Advanced Quantitative Reasoning

Apply mathematics to problems arising in everyday life, society, and the workplace.

Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.

Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Create and use representations to organize, record, and communicate mathematical ideas.

Analyze mathematical relationships to connect and communicate mathematical ideas.

Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Use precision and accuracy in real-life situations related to measurement and significant figures.

Apply and analyze published ratings, weighted averages, and indices to make informed decisions.

Solve problems involving quantities that are not easily measured using proportionality.

Solve geometric problems involving indirect measurement, including similar triangles, the Pythagorean Theorem, Law of Sines, Law of Cosines, and the use of dynamic geometry software.

Solve problems involving large quantities using combinatorics.

Use arrays to efficiently manage large collections of data and add, subtract, and multiply matrices to solve applied problems, including geometric transformations.

Analyze various voting and selection processes to compare results in given situations.

Select and apply an algorithm of interest to solve real-life problems such as problems using recursion or iteration involving population growth or decline, fractals, and compound interest; the validity in recorded and transmitted data using checksums and hashing; sports rankings, weighted class rankings, and search engine rankings; and problems involving scheduling or routing situations using vertex-edge graphs, critical paths, Euler paths, and minimal spanning trees and communicate to peers the application of the algorithm in precise mathematical and nontechnical language.

Collect numerical bivariate data to create a scatterplot, select a function to model the data, justify the model selection, and use the model to interpret results and make predictions.

Describe the degree to which uncorrelated variables may or may not be related and analyze situations where correlated variables do or do not indicate a cause-and-effect relationship.

Determine or analyze an appropriate growth or decay model for problem situations, including linear, exponential, and logistic functions.

Determine or analyze an appropriate cyclical model for problem situations that can be modeled with periodic functions.

Determine or analyze an appropriate piecewise model for problem situations.

Create, represent, and analyze mathematical models for various types of income calculations to determine the best option for a given situation.

Create, represent, and analyze mathematical models for expenditures, including those involving credit, to determine the best option for a given situation.

Create, represent, and analyze mathematical models and appropriate representations, including formulas and amortization tables, for various types of loans and investments to determine the best option for a given situation.

Use a two-way frequency table as a sample space to identify whether two events are independent and to interpret the results.

Use the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), in mathematical and real-world problems.

Calculate conditional probabilities and probabilities of compound events using tree diagrams, Venn diagrams, area models, and formulas.

Interpret conditional probabilities and probabilities of compound events by analyzing representations to make decisions in problem situations.

Use probabilities to make and justify decisions about risks in everyday life.

Calculate expected value to analyze mathematical fairness, payoff, and risk.

Determine the validity of logical arguments that include compound conditional statements by constructing truth tables.

Identify limitations and lack of relevant information in studies reporting statistical information, especially when studies are reported in condensed form.

Interpret and compare statistical results using appropriate technology given a margin of error.

Identify potential misuses of statistics to justify particular conclusions, including assertions of a cause-and-effect relationship rather than an association, and missteps or fallacies in logical reasoning; Page 22 October 2015 Update.

Describe strengths and weaknesses of sampling techniques, data and graphical displays, and interpretations of summary statistics and other results appearing in a study, including reports published in the media.

Determine the need for and purpose of a statistical investigation and what type of statistical analysis can be used to answer a specific question or set of questions.

Identify the population of interest for a statistical investigation, select an appropriate sampling technique, and collect data.

Identify the variables to be used in a study.

Determine possible sources of statistical bias in a study and how bias may affect the validity of the results.

Create data displays for given data sets to investigate, compare, and estimate center, shape, spread, and unusual features of the data.

Analyze possible sources of data variability, including those that can be controlled and those that cannot be controlled.

Report results of statistical studies to a particular audience, including selecting an appropriate presentation format, creating graphical data displays, and interpreting results in terms of the question studied.

Justify the design and the conclusion(s) of statistical studies, including the methods used.

Communicate statistical results in oral and written formats using appropriate statistical and nontechnical language.