21st Century Mathematics

M.O.PC.2: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will demonstrate understanding of patterns, relations, and functions, represent and analyze mathematical situations and structures using algebraic symbols, use mathematical models to represent and understand quantitative relationships, and analyze change in various contexts.

M.O.PC.2.1: investigate and sketch the graphs of polynomials and rational functions by analyzing and using the characteristics of zeros, upper and lower bounds, y-intercepts, symmetry, asymptotes and end behavior, maximum and minimum points, and domain and range.

General Form of a Rational Function

Graphs of Polynomial Functions

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Vertex Form

Rational Functions

M.O.PC.2.3: relate Pascal?s Triangle and the Binomial Theorem; use both to expand binomials with positive integral exponents.

M.O.PC.2.4: establish and explain the inverse relationship between exponential and logarithmic functions; graph related functions and include their domain and range using interval notation.

M.O.PC.2.8: analyze and describe the geometry of vectors, perform mathematical operations with vectors and use vectors to solve practical problems.

M.O.PC.2.11: use multiple representations, such as words, graphs, tables, and equations, to solve practical problems involving logarithmic, exponential, polynomial, rational, and radical functions; explain how the representations are related to each other, as well as to the problem.

Compound Interest

General Form of a Rational Function

Rational Functions

M.O.PC.3: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships, specify locations and describe spatial relationships using coordinate geometry and other representational systems, apply transformations and use symmetry to analyze mathematical situations, and solve problems using visualization, spatial reasoning, and geometric modeling.

M.O.PC.3.1: graph functions and conic sections using transformations.

Absolute Value with Linear Functions

Exponential Functions

Introduction to Exponential Functions

Quadratics in Vertex Form

Rational Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Translations

M.O.PC.3.2: analyze and describe properties of conic sections; explain the interrelationship among the properties; solve practical problems involving conic sections.

M.O.PC.5: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them, select and use appropriate statistical methods to analyze data, develop and evaluate inferences and predictions that are based on models, and apply and demonstrate an understanding of basic concepts of probability.

M.O.PC.5.1: identify a real life situation that exhibits characteristics of exponential or logistic growth or decay; pose a question; make a hypothesis as to the answer; develop, justify, and implement a method to collect, organize, and analyze related data; extend the nature of collected, discrete data to that of a continuous function that describes the known data set; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project numerically, analytically, graphically and verbally using the predictive and analytic tools of pre-calculus (with and without technology).

Correlation last revised: 5/31/2018

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