The Real Number System  eTAP Lesson 

Extend the properties of exponents to rational exponents.  
Explore how the meaning of rational exponents follows from extending the properties of integer exponents.
NY.AIIN.RN.1 
Negative and Rational Exponents The number e 
Convert between radical expressions and expressions with rational exponents using the properties of exponents.
NY.AIIN.RN.2 
Exponential Functions and Data Graphs of Exponential Functions 
The Complex Number System  eTAP Lesson 
Perform arithmetic operations with complex numbers.  
Know there is a complex numberisuch that i^{2}= –1, and every complex number has the form a + bi with a and b real.
NY.AIIN.CN.1 
Complex Numbers Square Root Functions 
Use the relation i^{2}= –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
NY.AIIN.CN.2 
Complex Plane Radical Functions Radical Equations 
Seeing Structure in Expressions  eTAP Lesson 
Interpret the structure of expressions.  
Recognize and use the structure of an expression to identify ways to rewrite it.
NY.AIIA.SSE.2 
Function Notation 
Write expressions in equivalent forms to reveal their characteristics.  
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Factor quadratic expressions including leading coefficients other than 1 to reveal the zeros of the function it defines.
NY.AIIN.SSE.3a 
Direct Variation Linear Parametric equations 
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Use the properties of exponents to rewrite exponential expressions.
NY.AIIN.SSE.3b 
Comparing and Ordering Rational Numbers 
Arithmetic with Polynomials and Rational Expressions  eTAP Lesson 
Understand the relationship between zeros and factors of polynomials.  
Apply the Remainder Theorem: For a polynomial p(x)and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
NY.AIIA.APR.2 
Multiplying and Dividing Polynomials Graphs of Polynomial Functions 
Identify zeros of polynomialfunctionswhen suitable factorizations are available.
NY.AIIA.APR.3 
Cubic Equations 
Rewrite rational expressions.  
Rewrite rational expressions in different forms: Write a(x)/b(x)in the formq(x)+ r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x).
NY.AIIA.APR.6 
Zeros of Polynomial Functions Inverse Variation 
Creating Equations  eTAP Lesson 
Create equations that describe numbers or relationships.  
Create equations and inequalities in one variable to represent a realworld context.
NY.AIIA.CED.1 

Reasoning with Equations and Inequalities  eTAP Lesson 
Understand solving equations as a process of reasoning and explain the reasoning.  
Explain each step when solving rational or radical equations 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.AIIA.REI.1b 
Radical Equations 
Solve rational and radical equations in one variable, identify extraneous solutions, and explain how they arise.
NY.AIIA.REI.2 
Substitution 
Solve equations and inequalities in one variable.  
Solve quadratic equations in one variable. Solve quadratic equations by:
NY.AIIA.REI.4b 
Simple Quadratic Functions Parabolas Quadratic Functions in Intercept Form Factoring Quadratics 
Solve systems of equations.  
Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
NY.AIIA.REI.7b 
Graphs and Dipgrahs 
Represent and solve equations and inequalities graphically.  
Given the equations y=f(x)and y=g(x):
NY.AIIA.REI.11 
Dividing Rational Numbers Slope Intercept Form of Equations 
Interpreting Functions  eTAP Lesson 
Understand the concept of a function and use function notation.  
Recognize that a sequence is a function whose domain is a subset of the integers.
NY.AIIF.IF.3 
Arithmetic and Geometric Series 
Interpret functions that arise in applications in terms of the context.  
For a function that models a relationship between two quantities:
NY.AIIF.IF.4 
Determine the Equation from a Relation 
Calculate and interpret the average rate of change of a function over a specified interval.
NY.AIIF.IF.6 

Analyze functions using different representations.  
Graph functions and show key features of the graphby hand and using technology when appropriate. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
NY.AIIF.IF.7c 
Graphs of Polynomial Functions Zeros of Polynomial Functions 
Graph cube root, exponential and logarithmic functions, showing intercepts and end behavior; and trigonometric functions, showing period, midline, and amplitude.
NY.AIIF.IF.7e 
Cubic Equations Amplitude and Period 
Analyze functions using different representations.  
Write a function in different but equivalent forms to reveal and explain different properties of the function. Use the properties of exponents to interpret exponential functions, and classify them as representing exponential growth or decay.
NY.AIIF.IF.8b 
The number e 
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
NY.AIIF.IF.9 
Sums of Geometric Series 
Building Functions  eTAP Lesson 
Build a function that models a relationship between two quantities.  
Write a function that describes a relationship between two quantities. Determine a function from context.Determine an explicit expression, a recursive process, or steps for calculation from a context.
NY.AIIF.BF.1a 
Functions 
Write a function that describes a relationship between two quantities. Combine standard function types using arithmetic operations.
NY.AIIF.BF.1b 
Sums of Arithmetic Series Combinations 
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
NY.AIIF.BF.2 
Recursion 
Build new functions from existing functions.  
Using f(x) + k,kf(x), f(kx),and f(x+ k):
NY.AIIF.BF.3b 
Basic Operations Correlations Functions as Graphs in the Coordinate System 
Find the inverse of a onetoone function both algebraically and graphically.
NY.AIIF.BF.4a 
Inverse Variation 
Understand inverse relationships between exponents and logarithms algebraically and graphically.
NY.AIIF.BF.5a 
Inverses of Linear Functions 
Represent and evaluate the sum of a finite arithmetic or finite geometric series, using summation (sigma) notation.
NY.AIIF.BF.6 
Geometric Mean, Harmonic Mean, and Weighted Arithmetic Mean 
Explore the derivation of the formulas for finite arithmetic and finite geometric series. Use the formulas to solve problems.
NY.AIIF.BF.7 
Frequency Distribution Table, Summation Notation, and Mean Formula 
Linear, Quadratic, and Exponential Models  eTAP Lesson 
Interpret expressions for functions in terms of the situation they model.  
Construct a linear or exponential function symbolically given:
NY.AIIF.LE.2 
Inverses of Linear Functions Inverses of Exponential Functions 
Use logarithms to solve exponential equations, such as ab^{ct}= d(where a, b, c,and d are real numbers and b > 0) and evaluate the logarithm using technology.
NY.AIIF.LE.4 
Exponential and Logarithmic Equations 
Interpret the parameters in a linear or exponential function in terms of a context.
NY.AIIF.LE.5 
Using Logarithms to Model Data 
Trigonometric Functions  eTAP Lesson 
Extend the domain of trigonometric functions using the unit circle.  
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
NY.AIIF.TF.1 
Sine and Cosine and the Unit Circle 
Apply concepts of the unit circle in the coordinate plane to calculate the values of the six trigonometric functions given angles in radian measure.
NY.AIIF.TF.2 
Radians 
Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
NY.AIIF.TF.4 
Amplitude and Period 
Model periodic phenomena with trigonometric functions.  
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, horizontal shift, and midline.
NY.AIIF.TF.5 
Tangent Function 
Prove and apply trigonometric identities.  
Prove the Pythagorean identity sin^{2}(θ) + cos^{2}(θ) = 1. Find the value of any of the six trigonometric functions given any other trigonometric function value and when necessary find the quadrant of the angle.
NY.AIIF.TF.8 
Converse 
Interpreting Categorical and Quantitative Data  eTAP Lesson 
Summarize, represent, and interpret data on a single count or measurement variable.  
Recognize whether or not a normal curve is appropriate for a given data set.
NY.AIIS.ID.4a 
Normal Distributions 
If appropriate, determine population percentages using a graphing calculator for an appropriate normal curve.
NY.AIIS.ID.4b 

Summarize, represent, and interpret data on two categorical and quantitative variables.  
Represent bivariate data on a scatter plot, and describe how the variables’ values are related. Fit a function to realworld data; use functions fitted to data to solve problems in the context of the data.
NY.AIIS.ID.6a 
Paired Data Sets and Scatterplots 
Making Inferences and Justifying Conclusions  eTAP Lesson 
Understand and evaluate random processes underlying statistical experiments.  
Determine if a value for a sample proportion or sample mean is likely to occur based on a given simulation.
NY.AIIS.IC.2 
Indirect Proof 
Make inferences and justify conclusions from sample surveys, experiments, and observational studies.  
Recognize the purposes of and differences among surveys, experiments, and observational studies. Explain how randomization relates to each.
NY.AIIS.IC.3 
Discrete Probability Distribution 
Given a simulation model based on a sample proportion or mean, construct the 95% interval centered on the statistic (+/ two standard deviations) and determine if a suggested parameter is plausible.
NY.AIIS.IC.4 
Standard Deviation of Random Variable 
Use the tools of statistics to draw conclusions from numerical summaries.
NY.AIIS.IC.6a 
Data Classification, Range, and Midrange 
Use the language of statistics to critique claims from informational texts. For example, causation vs correlation, bias, measures of center and spread.
NY.AIIS.IC.6b 
Mean and Variance of Random Variable 
Conditional Probability and the Rules of Probability  eTAP Lesson 
Understand independence and conditional probability and use them to interpret data.  
Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
NY.AIIS.CP.1 
Multiple Events Conditional Probability 
Interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway table as a sample space to decide if events are independent and calculate conditional probabilities.
NY.AIIS.CP.4 
Binomial Distributions Normal Distributions 
Use the rules of probability to compute probabilities of compound events in a uniform probability model.  
Apply the Addition Rule,P(A or B) = P(A) + P(B) P(A and B), and interpret the answer in terms of the model.
NY.AIIS.CP.7 
Probability Data Plots Dependent & Independent Variables 