Advanced Quantitative Reasoning

Other Texas Mathematics sets

• Grade K
• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6
• Grade 7
• Algebra I (2012)
• Grade 8
• Algebra II
• Algebraic Reasoning
• Discrete Mathematics
• Grade 9
• Statistics
• Geometry (2012)
• Grades 10, 11, 12
• Independent Study in Mathematics
• Mathematical Models with Applications
• Precalculus

The student applies the process standards in mathematics to generate new understandings by extending existing knowledge. The student generates new mathematical understandings through problems involving numerical data that arise in everyday life, society, and the workplace. The student extends existing knowledge and skills to analyze real-world situationsAQR.9-12.2

use precision and accuracy in real-life situations related to measurement and significant figuresAQR.9-12.2.A

apply and analyze published ratings, weighted averages, and indices to make informed decisionsAQR.9-12.2.B

solve problems involving quantities that are not easily measured using proportionalityAQR.9-12.2.C

solve geometric problems involving indirect measurement, including similar triangles, the Pythagorean Theorem, Law of Sines, Law of Cosines, and the use of dynamic geometry softwareAQR.9-12.2.D

solve problems involving large quantities using combinatoricsAQR.9-12.2.E

use arrays to efficiently manage large collections of data and add, subtract, and multiply matrices to solve applied problems, including geometric transformationsAQR.9-12.2.F

analyze various voting and selection processes to compare results in given situationsAQR.9-12.2.G

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 languageAQR.9-12.2.H

The student applies the process standards in mathematics to create and analyze mathematical models of everyday situations to make informed decisions related to earning, investing, spending, and borrowing money by appropriate, proficient, and efficient use of tools, including technology. The student uses mathematical relationships to make connections and predictions. The student judges the validity of a prediction and uses mathematical models to represent, analyze, and solve dynamic real-world problemsAQR.9-12.3

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 predictionsAQR.9-12.3.A

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 relationshipAQR.9-12.3.B

determine or analyze an appropriate growth or decay model for problem situations, including linear, exponential, and logistic functionsAQR.9-12.3.C

determine or analyze an appropriate cyclical model for problem situations that can be modeled with periodic functionsAQR.9-12.3.D

determine or analyze an appropriate piecewise model for problem situationsAQR.9-12.3.E

create, represent, and analyze mathematical models for various types of income calculations to determine the best option for a given situationAQR.9-12.3.F

create, represent, and analyze mathematical models for expenditures, including those involving credit, to determine the best option for a given situationAQR.9-12.3.G

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 situationAQR.9-12.3.H

The student uses the process standards in mathematics to generate new understandings of probability and statistics. The student analyzes statistical information and evaluates risk and return to connect mathematical ideas and make informed decisions. The student applies a problem-solving model and statistical methods to design and conduct a study that addresses one or more particular question(s). The student uses multiple representations to communicate effectively the results of student-generated statistical studies and the critical analysis of published statistical studiesAQR.9-12.4

use a two-way frequency table as a sample space to identify whether two events are independent and to interpret the resultsAQR.9-12.4.A

use the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), in mathematical and real-world problemsAQR.9-12.4.B

calculate conditional probabilities and probabilities of compound events using tree diagrams, Venn diagrams, area models, and formulasAQR.9-12.4.C

interpret conditional probabilities and probabilities of compound events by analyzing representations to make decisions in problem situationsAQR.9-12.4.D

use probabilities to make and justify decisions about risks in everyday lifeAQR.9-12.4.E

calculate expected value to analyze mathematical fairness, payoff, and riskAQR.9-12.4.F

determine the validity of logical arguments that include compound conditional statements by constructing truth tablesAQR.9-12.4.G

identify limitations and lack of relevant information in studies reporting statistical information, especially when studies are reported in condensed formAQR.9-12.4.H

interpret and compare statistical results using appropriate technology given a margin of errorAQR.9-12.4.I

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 reasoningAQR.9-12.4.J

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 mediaAQR.9-12.4.K

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 questionsAQR.9-12.4.L

identify the population of interest for a statistical investigation, select an appropriate sampling technique, and collect dataAQR.9-12.4.M

identify the variables to be used in a studyAQR.9-12.4.N

determine possible sources of statistical bias in a study and how bias may affect the validity of the resultsAQR.9-12.4.O

create data displays for given data sets to investigate, compare, and estimate center, shape, spread, and unusual features of the dataAQR.9-12.4.P

analyze possible sources of data variability, including those that can be controlled and those that cannot be controlledAQR.9-12.4.Q

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 studiedAQR.9-12.4.R

justify the design and the conclusion(s) of statistical studies, including the methods usedAQR.9-12.4.S

communicate statistical results in oral and written formats using appropriate statistical and nontechnical languageAQR.9-12.4.T