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South Carolina: Math Grades 9-12

This content correlation lists the recommended Gizmos for the above state curriculum standard.

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Correlation by State

South Carolina: Math Grades 9-12

ALGEBRA

I. Understand patterns, relations, and functions.

A. Generalize patterns using explicitly defined and recursively defined functions.

1. Interpret and make inferences from explicit and recursive functional relationships.

2. Describe independent and dependent quantities in functional relationships.

3. Use patterns to generate the laws of exponents and apply them in problem-solving situations.

B. Understand relations and functions and select, convert flexibly among, and use various representations for them.

1. Gather and record data, or use data sets, to determine functional (systematic) relationships between quantities.

2. Represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities including representations involving computer algebra systems, spreadsheets, and graphing calculators.

C. Analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior.

1. Relate the solution(s) of quadratic equations to the root(s) of the quadratic functions.

3. Analyze graphs of quadratic functions and write conclusions for problem situations.

E. Understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions.

2. Determine reasonable domain and range values for a variety of situations.

3. Relate direct variation to linear functions and solve problems involving proportional change.

F. Interpret representations of functions of two variables.

1. Recognize that real-world phenomena can be modeled by specific functions (e.g., population growth can be modeled by exponential functions, periodicity can be modeled by trigonometric functions).

II. Represent and analyze mathematical situations and structures using algebraic symbols.

A. Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations.

2. Simplify polynomial expressions and perform polynomial arithmetic.

B. Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency-mentally or with paper and pencil in simple cases and using technology in all cases.

2. Solve systems of linear equations using concrete models, graphs, tables, and algebraic methods.

4. Solve quadratic equations using concrete models, tables, graphs, and algebraic methods that include factoring, the quadratic formula, and computer algebra systems, spreadsheets, and graphing calculators.

C. Use symbolic algebra to represent and explain mathematical relationships.

1. Look for patterns and represent generalizations algebraically in given situations.

D. Use a variety of symbolic representations, including recursive and parametric equations, for functions and relations.

1. Translate among and use algebraic, tabular, graphical, or verbal descriptions of linear functions using computer algebra systems, spreadsheets, and graphing calculators.

III. Use mathematical models to represent and understand quantitative relationships.

A. Identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships.

2. Analyze situations involving linear functions and formulate linear equations or inequalities to solve problems.

B. Use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts.

2. Graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept.

3. Analyze data and represent situations involving inverse variation using concrete models, tables, graphs, or algebraic methods as well as computer algebra systems, spreadsheets, and graphing calculators.

4. Analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods as well as computer algebra systems, spreadsheets, and graphing calculators.

IV. Analyze change in various contexts.

A. Approximate and interpret rates of change from graphical and numerical data.

1. Interpret rates of change as they apply to phenomena such as inflation, spread of disease, population growth, tax brackets, and pollution.

2. Analyze graphical data gathered by technical equipment including combinations of graphs, periodic phenomena, and rates of change.

DATA ANALYSIS & PROBABILITY

I. Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

A. Understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each.

2. Evaluate the legitimacy of conclusions about the population based on the sample(s) studied.

C. Understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable.

2. Given a problem situation, distinguish between independent/explanatory and dependent/response variables.

D. Understand histograms, parallel box plots, and scatterplots and use them to display data.

1. Represent, display, and interpret data using scatterplots, bar graphs, stem-and-leaf plots, and box-and-whiskers diagrams including representations on graphing calculators and computers.

2. Display univariate data in problem situations with parallel box plots, histograms, or stem-and-leaf plots.

E. Compute basic statistics and understand the distinction between a statistic and a parameter.

2. Calculate measures of center and spread for univariate statistics.

3. Determine positive, negative, or no correlation between bivariate statistics.

II. Select and use appropriate statistical methods to analyze data.

B. For bivariate measurement data, be able to display a scatterplot, describe its shape, and determine regression coefficients, regression equations, and correlation coefficients using technological tools.

1. Interpret the value of the correlation coefficient as it pertains to the relationship between the two variables.

2. Write a linear equation that fits a data set, check the model for "goodness of fit," and make predictions using the model.

D. Recognize how linear transformations of univariate data affect shape, center, and spread.

1. Describe the effect of transformations of data on measures of central tendency and variability.

2. Describe the effect of transformations of data on the shape of the data's distribution.

E. Identify trends in bivariate data and find functions that model the data or transform the data so that they can be modeled.

1. Draw a line-of-best-fit or a curve-of-best-fit for a scatterplot.

III. Develop and evaluate inferences and predictions that are based on data.

A. Use simulations to explore the variability of sample statistics from a known population and to construct sampling distributions.

2. Conduct simulations to construct sampling distributions.

B. Understand how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference.

2. Examine sampling distributions to make inferences and predictions about population parameters.

IV. Understand and apply basic concepts of probability.

A. Understand the concepts of sample space and probability distribution and construct sample spaces and distributions in simple cases.

1. Describe all possible outcomes of an event containing a finite number of outcomes.

2. Determine a sample space for selected experiments and represent it in the form of a list, chart, picture, or tree diagram.

B. Use simulations to construct empirical probability distributions and interpret the results in the context of an applied problem.

1. Use simulations to construct empirical probability distributions.

2. Interpret the results in the context of an applied problem.

E. Understand how to compute the probability of a compound event.

Empirically and theoretically calculate the probabilities of a compound event.

GEOMETRY

I. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

A. Analyze properties and determine attributes of two- and three-dimensional objects.

2. Analyze ratios of similar figures and analyze the properties of circles, polygons, and their angle relationships.

B. Explore relationships (including congruence and similarity) among classes of two- and threedimensional geometric objects, make and test conjectures about them, and solve problems involving them.