Advanced Mathematical Decision Making Version: 2011-2012

Scholastic Area that Course Is Active In: Mathematics

Strand: Number and Operations

Students will extend the understanding of proportional reasoning, ratios, rates, and percents by applying them to various settings to include business, media, and consumerism.
Element: MAMDMN1.a
Use proportional reasoning to solve problems involving ratios.
Element: MAMDMN1.b
Understand and use averages, weighted averages, and indices.
Element: MAMDMN1.c
Solve problems involving large quantities that are not easily measured.
Element: MAMDMN1.c
Solve problems involving large quantities that are not easily measured.
Element: MAMDMN1.d
Understand how identification numbers, such as UPCs, are created and verified.

Strand: Algebra

Students will use vectors and matrices to organize and describe problem situations.
Element: MAMDMA1.a
Represent situations and solve problems using vectors in areas such as transportation, computer graphics, and the physics of force and motion.
Element: MAMDMA1.b
Represent geometric transformations and solve problems using matrices in fields such as computer animations.

Students will use a variety of network models to organize data in quantitative situations, make informed decisions, and solve problems. a. Solve problems represented by a vertex-edge graph, and find critical paths,
Element: MAMDMA1.a
Solve problems represented by a vertex-edge graph, and find critical paths, Euler paths, and minimal spanning trees.
Element: MAMDMA2.b
Construct, analyze, and interpret flow charts to develop an algorithm to describe processes such as quality control procedures.
Element: mamdma2.c
Investigate the scheduling of projects using PERT.
Element: MAMDMA2.d
Consider problems that can be resolved by coloring graphs.

Students will create and analyze mathematical models to make decisions related to earning, investing, spending, and borrowing money.
Element: MAMDMA3.a
Use exponential functions to model change in a variety of financial situations.
Element: MAMDMA3.b
Determine, represent, and analyze mathematical models for income, expenditures, and various types of loans and investments.

Students will analyze and evaluate the mathematics behind various methods of voting and selection.
Element: MAMDMA4.a
Evaluate various voting and selection processes to determine an appropriate method for a given situation.
Element: MAMDMA4.b
Apply various ranking algorithms to determine an appropriate method for a given situation.

Strand: Data Analysis and Probability

Students will determine probability and expected value to inform everyday decision making.
Element: MAMDMD1.a
Determine conditional probabilities and probabilities of compound events to make decisions in problem situations.
Element: MAMDMD1.b
Use probabilities to make and justify decisions about risks in everyday life.
Element: MAMDMD1.c
Calculate expected value to analyze mathematical fairness, payoff, and risk.

Students will build the skills and vocabulary necessary to analyze and critique reported statistical information, summaries, and graphical displays.

Students will apply statistical methods to design, conduct, and analyze statistical studies.

Students will use functions to model problem situations in both discrete and continuous relationships.
Element: MAMDMD4.a
Determine whether a problem situation involving two quantities is best modeled by a discrete (pattern identification, population growth, compound interest) or continuous (medication dosage, climate change, bone decay) relationship.
Element: MAMDMD4.b
Use linear, exponential, logistic, piecewise and sine functions to construct a model.

Strand: Geometry

Students will create and use two- and three-dimensional representations of authentic situations.

Students will solve geometric problems involving inaccessible distances using basic trigonometric principles, including the Law of Sines and the Law of Cosines.

Strand: Process Standards

Students will solve problems (using appropriate technology).
Element: MM1P1.a
Build new mathematical knowledge through problem solving.
Element: MM1P1.b
Solve problems that arise in mathematics and in other contexts.
Element: MM1P1.c
Apply and adapt a variety of appropriate strategies to solve problems.
Element: MM1P1.d
Monitor and reflect on the process of mathematical problem solving.

Students will reason and evaluate mathematical arguments.
Element: MM1P2.a
Recognize reasoning and proof as fundamental aspects of mathematics.
Element: MM1P2.b
Make and investigate mathematical conjecture.
Element: MM1P2.c
Develop and evaluate mathematical arguments and proofs.
Element: MM1P2.d
Select and use various types of reasoning and methods of proof.

Students will communicate mathematically.
Element: MM1P3.a
Organize and consolidate their mathematical thinking through communication.
Element: MM1P3.b
Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
Element: MM1P3.c
Analyze and evaluate the mathematical thinking and strategies of others.
Element: MM1P3.d
Use the language of mathematics to express mathematical ideas precisely.

Students will make connections among mathematical ideas and to other disciplines.
Element: MM1P4.a
Recognize and use connections among mathematical ideas.
Element: MM1P4.b
Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
Element: MM1P4.c
Recognize and apply mathematics in contexts outside of mathematics.

Students will represent mathematics in multiple ways.
Element: MM1P5.a
Create and use representations to organize, record, and communicate mathematical ideas.
Element: MM1P5.b
Select, apply, and translate among mathematical representations to solve problems.
Element: MM1P5.c
Use representations to model and interpret physical, social, and mathematical phenomena.

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