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Skills available for Alabama Algebra 1 standards

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Alabama Course of Study (adopted in 2019): Algebra I with Probability Alabama Course of Study (adopted in 2019): Algebra I with Probability
Alabama Course of Study (Common Core): Algebra I Alabama Course of Study (Common Core): Algebra I

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9-12.S Statistics and Probability

9-12.S-ID Interpreting Categorical and Quantitative Data
- Summarize, represent, and interpret data on a single count or measurement variable
  - 9-12.S-ID.41 Represent data with plots on the real number line (dot plots, histograms, and box plots).
  - 9-12.S-ID.42 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.
  - 9-12.S-ID.43 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
    - Box plots (A1-N.9)
    - Identify an outlier and describe the effect of removing it (A1-MM.5)
- Summarize, represent, and interpret data on two categorical and quantitative variables
  - 9-12.S-ID.44 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.
    - Find probabilities using two-way frequency tables (A1-LL.3)
    - Find conditional probabilities using two-way frequency tables (A1-LL.4)
  - 9-12.S-ID.45 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
    - 9-12.S-ID.45.a Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
    - 9-12.S-ID.45.b Informally assess the fit of a function by plotting and analyzing residuals.
      - Interpret a scatter plot (A1-MM.8)
    - 9-12.S-ID.45.c Fit a linear function for a scatter plot that suggests a linear association.
      - Write equations for lines of best fit (A1-MM.12)
- Interpret linear models
  - 9-12.S-ID.46 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
    - Interpret regression lines (A1-MM.14)
    - Analyze a regression line of a data set (A1-MM.15)
9-12.S-CP Conditional Probability and the Rules of Probability
- Understand independence and conditional probability and use them to interpret data
  - 9-12.S-CP.50 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
    - Identify independent and dependent events (A1-LL.6)
    - Probability of independent and dependent events (A1-LL.7)

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9-12.N Number and Quantity

9-12.N-RN The Real Number System

Extend the properties of exponents to rational exponents.

9-12.N-RN.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.

9-12.N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Use properties of rational and irrational numbers.

9-12.N-RN.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.

9-12.N-Q Quantities

Reason quantitatively and use units to solve problems.

9-12.N-Q.4 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

9-12.N-Q.5 Define appropriate quantities for the purpose of descriptive modeling.

9-12.N-Q.6 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

9-12.A Algebra

9-12.A-SSE Seeing Structure in Expressions

Interpret the structure of expressions

9-12.A-SSE.7 Interpret expressions that represent a quantity in terms of its context.

9-12.A-SSE.7.a Interpret parts of an expression, such as terms, factors, and coefficients.

9-12.A-SSE.7.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

9-12.A-SSE.8 Use the structure of an expression to identify ways to rewrite it.

Write expressions in equivalent forms to solve problems

9-12.A-SSE.9 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

9-12.A-SSE.9.a Factor a quadratic expression to reveal the zeros of the function it defines.

9-12.A-SSE.9.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

9-12.A-SSE.9.c Determine a quadratic equation when given its graph or roots.

9-12.A-SSE.9.d Use the properties of exponents to transform expressions for exponential functions.

9-12.A-APR Arithmetic with Polynomials and Rational Expressions

Perform arithmetic operations on polynomials

9-12.A-APR.10 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.

Rewrite rational expressions.

9-12.A-APR.11 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

9-12.A-CED Creating Equations

Create equations that describe numbers or relationships

9-12.A-CED.12 Create equations and inequalities in one variable and use them to solve problems.

9-12.A-CED.13 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

9-12.A-CED.14 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.

9-12.A-CED.15 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

9-12.A-REI Reasoning with Equations and Inequalities

Understand solving equations as a process of reasoning and explain the reasoning

9-12.A-REI.16 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.

Solve equations and inequalities in one variable

9-12.A-REI.17 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

9-12.A-REI.18 Solve quadratic equations in one variable.

9-12.A-REI.18.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.

Solve systems of equations

9-12.A-REI.19 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.

9-12.A-REI.20 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

9-12.A-REI.21 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

Represent and solve equations and inequalities graphically

9-12.A-REI.22 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).

9-12.A-REI.24 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.

9-12.F Functions

9-12.F-IF Interpreting Functions

Understand the concept of a function and use function notation

9-12.F-IF.26 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

9-12.F-IF.27 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

Interpret functions that arise in applications in terms of the context

9-12.F-IF.28 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.

9-12.F-IF.29 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

9-12.F-IF.30 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.

Analyze functions using different representations

9-12.F-IF.31 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

9-12.F-IF.31.a Graph linear and quadratic functions and show intercepts, maxima, and minima.

9-12.F-IF.31.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

9-12.F-IF.32 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

9-12.F-IF.32.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.

9-12.F-IF.32.b Use the properties of exponents to interpret expressions for exponential functions.

9-12.F-IF.33 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

9-12.F-BF Building Functions

Build a function that models a relationship between two quantities

9-12.F-BF.34 Write a function that describes a relationship between two quantities.

9-12.F-BF.34.a Determine an explicit expression, a recursive process, or steps for calculation from a context.

9-12.F-BF.34.b Combine standard function types using arithmetic operations.

9-12.F-BF.35 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Build new functions from existing functions

9-12.F-BF.36 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.

9-12.F-LE Linear, Quadratic, and Exponential Models

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

9-12.A-REI.18.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.