e.g., simple random, stratified) and methods to reduce bias.

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

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