OCG - Foundations in Algebra

Key Concepts

Standards

Creating Equations

The student will:

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

The student will:

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.)

a.       Solve systems of linear equations using the substitution method.

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 graphically by identifying the x- coordinate(s) of the point(s) of intersection of the graphs of

�(�). (Limit to linear; quadratic; exponential.)

FA.AREI.12*

Graph the solutions to a linear inequality in two variables.

Structure and Expressions

The student will:

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

The student will:

FA.FBF.3*

Describe the effect of the transformations and combinations of such transformations on the graph of 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

The student will:

FA.FIF.1*

Extend previous knowledge of a function to apply to general behavior and features of a function.

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.

b.      Represent a function using function notation and explain that denotes the output of functionf  that corresponds to the input .

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

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.)

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.)

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.)

Linear, Quadratic, and Exponential

The student will:

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.)

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.)

Quantities

The student will:

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

The student will:

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

The student will:

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.

Making Inferences and Justifying Conclusions

The student will:

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.

Using Probability to Make Decisions

The student will:

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.