Gizmos for New York - Mathematics: The Plus Standards (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.

N: : Number and Quantity

N.CN: : The Complex Number System

1.1.1: : Perform arithmetic operations with complex numbers.

N.CN.3: : Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

1.1.2: : Represent complex numbers and their operations on the complex plane.

N.CN.4a: : Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and convert between rectangular and polar forms of a given complex number.

N.CN.5: : Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

N.CN.6a: : Calculate the distance between two points in the complex plane.

1.1.3: : Use complex numbers in polynomial identities and equations.

N.CN.8: : Extend polynomial identities to the complex numbers.

N.VM: : Vector and Matrix Quantities

1.2.1: : Represent and model with vector quantities.

N.VM.1: : Represent a vector analytically and geometrically.

N.VM.2: : Find the magnitude and direction of a given vector.

N.VM.3: : Solve problems using vectors analytically and geometrically.

1.2.2: : Perform operations on vectors.

N.VM.4: : Add and subtract vectors analytically and geometrically.

1.2.3: : Perform operations on matrices and use matrices in applications.

N.VM.7: : Multiply matrices by scalars.

N.VM.8: : Add, subtract, and multiply matrices.

N.VM.11: : Use matrices to perform linear transformations in the plane.

N.VM.12: : Calculate and interpret the determinant of a matrix.

A: : Algebra

A.APR: : Arithmetic with Polynomial and Rational Expressions

2.1.1: : Use polynomial identities to solve problems.

A.APR.5: : Use the Binomial Theorem for the expansion of (x + y)^n for a positive integer n.

A.REI: : Reasoning with Equations and Inequalities

2.2.1: : Solve systems of equations.

A.REI.8: : Represent a system of linear equations as a single matrix equation in a vector variable.

A.REI.9: : Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

F: : Functions

F.IF: : Interpreting Functions

3.1.1: : Analyze functions using different representations.

F.IF.7d: : Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available.

F.BF: : Building Functions

3.2.2: : Build new functions from existing functions.

F.BF.3c: : Determine algebraically whether or not a function is even or odd.

F.BF.4c: : Given the graph or table of an invertible function, determine coordinates of its inverse.

F.BF.5b: : Use inverse relationships to solve problems involving logarithms and exponents.

F.TF: : Trigonometric Functions

3.3.1: : Extend the domain of trigonometric functions using the unit circle.

F.TF.3: : Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosines, and tangent for x, pi + x, and 2pi – x in terms of their values for x, where x is any real number.

3.3.3: : Prove and apply trigonometric identities.

F.TF.9: : Prove the sum and difference formulas for sine, cosine, and tangent and use them to solve problems.

G: : Geometry

G.GPE: : Expressing Geometric Properties with Equations

4.3.1: : Translate between the geometric description and the equation for a conic section.

G.GPE.2: : Explore the relationship among the parabola, focus, and directrix and use the equation to model a real-life situation, using technology as appropriate.

G.GPE.3a: : Derive the equations of ellipses and hyperbolas given the foci.

G.GMD: : Geometric Measurement and Dimension

4.4.1: : Explain volume formulas and use them to solve problems.

G.GMD.2: : Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

S: : Statistics and Probability

S.ID: : Interpreting Categorical and Quantitative Data

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

S.ID.6b: : Informally assess the fit of a function by plotting and analyzing residuals.

S.CP: : Conditional Probability and the Rules of Probability

5.2.1: : Use the rules of probability to compute probabilities of compound events in a uniform probability model.

S.CP.9: : Solve problems using permutations and combinations to compute probabilities of compound events.

S.MD: : Using Probability to Make Decisions

5.3.1: : Calculate expected values and use them to solve problems.

S.MD.1a: : Define a random variable for a quantity of interest.

S.MD.1b: : Graph a probability distribution for a discrete random variable based on either empirical or theoretical probabilities.

S.MD.2: : Calculate and interpret the expected value of a random variable.

5.3.2: : Use probability to evaluate outcomes of decisions.

S.MD.5: : Use expected values from probability distributions to evaluate and compare the outcomes of decisions.

S.MD.6: : Use probabilities to make fair decisions.

S.MD.7: : Using probability concepts, evaluate decisions and strategies.

Correlation last revised: 12/9/2022

New York - Mathematics: The Plus Standards

Next Generation Learning Standards | Adopted: 2017

N: : Number and Quantity

A: : Algebra

F: : Functions

G: : Geometry

S: : Statistics and Probability