PennsylvaniaPennsylvania Algebra I Curriculum
Video lessons and practice for every Algebra I topic. Aligned to Pennsylvania Core Standards in Math so students can keep up with class or get ahead.
Pennsylvania Algebra I Curriculum | StudyPugHelp
ID | Standard | StudyPug Topic |
|---|---|---|
CC.HSA.CED.A.1 | Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. |
CC.HSA.CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. |
CC.HSA.CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. |
CC.HSA.CED.A.4 | Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. |
CC.HSA.REI.A.1 | Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. |
CC.HSA.REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. |
CC.HSA.REI.C.5 | Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. |
CC.HSA.REI.C.6 | Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. |
CC.HSA.REI.D.10 | Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). |
CC.HSA.REI.D.11 | Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. |
CC.HSA.REI.D.12 | Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. |
CC.HSA.SSE.A.1 | Interpret expressions that represent a quantity in terms of its context. |
CC.HSA.SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. |
CC.HSA.SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. |
CC.HSA.APR.A.1 | Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. |
CC.HSA.APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. |
CC.HSN.RN.A.1 | Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. |
CC.HSN.RN.A.2 | Rewrite expressions involving radicals and rational exponents using the properties of exponents. |
CC.HSF.IF.A.1 | 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. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). |
CC.HSF.IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. |
CC.HSF.IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. |
CC.HSF.IF.B.5 | Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. |
CC.HSF.IF.B.6 | Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. |
CC.HSF.IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. |
CC.HSF.IF.C.9 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). |
CC.HSF.BF.A.1 | Write a function that describes a relationship between two quantities. |
CC.HSF.BF.A.2 | Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. |
CC.HSF.BF.B.3 | Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. |
CC.HSF.LE.A.1 | Distinguish between situations that can be modeled with linear functions and with exponential functions. |
CC.HSF.LE.A.2 | Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). |
CC.HSF.LE.A.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. |
CC.HSF.LE.B.5 | Interpret the parameters in a linear or exponential function in terms of a context. |
CC.HSA.REI.B.4 | Solve quadratic equations in one variable. |
CC.HSA.REI.C.7 | Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. |
CC.HSF.IF.C.8 | Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. |
CC.HSS.ID.A.1 | Represent data with plots on the real number line (dot plots, histograms, and box plots). |
CC.HSS.ID.A.2 | Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. |
CC.HSS.ID.A.3 | Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). |
CC.HSS.ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. |
CC.HSS.ID.C.7 | Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. |
Pennsylvania Algebra I: What Students Learn
Algebra I is one of the most important math courses in high school. It introduces the tools students use in every math class that follows — from Geometry to Calculus. Pennsylvania Core Standards in Math define exactly what Algebra I students need to know, and StudyPug covers every one of those standards with clear video lessons and practice problems.
Equations and Inequalities
A large part of Algebra I focuses on creating and solving equations. Students learn to write equations from real-world situations, solve linear equations and inequalities in one variable, and rearrange formulas to isolate a specific quantity. They also learn how to justify each step of a solution using the properties of equality.
- Create equations in one variable from linear, quadratic, and exponential contexts
- Solve linear equations and inequalities, including those with literal coefficients
- Rearrange formulas to highlight a quantity of interest
- Construct arguments to justify solution methods
Systems of Equations and Inequalities
Students extend their equation-solving skills to systems of two or more equations. They solve systems exactly using substitution and elimination, and approximately using graphs. They also graph linear inequalities and systems of inequalities as regions in the coordinate plane.
- Solve systems of linear equations algebraically and graphically
- Prove that equivalent systems have the same solutions
- Graph solution sets for linear inequalities and systems of inequalities
Functions
Understanding functions is a central goal of Algebra I. Students learn what makes a relationship a function, how to use function notation, and how to interpret graphs and tables. They compare linear and exponential functions, identify key features like slope and intercepts, and write functions that model real-world relationships.
- Define functions using domain, range, and function notation
- Interpret key features of graphs and tables including intercepts, slope, and end behavior
- Calculate and interpret average rate of change over an interval
- Write arithmetic and geometric sequences recursively and explicitly
- Compare properties of functions given in different representations
Linear and Exponential Models
Students distinguish between situations that grow linearly versus exponentially. They build linear and exponential functions from graphs, tables, and descriptions, and interpret the meaning of parameters like slope and initial value in context. They also observe that exponential growth eventually overtakes linear or polynomial growth.
Expressions and Polynomials
Algebra I also develops fluency with algebraic expressions. Students learn to interpret, rewrite, and manipulate expressions — including polynomial expressions. They add, subtract, and multiply polynomials, factor to find zeros, and use the structure of expressions to reveal properties of the quantities they represent.
- Interpret and rewrite algebraic expressions
- Add, subtract, and multiply polynomials
- Factor polynomials and identify zeros
- Understand rational exponents and rewrite radical expressions
Quadratic Equations
Students solve quadratic equations in one variable using factoring, completing the square, and the quadratic formula. They also solve simple systems involving a linear and a quadratic equation, and write quadratic functions in different equivalent forms to reveal vertex, intercepts, and other properties.
Statistics and Data Analysis
The final strand of Algebra I covers data analysis. Students represent data using dot plots, histograms, and box plots. They compare data sets by analyzing center and spread, and they work with scatter plots to model relationships between two quantitative variables using linear functions. They interpret slope and intercepts in context and understand the difference between correlation and causation.
- Represent data with dot plots, histograms, and box plots
- Compare data sets using mean, median, IQR, and standard deviation
- Fit linear models to scatter plots and interpret slope and intercept
- Compute and interpret correlation coefficients
- Distinguish between correlation and causation
How StudyPug Helps Pennsylvania Algebra I Students
StudyPug's Algebra I content is built around Pennsylvania Core Standards in Math. Every video lesson targets a specific standard, and every lesson is followed by practice problems so students can apply what they just learned. Lessons are short — most run 5 to 15 minutes — so they fit easily into a homework session. Students can pause, rewind, and replay any lesson as many times as they need. StudyPug works on any device, so students can get help whether they're at home, at school, or on the go.