Gizmos for New York - Mathematics: Algebra I (Next Generation Learning Standards adopted 2017)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

AI-N: : Number and Quantity

AI-N.RN: : The Real Number System

1.1.1: : 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.3.a: : Perform all four arithmetic operations and apply properties to generate equivalent forms of rational numbers and square roots.

AI-N.Q: : Quantities

1.2.1: : 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.

AI-A: : Algebra

AI-A.SSE: : Seeing Structure in Expressions

2.1.1: : Interpret the structure of expressions.

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

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

AI-A.SSE.1.b: : 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.

2.1.2: : 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.3.c: : Use the properties of exponents to rewrite exponential expressions.

AI-A.APR: : Arithmetic with Polynomials and Rational Expressions

2.2.1: : 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.

2.2.2: : 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

2.3.1: : 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.

AI-A.REI: : Reasoning with Equations and Inequalities

2.4.1: : 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.

2.4.2: : 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.4.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. Understand that the quadratic formula is a derivative of this process.

AI-A.REI.4.b: : Solve quadratic equations by: Recognize when the process yields no real solutions.

AI-A.REI.4.b.iii: : factoring,

AI-A.REI.4.b.iv: : completing the square,

AI-A.REI.4.b.v: : the quadratic formula, and

AI-A.REI.4.b.vi: : graphing.

2.4.3: : Solve systems of equations.

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

2.4.4: : 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.

AI-F: : Functions

AI-F.IF: : Interpreting Functions

3.1.1: : Understand the concept of a function and use function notation.

AI-F.IF.1: : 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).

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.

3.1.2: : 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.

3.1.3: : 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.7.a: : Graph linear, quadratic, and exponential functions and show key features.

AI-F.IF.7.b: : 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.8.a: : 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.BF: : Building Functions

3.2.1: : Build a function that models a relationship between two quantities.

AI-F.BF.1: : Write a function that describes a relationship between two quantities.

AI-F.BF.1.a: : Determine a function from context. Define a sequence explicitly or steps for calculation from a context.

3.2.2: : Build new functions from existing functions.

AI-F.BF.3a: : Using f(x) + k, k f(x), and f(x + k):

AI-F.BF.3a.i: : identify the effect on the graph when replacing f(x) by f(x) + k, k f(x), and f(x + k) for specific values of k (both positive and negative);

AI-F.BF.3a.ii: : find the value of k given the graphs;

AI-F.BF.3a.iii: : write a new function using the value of k; and

AI-F.BF.3a.iv: : use technology to experiment with cases and explore the effects on the graph.

AI-F.LE: : Linear, Quadratic, and Exponential Models

3.3.1: : Construct and compare linear, quadratic, and exponential models and solve problems.

AI-F.LE.1: : Distinguish between situations that can be modeled with linear functions and with exponential functions.

AI-F.LE.1.a: : 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.

AI-F.LE.1.b: : Recognize situations in which one quantity changes at a constant rate per unit interval relative to another, and therefore can be modeled linearly.

AI-F.LE.1.c: : 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.

AI-F.LE.2: : Construct a linear or exponential function symbolically given:

AI-F.LE.2.i: : a graph;

AI-F.LE.2.ii: : a description of the relationship;

AI-F.LE.2.iii: : two input-output pairs (include reading these from a table).

AI-F.LE.3: : Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

3.3.2: : Interpret expressions for functions in terms of the situation they model.

AI-F.LE.5: : Interpret the parameters in a linear or exponential function in terms of a context.

AI-S: : Statistics and Probability

AI-S.ID: : Interpreting Categorical and Quantitative Data

4.1.1: : 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).

4.1.2: : Summarize, represent, and interpret data on two categorical and quantitative variables.

AI-S.ID.6: : Represent bivariate data on a scatter plot, and describe how the variables’ values are related.

AI-S.ID.6.a: : Fit a function to real-world data; use functions fitted to data to solve problems in the context of the data.

4.1.3: : 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.

AI-S.ID.8: : Calculate (using technology) and interpret the correlation coefficient of a linear fit.

AI-S.ID.9: : Distinguish between correlation and causation.

Correlation last revised: 12/9/2022

New York - Mathematics: Algebra I

Next Generation Learning Standards | Adopted: 2017

AI-N: : Number and Quantity

AI-A: : Algebra

AI-F: : Functions

AI-S: : Statistics and Probability