Skill plan for the Pennsylvania Keystone Exams - Algebra 1
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Module
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Operations and Linear Equations & Inequalities
A1.1.1 - Operations with Real Numbers and Expressions
A1.1.1.1: Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, and exponents).
A1.1.1.1: Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, and exponents).
A1.1.1.1.1: Compare and/or order any real numbers.
A1.1.1.1.1: Compare and/or order any real numbers.
A1.1.1.1.2: Simplify square roots (e.g., √24 = 2√6).
A1.1.1.1.2: Simplify square roots (e.g., √24 = 2√6).
A1.1.1.2: Apply number theory concepts to show relationships between real numbers in problem-solving settings.
A1.1.1.2: Apply number theory concepts to show relationships between real numbers in problem-solving settings.
A1.1.1.2.1: Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.
A1.1.1.2.1: Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.
A1.1.1.3: Use exponents, roots, and/or absolute values to solve problems.
A1.1.1.3: Use exponents, roots, and/or absolute values to solve problems.
A1.1.1.3.1: Simplify/evaluate expressions involving properties/laws of exponents, roots, and/or absolute values to solve problems.
Roots
Exponents
Radical expressions
Square root functions
Absolute value expressions
A1.1.1.3.1: Simplify/evaluate expressions involving properties/laws of exponents, roots, and/or absolute values to solve problems.
Roots
Exponents
Radical expressions
Square root functions
Absolute value expressions
A1.1.1.4: Use estimation strategies in problem-solving situations.
A1.1.1.4: Use estimation strategies in problem-solving situations.
A1.1.1.4.1: Use estimation to solve problems.
Roots
Proportions
Percents
A1.1.1.4.1: Use estimation to solve problems.
Roots
Proportions
Percents
A1.1.1.5: Simplify expressions involving polynomials.
A1.1.1.5: Simplify expressions involving polynomials.
A1.1.1.5.1: Add, subtract, and/or multiply polynomial expressions (express answers in simplest form).
Add and subtract polynomials
Multiply polynomials
A1.1.1.5.1: Add, subtract, and/or multiply polynomial expressions (express answers in simplest form).
Add and subtract polynomials
Multiply polynomials
A1.1.1.5.2: Factor algebraic expressions, including difference of squares and trinomials.
A1.1.1.5.2: Factor algebraic expressions, including difference of squares and trinomials.
A1.1.1.5.3: Simplify/reduce a rational algebraic expression.
A1.1.1.5.3: Simplify/reduce a rational algebraic expression.
A1.1.2 - Linear Equations
A1.1.2.1: Write, solve, and/or graph linear equations using various methods.
A1.1.2.1: Write, solve, and/or graph linear equations using various methods.
A1.1.2.1.1: Write, solve, and/or apply a linear equation (including problem situations).
Models and diagrams
Solve equations
Real-world problems
Solutions to equations
Arithmetic sequences
A1.1.2.1.1: Write, solve, and/or apply a linear equation (including problem situations).
Models and diagrams
Solve equations
Real-world problems
Solutions to equations
Arithmetic sequences
A1.1.2.1.2: Use and/or identify an algebraic property to justify any step in an equation-solving process.
A1.1.2.1.2: Use and/or identify an algebraic property to justify any step in an equation-solving process.
A1.1.2.1.3: Interpret solutions to problems in the context of the problem situation.
A1.1.2.1.3: Interpret solutions to problems in the context of the problem situation.
A1.1.2.2: Write, solve, and/or graph systems of linear equations using various methods.
A1.1.2.2: Write, solve, and/or graph systems of linear equations using various methods.
A1.1.2.2.1: Write and/or solve a system of linear equations (including problem situations) using graphing, substitution, and/or elimination.
Solutions to systems of equations
Graphing
Solve systems of equations
A1.1.2.2.1: Write and/or solve a system of linear equations (including problem situations) using graphing, substitution, and/or elimination.
Solutions to systems of equations
Graphing
Solve systems of equations
A1.1.2.2.2: Interpret solutions to problems in the context of the problem situation.
A1.1.2.2.2: Interpret solutions to problems in the context of the problem situation.
A1.1.3 - Linear Inequalities
A1.1.3.1: Write, solve, and/or graph linear inequalities using various methods.
A1.1.3.1: Write, solve, and/or graph linear inequalities using various methods.
A1.1.3.1.1: Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities).
Compound inequalities
Absolute value inequalities
A1.1.3.1.1: Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities).
Compound inequalities
Absolute value inequalities
A1.1.3.1.2: Identify or graph the solution set to a linear inequality on a number line.
Solutions to inequalities
Graph inequalities
A1.1.3.1.2: Identify or graph the solution set to a linear inequality on a number line.
Solutions to inequalities
Graph inequalities
A1.1.3.1.3: Interpret solutions to problems in the context of the problem situation.
A1.1.3.1.3: Interpret solutions to problems in the context of the problem situation.
A1.1.3.2: Write, solve, and/or graph systems of linear inequalities using various methods.
A1.1.3.2: Write, solve, and/or graph systems of linear inequalities using various methods.
A1.1.3.2.1: Write and/or solve a system of linear inequalities using graphing.
A1.1.3.2.1: Write and/or solve a system of linear inequalities using graphing.
A1.1.3.2.2: Interpret solutions to problems in the context of the problem situation.
A1.1.3.2.2: Interpret solutions to problems in the context of the problem situation.
Linear Functions and Data Organizations
A1.2.1 - Functions
A1.2.1.1: Analyze and/or use patterns or relations.
A1.2.1.1: Analyze and/or use patterns or relations.
A1.2.1.1.1: Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.
A1.2.1.1.1: Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.
A1.2.1.1.2: Determine whether a relation is a function, given a set of points or a graph.
A1.2.1.1.2: Determine whether a relation is a function, given a set of points or a graph.
A1.2.1.1.3: Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table).
A1.2.1.1.3: Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table).
A1.2.1.2: Interpret and/or use linear functions and their equations, graphs, or tables.
A1.2.1.2: Interpret and/or use linear functions and their equations, graphs, or tables.
A1.2.1.2.1: Create, interpret, and/or use the equation, graph, or table of a linear function.
Direct variation
Slope
Slope-intercept form
Linear functions
Standard form
Horizontal and vertical lines
Point-slope form
Parallel and perpendicular lines
A1.2.1.2.1: Create, interpret, and/or use the equation, graph, or table of a linear function.
Direct variation
Slope
Slope-intercept form
Linear functions
Standard form
Horizontal and vertical lines
Point-slope form
Parallel and perpendicular lines
A1.2.1.2.2: Translate from one representation of a linear function to another (i.e., graph, table, and equation).
Slope-intercept form
Standard form
Horizontal and vertical lines
Point-slope form
A1.2.1.2.2: Translate from one representation of a linear function to another (i.e., graph, table, and equation).
Slope-intercept form
Standard form
Horizontal and vertical lines
Point-slope form
A1.2.2 - Coordinate Geometry
A1.2.2.1: Describe, compute, and/or use the rate of change (slope) of a line.
A1.2.2.1: Describe, compute, and/or use the rate of change (slope) of a line.
A1.2.2.1.1: Identify, describe, and/or use constant rates of change.
A1.2.2.1.1: Identify, describe, and/or use constant rates of change.
A1.2.2.1.2: Apply the concept of linear rate of change (slope) to solve problems.
A1.2.2.1.2: Apply the concept of linear rate of change (slope) to solve problems.
A1.2.2.1.3: Write or identify a linear equation when given
A1.2.2.1.3: Write or identify a linear equation when given
A1.2.2.1.3.a: the graph of the line,
A1.2.2.1.3.a: the graph of the line,
A1.2.2.1.3.b: two points on the line, or
A1.2.2.1.3.b: two points on the line, or
A1.2.2.1.3.c: the slope and a point on the line.
A1.2.2.1.3.c: the slope and a point on the line.
A1.2.2.1.4: Determine the slope and/or y-intercept represented by a linear equation or graph.
A1.2.2.1.4: Determine the slope and/or y-intercept represented by a linear equation or graph.
A1.2.2.2: Analyze and/or interpret data on a scatter plot.
A1.2.2.2: Analyze and/or interpret data on a scatter plot.
A1.2.2.2.1: Draw, identify, find, and/or write an equation for a line of best fit for a scatter plot.
A1.2.2.2.1: Draw, identify, find, and/or write an equation for a line of best fit for a scatter plot.
A1.2.3 - Data Analysis
A1.2.3.1: Use measures of dispersion to describe a set of data.
A1.2.3.1: Use measures of dispersion to describe a set of data.
A1.2.3.1.1: Calculate and/or interpret the range, quartiles, and interquartile range of data.
A1.2.3.1.1: Calculate and/or interpret the range, quartiles, and interquartile range of data.
A1.2.3.2: Use data displays in problem-solving settings and/or to make predictions.
A1.2.3.2: Use data displays in problem-solving settings and/or to make predictions.
A1.2.3.2.1: Estimate or calculate to make predictions based on a circle, line, bar graph, measures of central tendency, or other representations.
A1.2.3.2.1: Estimate or calculate to make predictions based on a circle, line, bar graph, measures of central tendency, or other representations.
A1.2.3.2.2: 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).
A1.2.3.2.2: 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).
A1.2.3.2.3: Make predictions using the equations or graphs of best-fit lines of scatter plots.
A1.2.3.2.3: Make predictions using the equations or graphs of best-fit lines of scatter plots.
A1.2.3.3: Apply probability to practical situations.
A1.2.3.3: Apply probability to practical situations.
A1.2.3.3.1: 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.
A1.2.3.3.1: 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.
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