Number and Quantity - The Real Number System | eTAP Lesson |
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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.AI-N.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.AI-N.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.AI-N.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.AI-N.Q.3 |
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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.AI-A.SSE.1a |
Polynomials |
Interpret expressions by viewing one or more of their parts as a single entity.
NY.AI-A.SSE.1b |
Variables and Expressions Open Sentences |
Recognize and use the structure of an expression to identify ways to rewrite it.
NY.AI-A.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.AI-A.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.AI-A.APR.1 |
Polynomials |
Understand the relationship between zeros and factors of polynomials. | |
Identify zeros of polynomial functions when suitable factorizations are available.
NY.AI-A.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 real-world context.
NY.AI-A.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 real-world context.
NY.AI-A.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 non-viable options in a modeling context.
NY.AI-A.CED.3 |
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Rewrite formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
NY.AI-A.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.AI-A.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.AI-A.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.AI-A.REI.4a |
Completing the Square |
Solve quadratic equations by:
NY.AI-A.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.AI-A.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.AI-A.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.AI-A.REI.10 |
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Given the equations y=f(x)and y=g(x):
NY.AI-A.REI.11 |
Solving Quadratic Equations by Graphing |
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.
NY.AI-A.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.AI-F.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.AI-F.IF.2 |
Functions |
Recognize that a sequence is a function whose domain is a subset of the integers.
NY.AI-F.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.AI-F.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.AI-F.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.AI-F.IF.6 |
Slope of a Line |
Analyze functions using different representations. | |
Graph linear, quadratic,and exponential functions and show key features
NY.AI-F.IF.7a |
Graphing Quadratic Functions Solving Quadratic Equations by Graphing |
Graph square root, and piecewise-defined functions, including step functions and absolute value functions and show key features.
NY.AI-F.IF.7b |
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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.AI-F.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.AI-F.IF.9 |
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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.AI-F.BF.1a |
Functions |
Build new functions from existing functions. | |
Using f(x)+ k, k f(x), andf(x+ k):
NY.AI-F.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.AI-F.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.AI-F.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.AI-F.LE.1c |
Direct Variation Exponential Functions and Data |
Construct a linear or exponential function symbolically given:
NY.AI-F.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.AI-F.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.AI-F.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.AI-S.ID.1 |
Showing Orderly Data with Histograms |
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (inter-quartile range, sample standard deviation) of two or more different data sets.
NY.AI-S.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.AI-S.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 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.
NY.AI-S.ID.5 |
Methods of Collecting, Representing, & Displaying Data |
Fit a function to real-world data; use functions fitted to data to solve problems in the context of the data.
NY.AI-S.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.AI-S.ID.7 |
Slope of a Line |
Calculate (using technology) and interpret the correlation coefficient of a linear fit.
NY.AI-S.ID.8 |
Correlations |
Distinguish between correlation and causation.
NY.AI-S.ID.9 |
Correlations |