Algebra 1 Resources

Plan your year of Algebra 1 with this resource guide. Find activities, lessons, and ideas for discovery learning, real world connections, and maximum engagement.

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Unit 1.1 Expressions & Equations

Common Core Standards
  • HSA.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.
  • HSA.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients.
  • HSA.SSE.A.2 Use the structure of an expression to identify ways to rewrite it.
  • HSA.CED.A.1 Create equations and inequalities in one variable and use them to solve problems.
  • HSA.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Unit 1.2 Equations with Variables on Both Sides + Literal Equations

Common Core Standards
  • HSA.CED.A.1 Create equations and inequalities in one variable and use them to solve problems.
  • HSA.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • HSA.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.

Unit 2.1 Interpreting Graphs

Common Core Standards
  • 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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

Unit 2.2 Graphing Linear Relationships

Common Core Standards
  • HSA.F.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.
  • 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.
  • 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).
  • HSF.IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
  • HSF.BF.A.1 Write a function that describes a relationship between two quantities.
  • HSF.BF.A.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context.

Unit 2.3 Scatter Plots

Common Core Standards
  • HSS.ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
  • HSS.ID.B.6.a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
  • HSS.ID.B.6.b Informally assess the fit of a function by plotting and analyzing residuals.
  • HSS.ID.B.6.c Fit a linear function for a scatter plot that suggests a linear association.
  • 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.
  • HSS.ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.
  • HSS.ID.C.9 Distinguish between correlation and causation.

Unit 2.4 Systems of Equations

Common Core Standards
  • 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.
  • 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.
  • HAS.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.

Unit 3 Functions

Common Core Standards
  • 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).
  • 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.
  • HSF.IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

Unit 4.1 Exponents and Roots

Common Core Standards
  • HSA.SSE.B.3.c Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

Unit 4.2 Rational & Irrational Numbers

Common Core Standards
  • HSN.RN.B.3 Explain why the sum or product of two 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.

Unit 5 Exponential Functions

Common Core Standards
  • 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.
  • 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.
  • HSF.LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
  • HSF.LE.A.1.a Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
  • HSF.LE.A.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
  • HSF.LE.A.1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
  • 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).
  • 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.
  • HSF.LE.B.5 Interpret the parameters in a linear or exponential function in terms of a context.

Unit 6 Sequences

Common Core Standards
  • HSF.IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
  • 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.*

Unit 7 Absolute Value Equations & Functions

Common Core Standards
  • HSF.IF.C.6 Graph functions expressed symbolically and show key features of the graph, by hand and using technology. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
  • 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.
  • HSA.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Unit 8 One-Variable Inequalities

Common Core Standards
  • HSA.CED.A.1 Create equations and inequalities in one variable and use them to solve problems.
  • HSA.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Unit 9.1 Quadratics in Vertex Form

Common Core Standards
  • HSA.REI.B.4 Solve quadratic equations in one variable.
  • HSA.REI.B.4.b Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.
  • CCSS.Math.Content.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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
  • CCSS.Math.Content.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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*
  • CCSS.Math.Content.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.*
  • CCSS.Math.Content.HSF.IF.C.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima.

Unit 9.2 Polynomials

Common Core Standards
  • 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.
  • 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.*
  • HSA.SSE.B.3.a Factor a quadratic expression to reveal the zeros of the function it defines.
  • 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.

Unit 9.3 Graphing Quadratics in Standard Form

Common Core Standards
  • 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.*
  • HSA.SSE.B.3.a Factor a quadratic expression to reveal the zeros of the function it defines.
  • HSA.SSE.B.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
  • HSA.REI.B.4 Solve quadratic equations in one variable.
  • HSA.REI.B.4.a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Derive the quadratic formula from this form.
  • HSA.REI.B.4.b Solve quadratic equations by inspection (e.g., for x2 = 49), 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.
  • 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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*
  • 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.
  • 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.*
  • HSF.IF.C.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima.

Unit 10 Piecewise Functions

Common Core Standards
  • HSF.IF.C.6 Graph functions expressed symbolically and show key features of the graph, by hand and using technology. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Unit 11 Two-Variable Inequalities

Common Core Standards
  • HSA.CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
  • 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.*
  • 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.

Unit 12 Nonlinear Graphs

Common Core Standards
  • 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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
  • 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.
  • HSS.ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
  • HSS.ID.B.6.a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
  • HSS.ID.B.6.b Informally assess the fit of a function by plotting and analyzing residuals.

Unit 13 Statistics

Common Core Standards
  • HSS.ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).
  • 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.
  • 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).
  • HSS.ID.B.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

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