Number and Quantity  The Real Number System  eTAP Lesson 

Use properties of rational and irrational numbers  
Perform all four arithmetic operations and apply properties to generate equivalent forms of rational numbers and square roots.
NY.AIN.RN.3a 
Distributive and Additive Identity, Multiplicative Identity Property and Properties of Equality Commutative and Associative Property Basic Operations Squares and Square Roots Setting Up and Solving Equations 
Categorize the sum or product of rational or irrational numbers.
NY.AIN.RN.3b 
Rational & Irrational Numbers 
Number and Quantity  Quantities  eTAP Lesson 
Reason quantitatively and use units to solve problems.  
Select quantities and use units as a way to:
NY.AIN.Q.1 
Functions as Graphs in the Coordinate System 
Choose a level of accuracy appropriate to limitations on measurement and context when reporting quantities
NY.AIN.Q.3 

Seeing Structure in Expressions  eTAP Lesson 
Interpret the structure of expressions.  
Write the standard form of a given polynomial and identify the terms, coefficients, degree, leading coefficient, and constant term.
NY.AIA.SSE.1a 
Polynomials 
Interpret expressions by viewing one or more of their parts as a single entity.
NY.AIA.SSE.1b 
Variables and Expressions Open Sentences 
Recognize and use the structure of an expression to identify ways to rewrite it.
NY.AIA.SSE.2 
Variables and Expressions Open Sentences 
Write expressions in equivalent forms to reveal their characteristics.  
Use the properties of exponents to rewrite exponential expressions.
NY.AIA.SSE.3c 
Rules of Exponents 
Arithmetic with Polynomials and Rational Expressions  eTAP Lesson 
Perform arithmetic operations on polynomials.  
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.
NY.AIA.APR.1 
Polynomials 
Understand the relationship between zeros and factors of polynomials.  
Identify zeros of polynomial functions when suitable factorizations are available.
NY.AIA.APR.3 
Zeros of Polynomial Functions 
Creating Equations  eTAP Lesson 
Create equations that describe numbers or relationships.  
Create equations and inequalities in one variable to represent a realworld context.
NY.AIA.CED.1 
Inequalities and the Number Line Solving Equations by Addition and Subtraction Changing Words into Math When to do What 
Create equations that describe numbers or relationships.  
Create equations and linear inequalities in two variables to represent a realworld context.
NY.AIA.CED.2 
Changing Words into Math When to do What 
Create equations that describe numbers or relationships.  
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.
NY.AIA.CED.3 

Rewrite formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
NY.AIA.CED.4 
The Application of Equation Rules to Formulas 
Reasoning with Equations and Inequalities  eTAP Lesson 
Understand solving equations as a process of reasoning and explain the reasoning.  
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.
NY.AIA.REI.1a 
When to do What 
Solve equations and inequalities in one variable.  eTAP Lesson 
Solve equations and inequalities in one variable.  
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
NY.AIA.REI.3 
When to do What 
Reasoning with Equations and Inequalities  eTAP Lesson 
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.
NY.AIA.REI.4a 
Completing the Square 
Solve quadratic equations by:
NY.AIA.REI.4b 
Completing the Square Solving Quadratic Equations Perfect Square Trinomial Quadratic Formula Joe's Method Graphing Quadratic Functions Solving Quadratic Equations by Graphing 
Solve systems of equations.  
Solve systems of linear equations in two variables both algebraically and graphically.
NY.AIA.REI.6a 
Why Do We Need Two Equations? Simultaneous Equations The Substitution Method The Addition  Subtraction Method 
Solve a system, with rational solutions, consisting of a linear equation and a quadratic equation (parabolas only) in two variables algebraically and graphically.
NY.AIA.REI.7a 
Graphing Quadratic Functions Graphing Systems of Equations 
Represent and solve equations and inequalities graphically.  
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.
NY.AIA.REI.10 

Given the equations y=f(x)and y=g(x):
NY.AIA.REI.11 
Solving Quadratic Equations by Graphing 
Graph the solutions to a linear inequality in two variables as a halfplane (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 halfplanes.
NY.AIA.REI.12 
Graphing Systems of Inequalities 
Interpreting Functions  eTAP Lesson 
Understand the concept of a function and use function notation.  
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).
NY.AIF.IF.1 
Functions 
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
NY.AIF.IF.2 
Functions 
Recognize that a sequence is a function whose domain is a subset of the integers.
NY.AIF.IF.3 
Functions 
Interpret functions that arise in applications in terms of the context.  
For a function that models a relationship between two quantities:
NY.AIF.IF.4 
Equations as Relations 
Interpret functions that arise in applications in terms of the context.  
Determine the domain of a function from its graph and, where applicable, identify the appropriate domain for a function in context.
NY.AIF.IF.5 
Ordered Pairs Equations as Relations 
Interpret functions that arise in applications in terms of the context.  
Calculate and interpret the average rate of change of a function over a specified interval.
NY.AIF.IF.6 
Slope of a Line 
Analyze functions using different representations.  
Graph linear, quadratic,and exponential functions and show key features
NY.AIF.IF.7a 
Graphing Quadratic Functions Solving Quadratic Equations by Graphing 
Graph square root, and piecewisedefined functions, including step functions and absolute value functions and show key features.
NY.AIF.IF.7b 

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.
NY.AIF.IF.8a 
Graphing Quadratic Functions 
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
NY.AIF.IF.9 

Building Functions  eTAP Lesson 
Build a function that models a relationship between two quantities.  
Determine a function from context.Define a sequence explicitly or steps for calculation from a context.
NY.AIF.BF.1a 
Functions 
Build new functions from existing functions.  
Using f(x)+ k, k f(x), andf(x+ k):
NY.AIF.BF.3a 
Graphing Systems of Equations 
Linear, Quadratic, and Exponential Models  eTAP Lesson 
Construct and compare linear, quadratic, and exponential models and solve problems.  
Justify that a function is linear because it grows by equal differences over equal intervals, and that a function is exponential because it grows by equal factors over equal intervals.
NY.AIF.LE.1a 
Function Notation Direct Variation 
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another, and therefore can be modeled linearly.
NY.AIF.LE.1b 
Direct Variation 
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another, and therefore can be modeled exponentially.
NY.AIF.LE.1c 
Direct Variation Exponential Functions and Data 
Construct a linear or exponential function symbolically given:
NY.AIF.LE.2 
Exponential Functions and Data 
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
NY.AIF.LE.3 
Exponential Functions and Data 
Interpret expressions for functions in terms of the situation they model.  
Interpret the parameters in a linear or exponential function in terms of a context.
NY.AIF.LE.5 
Exponential Functions and Data 
Interpreting Categorical and Quantitative Data  eTAP Lesson 
Summarize, represent, and interpret data on a single count or measurement variable.  
Represent data with plots on the real number line (dot plots, histograms, and box plots).
NY.AIS.ID.1 
Showing Orderly Data with Histograms 
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.
NY.AIS.ID.2 
Data Calculations 
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
NY.AIS.ID.3 
Methods of Collecting, Representing, & Displaying Data 
Summarize, represent, and interpret data on two categorical and quantitative variables.  
Summarize categorical data for two categories in twoway 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.
NY.AIS.ID.5 
Methods of Collecting, Representing, & Displaying Data 
Fit a function to realworld data; use functions fitted to data to solve problems in the context of the data.
NY.AIS.ID.6a 
Exponential Functions and Data 
Interpret linear models.  
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
NY.AIS.ID.7 
Slope of a Line 
Calculate (using technology) and interpret the correlation coefficient of a linear fit.
NY.AIS.ID.8 
Correlations 
Distinguish between correlation and causation.
NY.AIS.ID.9 
Correlations 