South Carolina: Foundations in Algebra Math Standards
44 standards · 11 domains
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.
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. (Note: FA.AREI.6a and 6b are not Graduation Standards.)
- FA.AREI.6a Solve systems of linear equations using the substitution method.
- FA.AREI.6b 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.
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.)
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.)
INTERPRETING FUNCTIONS
- FA.FIF.1 Extend previous knowledge of a function to apply to general behavior and features of a function.
- FA.FIF.1a 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.1b 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.1c 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.2 Evaluate functions and interpret the meaning of expressions involving function notation from a mathematical perspective and in terms of the context when the function describes a real-world situation.
- 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=a^x+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.) (Note: FA.FIF.8a is not a Graduation Standard.)
- FA.FIF.8a 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.)
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. (Note: FA.FLQE.1a is not a Graduation Standard.)
- FA.FLQE.1a Prove that linear functions grow by equal differences over equal intervals and those 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.)
QUANTITIES
- FA.NQ.1 Use units of measurement to guide the solution of multi-step tasks. Choose and interpret appropriate labels, units, and scales when constructing graphs and other data displays.
- FA.NQ.2 Label and define appropriate quantities in descriptive modeling contexts.
- FA.NQ.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities in context.
REAL NUMBER SYSTEM
- FA.NRNS.1 Rewrite expressions involving simple radicals and rational exponents in different forms.
- FA.NRNS.2 Use the definition of the meaning of rational exponents to translate between rational exponent and radical forms.
- FA.NRNS.3 Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
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 uses 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.
USING PROBABILITY TO MAKE DECISIONS
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.