Gizmos for South Carolina - Mathematics: Foundations in Algebra (SC--College- and Career-Ready Standards adopted 2015)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

FA.ACE: : Creating Equations

FA.ACE.1: : Create and solve equations and inequalities in one variable that model real-world problems involving linear, quadratic, simple rational, and exponential relationships. Interpret the solutions and determine whether they are reasonable. (Limit to linear; quadratic; exponential with integer exponents.)

FA.ACE.2: : Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales. (Limit to linear; quadratic; exponential with integer exponents; direct and indirect variation.)

FA.ACE.4: : Solve literal equations and formulas for a specified variable including equations and formulas that arise in a variety of disciplines.

FA.AREI: : Reasoning with Equations and Inequalities

FA.AREI.1: : Understand and justify that the steps taken when solving simple equations in one variable create new equations that have the same solution as the original.

FA.AREI.3: : Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

FA.AREI.5: : Justify that the solution to a system of linear equations is not changed when one of the equations is replaced by a linear combination of the other equation.

FA.AREI.6: : Solve systems of linear equations algebraically and graphically focusing on pairs of linear equations in two variables.

FA.AREI.6.a: : Solve systems of linear equations using the substitution method.

FA.AREI.6.b: : Solve systems of linear equations using linear combination.

FA.AREI.10: : Explain that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.

FA.AREI.11: : Solve an equation of the form f(x) = g(x) graphically by identifying the x- coordinate(s) of the point(s) of intersection of the graphs of y = f(x) and y = g(x). (Limit to linear; quadratic; exponential.)

FA.AREI.12: : Graph the solutions to a linear inequality in two variables.

FA.ASE: : Structure and Expressions

FA.ASE.1: : Interpret the meanings of coefficients, factors, terms, and expressions based on their real-world contexts. Interpret complicated expressions as being composed of simpler expressions. (Limit to linear; quadratic; exponential.)

FA.FBF: : Building Functions

FA.FBF.3: : Describe the effect of the transformations kf (x), f(x) + k, f(x + k), and combinations of such transformations on the graph of y = f (x) for any real number k. Find the value of k given the graphs and write the equation of a transformed parent function given its graph. (Limit to linear; quadratic; exponential with integer exponents; vertical shift and vertical stretch.)

FA.FIF: : Interpreting Functions

FA.FIF.1: : Extend previous knowledge of a function to apply to general behavior and features of a function.

FA.FIF.1.a: : Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.

FA.FIF.1.b: : Represent a function using function notation and explain that f(x) denotes the output of function f that corresponds to the input x.

FA.FIF.1.c: : Understand that the graph of a function labeled as f is the set of all ordered pairs (x,y) that satisfy the equation y = f(x).

FA.FIF.4: : Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. (Limit to linear; quadratic; exponential.)

FA.FIF.5: : Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes. (Limit to linear; quadratic; exponential.)

FA.FIF.7: : Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases. (Limit to linear; quadratic; exponential only in the form y Ϛˣ + k.)

FA.FIF.8: : Translate between different but equivalent forms of a function equation to reveal and explain different properties of the function. (Limit to linear; quadratic; exponential.)

FA.FIF.8.a: : Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

FA.FIF.9: : Compare properties of two functions given in different representations such as algebraic, graphical, tabular, or verbal. (Limit to linear; quadratic; exponential.)

FA.FLQE: : Linear, Quadratic, and Exponential

FA.FLQE.1: : Distinguish between situations that can be modeled with linear functions or exponential functions by recognizing situations in which one quantity changes at a constant rate per unit interval as opposed to those in which a quantity changes by a constant percent rate per unit interval.

FA.FLQE.1.a: : Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.

FA.FLQE.3: : Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or more generally as a polynomial function.

FA.FLQE.5: : Interpret the parameters in a linear or exponential function in terms of the context. (Limit to linear.)

FA.NRNS: : Real Number System

FA.NRNS.2: : Use the definition of the meaning of rational exponents to translate between rational exponent and radical forms.

FA.SPID: : Interpreting Data

FA.SPID.5: : Analyze bivariate categorical data using two-way tables and identify possible associations between the two categories using marginal, joint, and conditional frequencies.

FA.SPID.6: : Using technology, create scatterplots and analyze those plots to compare the fit of linear, quadratic, or exponential models to a given data set. Select the appropriate model, fit a function to the data set, and use the function to solve problems in the context of the data.

FA.SPID.7: : Create a linear function to graphically model data from a real-world problem and interpret the meaning of the slope and intercept(s) in the context of the given problem.

FA.SPID.8: : Using technology, compute and interpret the correlation coefficient of a linear fit.

FA.SPMJ: : Making Inferences and Justifying Conclusions

FA.SPMJ.1: : Understand statistics and sampling distributions as a process for making inferences about population parameters based on a random sample from that population.

FA.SPMJ.2: : Distinguish between experimental and theoretical probabilities. Collect data on a chance event and use the relative frequency to estimate the theoretical probability of that event. Determine whether a given probability model is consistent with experimental results.

FA.SPMD: : Using Probability to Make Decisions

FA.SPMD.4: : Use probability to evaluate outcomes of decisions by finding expected values and determine if decisions are fair.

FA.SPMD.5: : Use probability to evaluate outcomes of decisions. Use probabilities to make fair decisions.

FA.SPMD.6: : Analyze decisions and strategies using probability concepts.

Correlation last revised: 9/16/2020

South Carolina - Mathematics: Foundations in Algebra

SC--College- and Career-Ready Standards | Adopted: 2015