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M.IS.5
create and use representations to organize, record, and communicate mathematical ideas;
M.IS.6
analyze mathematical relationships to connect and communicate mathematical ideas; and
M.IS.7
display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
M.DMPS.1
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
M.DMPS.1.A
apply mathematics to problems arising in everyday life, society, and the workplace;
M.DMPS.1.B
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;
M.DMPS.1.C
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;
M.DMPS.1.D
communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
M.DMPS.1.E
create and use representations to organize, record, and communicate mathematical ideas;
M.DMPS.1.F
analyze mathematical relationships to connect and communicate mathematical ideas; and
M.DMPS.1.G
display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
M.DMPS.2
Graph theory. The student applies the concept of graphs to determine possible solutions to real-world problems. The student is expected to:
M.DMPS.2.A
explain the concept of graphs;
M.DMPS.2.B
use graph models for simple problems in management science;
M.DMPS.2.C
determine the valences of the vertices of a graph;
M.DMPS.2.D
identify Euler circuits in a graph;
M.DMPS.2.E
solve route inspection problems by Eulerizing a graph;
M.DMPS.2.F
determine solutions modeled by edge traversal in a graph;
M.DMPS.2.G
compare the results of solving the traveling salesman problem (TSP) using the nearest neighbor algorithm and using a greedy algorithm;
M.DMPS.2.H
distinguish between real-world problems modeled by Euler circuits and those modeled by Hamiltonian circuits;
M.DMPS.2.I
distinguish between algorithms that yield optimal solutions and those that give nearly optimal solutions;
M.DMPS.2.J
find minimum-cost spanning trees using Kruskal's algorithm;
M.DMPS.2.K
use the critical path method to determine the earliest possible completion time for a collection of tasks; and
M.DMPS.2.L
explain the difference between a graph and a directed graph.
M.DMPS.3
Planning and scheduling. The student uses heuristic algorithms to solve real-world problems. The student is expected to:
M.DMPS.3.A
use the list processing algorithm to schedule tasks on identical processors;
M.DMPS.3.B
recognize situations appropriate for modeling or scheduling problems;
M.DMPS.3.C
determine whether a schedule is optimal using the critical path method together with the list processing algorithm;
M.DMPS.3.D
identify situations appropriate for modeling by bin packing;
M.DMPS.3.E
use any of six heuristic algorithms to solve bin packing problems;
M.DMPS.3.F
solve independent task scheduling problems using the list processing algorithm; and
M.DMPS.3.G
explain the relationship between scheduling problems and bin packing problems.
M.DMPS.4
Group decision making. The student uses mathematical processes to apply decision-making schemes. The student analyzes the effects of multiple types of weighted voting and applies multiple voting concepts to real-world situations. The student is expected to:
M.DMPS.4.A
describe the concept of a preference schedule and how to use it;
M.DMPS.4.B
explain how particular decision-making schemes work;
M.DMPS.4.C
determine the outcome for various voting methods, given the voters' preferences;
M.DMPS.4.D
explain how different voting schemes or the order of voting can lead to different results;
M.DMPS.4.E
describe the impact of various strategies on the results of the decision-making process;
M.DMPS.4.F
explain the impact of Arrow's Impossibility Theorem;
M.DMPS.4.G
relate the meaning of approval voting;
M.DMPS.4.H
explain the need for weighted voting and how it works;
M.DMPS.4.I
identify voting concepts such as Borda count, Condorcet winner, dummy voter, and coalition; and
M.DMPS.4.J
compute the Banzhaf power index and explain its significance.
M.DMPS.5
Fair division. The student applies the adjusted winner procedure and Knaster inheritance procedure to real-world situations. The student is expected to:
M.DMPS.5.A
use the adjusted winner procedure to determine a fair allocation of property;
M.DMPS.5.B
use the adjusted winner procedure to resolve a dispute;
M.DMPS.5.C
explain how to reach a fair division using the Knaster inheritance procedure;
M.DMPS.5.D
solve fair division problems with three or more players using the Knaster inheritance procedure;
M.DMPS.5.E
explain the conditions under which the trimming procedure can be applied to indivisible goods;
M.DMPS.5.F
identify situations appropriate for the techniques of fair division;