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Skills available for New York high school math standards

Standards are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practice that skill.

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Next Generation Learning Standards: Algebra I Next Generation Learning Standards: Algebra I
Next Generation Learning Standards: Algebra II Next Generation Learning Standards: Algebra II
Next Generation Learning Standards: Geometry Next Generation Learning Standards: Geometry
Next Generation Learning Standards: The Plus Standards Next Generation Learning Standards: The Plus Standards
New York State P-12 Common Core Learning Standards New York State P-12 Common Core Learning Standards

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AI-S Statistics and Probability

AI-S.ID Interpreting Categorical and Quantitative Data
- Summarize, represent, and interpret data on a single count or measurement variable.
  - AI-S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).
  - AI-S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, sample standard deviation) of two or more different data sets.
  - AI-S.ID.3 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)
  - Checkpoint opportunity
    - Checkpoint: Line plots, histograms, and box plots (A1-N.10)
    - Checkpoint: Compare data sets (A1-MM.17)
- Summarize, represent, and interpret data on two categorical and quantitative variables.
  - AI-S.ID.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.
    - Find probabilities using two-way frequency tables (A1-LL.3)
    - Find conditional probabilities using two-way frequency tables (A1-LL.4)
  - AI-S.ID.6 Represent bivariate data on a scatter plot, and describe how the variables' values are related.
    - AI-S.ID.6a Fit a function to real-world data; use functions fitted to data to solve problems in the context of the data.
  - Checkpoint opportunity
    - Checkpoint: Two-way frequency tables (A1-LL.11)
- Interpret linear models.
  - AI-S.ID.7 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)
  - AI-S.ID.8 Calculate (using technology) and interpret the correlation coefficient of a linear fit.
    - Match correlation coefficients to scatter plots (A1-MM.10)
    - Calculate correlation coefficients (A1-MM.11)
  - AI-S.ID.9 Distinguish between correlation and causation.
    - Correlation and causation (A1-MM.16)
  - Checkpoint opportunity
    - Checkpoint: Linear modeling (A1-MM.18)

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AI-N Number and Quantity

AI-N.RN The Real Number System

Use properties of rational and irrational numbers.

AI-N.RN.3 Use properties and operations to understand the different forms of rational and irrational numbers.

AI-N.RN.3a Perform all four arithmetic operations and apply properties to generate equivalent forms of rational numbers and square roots.

AI-N.RN.3b Categorize the sum or product of rational or irrational numbers.

AI-N.Q Quantities

Reason quantitatively and use units to solve problems.

AI-N.Q.1 Select quantities and use units as a way to:

AI-N.Q.1.i interpret and guide the solution of multi-step problems;

AI-N.Q.1.ii choose and interpret units consistently in formulas; and

AI-N.Q.1.iii choose and interpret the scale and the origin in graphs and data displays.

AI-N.Q.3 Choose a level of accuracy appropriate to limitations on measurement and context when reporting quantities.

Checkpoint opportunity

AI-A Algebra

AI-A.SSE Seeing Structure in Expressions

Interpret the structure of expressions.

AI-A.SSE.1 Interpret expressions that represent a quantity in terms of its context.

AI-A.SSE.1a Write the standard form of a given polynomial and identify the terms, coefficients, degree, leading coefficient, and constant term.

AI-A.SSE.1b Interpret expressions by viewing one or more of their parts as a single entity.

AI-A.SSE.2 Recognize and use the structure of an expression to identify ways to rewrite it.

Write expressions in equivalent forms to reveal their characteristics.

AI-A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

AI-A.SSE.3c Use the properties of exponents to rewrite exponential expressions.

Checkpoint opportunity

AI-A.APR Arithmetic with Polynomials and Rational Expressions

Perform arithmetic operations on polynomials.

AI-A.APR.1 Add, subtract, and multiply polynomials and recognize that the result of the operation is also a polynomial. This forms a system analogous to the integers.

Checkpoint opportunity

Understand the relationship between zeros and factors of polynomials.

AI-A.APR.3 Identify zeros of polynomial functions when suitable factorizations are available.

AI-A.CED Creating Equations

Create equations that describe numbers or relationships.

AI-A.CED.1 Create equations and inequalities in one variable to represent a real-world context.

AI-A.CED.2 Create equations and linear inequalities in two variables to represent a real-world context.

AI-A.CED.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.

AI-A.CED.4 Rewrite formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Checkpoint opportunity

AI-A.REI Reasoning with Equations and Inequalities

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

AI-A.REI.1a Explain each step when solving a linear or quadratic 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.

AI-A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

AI-A.REI.4 Solve quadratic equations in one variable.

AI-A.REI.4a 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. Understand that the quadratic formula is a derivative of this process.

AI-A.REI.4b Solve quadratic equations by: inspection, taking square roots, factoring, completing the square, the quadratic formula, and graphing. Write complex solutions in a + bi form.

Checkpoint opportunity

Solve systems of equations.

AI-A.REI.6a Solve systems of linear equations in two variables both algebraically and graphically.

AI-A.REI.7a Solve a system, with rational solutions, consisting of a linear equation and a quadratic equation (parabolas only) in two variables algebraically and graphically.

Represent and solve equations and inequalities graphically.

AI-A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.

AI-A.REI.11 Given the equations y = f(x) and y = g(x):

AI-A.REI.11.i recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x);

AI-A.REI.11.ii find the solutions approximately using technology to graph the functions or make tables of values; and

AI-A.REI.11.iii interpret the solution in context.

AI-A.REI.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.

Checkpoint opportunity

AI-F Functions

AI-F.IF Interpreting Functions

Understand the concept of a function and use function notation.

AI-F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

AI-F.IF.3 Recognize that a sequence is a function whose domain is a subset of the integers.

Interpret functions that arise in applications in terms of the context.

AI-F.IF.4 For a function that models a relationship between two quantities:

AI-F.IF.4.i interpret key features of graphs and tables in terms of the quantities; and

AI-F.IF.4.ii sketch graphs showing key features given a verbal description of the relationship.

AI-F.IF.5 Determine the domain of a function from its graph and, where applicable, identify the appropriate domain for a function in context.

AI-F.IF.6 Calculate and interpret the average rate of change of a function over a specified interval.

Checkpoint opportunity

Analyze functions using different representations.

AI-F.IF.7 Graph functions and show key features of the graph by hand and by using technology where appropriate.

AI-F.IF.7a Graph linear, quadratic, and exponential functions and show key features.

AI-F.IF.7b Graph square root and piecewise-defined functions, including step functions and absolute value functions, and show key features.

AI-F.IF.8 Write a function in different but equivalent forms to reveal and explain different properties of the function.

AI-F.IF.8a For a quadratic function, use an algebraic process to find zeros, maxima, minima, and symmetry of the graph, and interpret these in terms of context.

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