High School Math PA Core Standards

Write, solve, and/or graph systems of linear inequalities using various methods.

Write, solve, and/or graph linear inequalities using various methods.

Linear Inequalities

Write, solve, and/or graph systems of linear equations using various methods.

Write, solve, and/or graph linear equations using various methods.

Linear Equations

Simplify expressions involving polynomials.

Use estimation strategies in problem-solving situations.

Use exponents, roots, and/or absolute values to solve problems.

Apply number theory concepts to show relationships between real numbers in problem- solving settings.

A1.1.1.1 Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, and exponents).

Operations with Real Numbers and Expressions

Compare and/or order any real numbers.

Simplify square roots

Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.

Simplify/evaluate expressions involving properties/laws of exponents, roots, and/or absolute values to solve problems.

Use estimation to solve problems.

Add, subtract, and/or multiply polynomial expressions (express answers in simplest form).

Factor algebraic expressions, including difference of squares and trinomials.

Simplify/reduce a rational algebraic expression.

Write, solve, and/or apply a linear equation (including problem situations).

Use and/or identify an algebraic property to justify any step in an equation-solving process.

Interpret solutions to problems in the context of the problem situation.

Write and/or solve a system of linear equations (including problem situations) using graphing, substitution, and/or elimination.

Interpret solutions to problems in the context of the problem situation.

Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities).

Identify or graph the solution set to a linear inequality on a number line.

Interpret solutions to problems in the context of the problem situation.

Write and/or solve a system of linear inequalities using graphing.

Interpret solutions to problems in the context of the problem situation.

Apply probability to practical situations.

Use data displays in problem- solving settings and/or to make predictions.

Use measures of dispersion to describe a set of data.

Data Analysis

Analyze and/or interpret data on a scatter plot.

Describe, compute, and/or use the rate of change (slope) of a line.

Coordinate Geometry

Interpret and/or use linear functions and their equations, graphs, or tables.

Analyze and/or use patterns or relations

Functions

Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.

Determine whether a relation is a function, given a set of points or a graph.

Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table).

Create, interpret, and/or use the equation, graph, or table of a linear function.

Translate from one representation of a linear function to another (i.e., graph, table, and equation).

Identify, describe, and/or use constant rates of change.

Apply the concept of linear rate of change (slope) to solve problems.

Write or identify a linear equation when given • the graph of the line, • two points on the line, or • the slope and a point on the line.

Determine the slope and/or y-intercept represented by a linear equation or graph

Draw, identify, find, and/or write an equation for a line of best fit for a scatter plot.

Calculate and/or interpret the range, quartiles, and interquartile range of data.

Estimate or calculate to make predictions based on a circle, line, bar graph, measure of central tendency, or other representation.

Analyze data, make predictions, and/or answer questions based on displayed data (box-and- whisker plots, stem-and-leaf plots, scatter plots, measures of central tendency, or other representations).

Make predictions using the equations or graphs of best-fit lines of scatter plots.

Find probabilities for compound events (e.g., find probability of red and blue, find probability of red or blue) and represent as a fraction, decimal, or percent.

The Standards of Mathematical Practices

Statistics and Probability

Geometry

Algebra

Functions

Number and Quantity

Numbers and Operations

Apply and extend the properties of exponents to solve problems with rational exponents.

Apply properties of rational and irrational numbers to solve real world or mathematical problems.

Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays.

Use units as a way to understand problems and to guide the solution of multi-step problems.

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Extend the knowledge of arithmetic operations and apply to complex numbers.

Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems.

Algebraic Concepts

Use the concept and notation of functions to interpret and apply them in terms of their context.

Graph and analyze functions and use their properties to make connections between the different representations.

Write functions or sequences that model relationships between two quantities.

Interpret the effects transformations have on functions and find the inverses of functions.

Construct and compare linear, quadratic, and exponential models to solve problems.

Interpret functions in terms of the situations they model.

Apply radian measure of an angle and the unit circle to analyze the trigonometric functions.

Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs.

Prove the Pythagorean identity and use it to calculate trigonometric ratios.

Interpret the structure of expressions to represent a quantity in terms of its context.

Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

Write expressions in equivalent forms to solve problems.

Extend the knowledge of arithmetic operations and apply to polynomials.

Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs.

Use polynomial identities to solve problems.

Extend the knowledge of rational functions to rewrite in equivalent forms.

Create and graph equations or inequalities to describe numbers or relationships.

Apply inverse operations to solve equations or formulas for a given variable.

Use reasoning to solve equations and justify the solution method.

Geometry

Use geometric figures and their properties to represent transformations in the plane.

Translate between the geometric description and the equation for a conic section.

Apply coordinate geometry to prove simple geometric theorems algebraically.

Explain volume formulas and use them to solve problems.

Analyze relationships between two-dimensional and three-dimensional objects.

Apply geometric concepts to model and solve real world problems.

Apply rigid transformations to determine and explain congruence.

Verify and apply geometric theorems as they relate to geometric figures.

Apply the concept of congruence to create geometric constructions.

Create justifications based on transformations to establish similarity of plane figures.

Verify and apply theorems involving similarity as they relate to plane figures.

Apply trigonometric ratios to solve problems involving right triangles.

Apply geometric theorems to verify properties of circles.

Extend the concept of similarity to determine arc lengths and areas of sectors of circles.

Measurement, Data, and Probability

Summarize, represent, and interpret data on a single count or measurement variable.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Analyze linear models to make interpretations based on the data.

Recognize and evaluate random processes underlying statistical experiments.

Make inferences and justify conclusions based on sample surveys, experiments, and observational studies.

Use the concepts of independence and conditional probability to interpret data.

Apply the rules of probability to compute probabilities of compound events in a uniform probability model.

Make sense of problems and persevere in solving them.

Construct viable arguments and critique the reasoning of others.

Use appropriate tools strategically.

Look for and make use of structure.

Reason abstractly and quantitatively.

Model with mathematics.

Attend to precision.

Look for and express regularity in repeated reasoning.