OCG - Algebra 1

South Carolina College and Career- Ready (SCCCR) Algebra I Standards:
● Standards denoted by an asterisk (*) are SCCCR Graduation Standards.
Arithmetic with Polynomials and Rational Expressions
The student will:
A1.AAPR.1* Add, subtract, and multiply polynomials and understand that polynomials are
closed under these operations. (Limit to linear; quadratic.)
Creating Equations
The student will:
A1.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.)
A1.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.)
A1.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:
A1.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.
A1.AREI.3* Solve linear equations and inequalities in one variable, including equations
with coefficients represented by letters.
A1.AREI.4* Solve mathematical and real-world problems involving quadratic equations in
one variable. (Note: A1.AREI.4a and 4b are not Graduation Standards.)
a. Use the method of completing the square to transform any
quadratic equation in into an equation x of the form (x − h) 2 = k that
has the same solutions. Derive the quadratic formula from this form.
b. Solve quadratic equations by inspection, taking square roots,
completing the square, the quadratic formula and factoring, as
appropriate to the initial form of the equation. Recognize when the
quadratic formula gives complex solutions and write them as a+ bi for
real numbers a and b . (Limit to non-complex roots.)
A1.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.
A1.AREI.6* Solve systems of linear equations algebraically and graphically focusing on
pairs of linear equations in two variables. (Note: A1.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.
A1.AREI.10* Explain that the graph of an equation in two variables is the set of all its
solutions plotted in the coordinate plane.
A1.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.)
A1.AREI.12* Graph the solutions to a linear inequality in two variables.
Structure and Expressions
The student will:
A1.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.)
A1.ASE.2* Analyze the structure of binomials, trinomials, and other polynomials in order
to rewrite equivalent expressions.
A1.ASE.3* Choose and produce an equivalent form of an expression to reveal and explain
properties of the quantity represented by the expression.
a. Find the zeros of a quadratic function by rewriting it in equivalent
factored form and explain the connection between the zeros of the
function, its linear factors, the x-intercepts of its graph, and the
solutions to the corresponding quadratic equation.
Building Functions
The student will:
A1.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
The student will:
A1.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 f(x)
denotes the output of function f that corresponds to the input x .
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) .
A1.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.
A1.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.)
A1.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.)
A1.FIF.6* Given a function in graphical, symbolic, or tabular form, determine the
average rate of change of the function over a specified interval. Interpret the
meaning of the average rate of change in a given context. (Limit to linear;
quadratic; exponential.)
A1.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 = ax + k ).
A1.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: A1.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.
A1.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:
A1.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.
a. Prove that linear functions grow by equal differences over equal
intervals and that exponential functions grow by equal factors over
equal intervals. (Note: A1.FLQE.1a is not a Graduation Standard.)
A1.FLQE.2* Create symbolic representations of linear and exponential functions, including
arithmetic and geometric sequences, given graphs, verbal descriptions, and
tables. (Limit to linear; exponential.)
A1.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.
A1.FLQE.5* Interpret the parameters in a linear or exponential function in terms of the
context. (Limit to linear.)
Quantities
The student will:
A1.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.
A1.NQ.2* Label and define appropriate quantities in descriptive modeling contexts.
A1.NQ.3* Choose a level of accuracy appropriate to limitations on measurement when
reporting quantities in context.
Real Number System
The student will:
A1.NRNS.1* Rewrite expressions involving simple radicals and rational exponents in
different forms.
A1.NRNS.2* Use the definition of the meaning of rational exponents to translate between
rational exponent and radical forms.
A1.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:
A1.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.
A1.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.
A1.SPID.8* Using technology, compute and interpret the correlation coefficient of a linear
fit.
South

South Carolina College- and Career-Ready Mathematical Process Standards
A mathematically literate student can:
1. Make sense of problems and persevere in solving them.
a. Relate a problem to prior knowledge.
b. Recognize there may be multiple entry points to a problem and more than
one path to a solution.
c. Analyze what is given, what is not given, what is being asked, and what
strategies are needed, and make an initial attempt to solve a problem.
d. Evaluate the success of an approach to solve a problem and refine it if
necessary.
2. Reason both contextually and abstractly.
a. Make sense of quantities and their relationships in mathematical and
real-world situations.
b. Describe a given situation using multiple mathematical representations.
c. Translate among multiple mathematical representations and
compare the meanings each representation conveys about the
situation.
d. Connect the meaning of mathematical operations to the context of a given
situation.
3. Use critical thinking skills to justify mathematical reasoning and critique the
reasoning of others.
a. Construct and justify a solution to a problem.
b. Compare and discuss the validity of various reasoning strategies.
c. Make conjectures and explore their validity.
d. Reflect on and provide thoughtful responses to the reasoning of others.
4. Connect mathematical ideas and real-world situations through modeling.
a. Identify relevant quantities and develop a model to describe their
relationships.
b. Interpret mathematical models in the context of the situation.
c. Make assumptions and estimates to simplify complicated situations.
d. Evaluate the reasonableness of a model and refine if necessary.
5. Use a variety of mathematical tools effectively and strategically.
a. Select and use appropriate tools when solving a mathematical problem.
b. Use technological tools and other external mathematical resources to explore
and deepen understanding of concepts.
6. Communicate mathematically and approach mathematical situations with precision.
a. Express numerical answers with the degree of precision appropriate for the
context of a situation.
b. Represent numbers in an appropriate form according to the context of the
situation.
c. Use appropriate and precise mathematical language.
d. Use appropriate units, scales, and labels.
7. Identify and utilize structure and patterns.
a. Recognize complex mathematical objects as being composed of more than
one simple object.
b. Recognize mathematical repetition in order to make generalizations.
c. Look for structures to interpret meaning and develop solution strategies.