Gizmos for West Virginia - Mathematics: STEM Readiness (College- and Career-Readiness Standards adopted 2015)

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

AAC: : Arithmetic and Algebra of Complex Numbers

1.1: : Perform arithmetic operations with complex numbers.

AAC.M.SRM.1: : Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real.

AAC.M.SRM.2: : Use the relation i² = -1 and the commutative, associative and distributive properties to add, subtract and multiply complex numbers.

AAC.M.SRM.3: : Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

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

AAC.M.SRM.4: : Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers) and explain why the rectangular and polar forms of a given complex number represent the same number.

AAC.M.SRM.5: : Represent addition, subtraction, multiplication and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. (e.g., (-1 + (square root of 3)i)³ = 8 because (-1 + (square root of 3)i) has modulus 2 and argument 120°.)

AAC.M.SRM.6: : Calculate the distance between numbers in the complex plane as the modulus of the difference and the midpoint of a segment as the average of the numbers at its endpoints.

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

AAC.M.SRM.7: : Solve quadratic equations with real coefficients that have complex solutions.

AAC.M.SRM.8: : Extend polynomial identities to the complex numbers. For example, rewrite x² + 4 as (x + 2i)(x – 2i).

PRR: : Polynomials, Rational, and Radical Relationships

2.1: : Use polynomial identities to solve problems.

PRR.M.SRM.10: : Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.

PD: : Probability for Decisions

3.1: : Use probability to evaluate outcomes of decisions.

PD.M.SRM.12: : Use probabilities to make fair decisions (e.g., drawing by lot or using a random number generator).

PD.M.SRM.13: : Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, and/or pulling a hockey goalie at the end of a game).

FM: : Functions and Modeling

5.1: : Analyze functions using different representations.

FM.M.SRM.17: : Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

FM.M.SRM.18: : Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available and showing end behavior.

FM.M.SRM.19: : Graph exponential and logarithmic functions, showing intercepts and end behavior and trigonometric functions, showing period, midline, and amplitude.

5.2: : Building a function that models a relationship between two quantities.

FM.M.SRM.20: : Write a function that describes a relationship between two quantities.

5.3: : Build new functions from existing functions.

FM.M.SRM.22: : Find inverse functions.

FM.M.SRM.24: : Read values of an inverse function from a graph or a table, given that the function has an inverse.

FM.M.SRM.26: : Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

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

FM.M.SRM.27: : 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, cosine, and tangent for pi – x, pi + x, and 2pi – x in terms of their values for x, where x is any real number.

FM.M.SRM.28: : Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

5.6: : Prove and apply trigonometric identities.

FM.M.SRM.31: : Prove the addition and subtraction formulas for sine, cosine and tangent and use them to solve problems.

Correlation last revised: 1/10/2023

West Virginia - Mathematics: STEM Readiness

College- and Career-Readiness Standards | Adopted: 2015

AAC: : Arithmetic and Algebra of Complex Numbers

PRR: : Polynomials, Rational, and Radical Relationships

PD: : Probability for Decisions

FM: : Functions and Modeling