School City of Hobart
School City of Hobart Mathematics

Mathematics - IN: Discrete Math

Mathematics

The ISTEP+ assessment measures the academic performance of students in Mathematics.

The Indiana Academic Standards provide educators and administrators with a complete set of Indiana's K-12 academic standards for Mathematics. Schools should work to align curriculum instruction and classroom assessment with the new standards. While the standards set expectations for student learning they do not prescribe how the standards should be taught.

Teachers should use their skills, experience, talents, and resources to design classroom lessons to meet the individual needs of their students. With these new academic standards in place students in Indiana will be well equipped with the skills and knowledge to prepare them for the future.

IN: Discrete Math

The ISTEP+ assesses the academic performance of students in Mathematics at grade 10.

The Indiana Academic Standards for Mathematics include standards for students in Discrete Math.


Algebraic Concepts
The Algebraic Concepts Unit includes Competencies/Objectives which focus on algebraic equations and operations. Students explore the symbolic nature of algebraic concepts by identifying and extending patterns in algebra, by following algebraic procedures, and by proving theorems with properties.

    Equation/Inequality: Comprehend/Use
The learner will be able to develop a comprehension of fundamental algebraic concepts and abilities, and use those abilities requiring algebraic manipulation to obtain solutions to equations and inequalities.
Strand Bloom's Scope Source
Equality/Inequality Master IN: Statewide Testing for Educational Progress (ISTEP+), 1999-2000, Grade 10, 10.4 week tested: 4.
  

Calculus and Pre-Calculus
The Calculus/Pre-Calculus Unit includes Competencies/Objectives which focus on calculus concepts. Students study limits, matrix algebra, functions, vectors, conic sections, mathematical induction, and sequence and series using graphical calculators, computers, and models.

    Simplex Method: Optimization Problems
The learner will be able to solve optimization problems by applying the Simplex method, using technology when necessary.
Strand Bloom's Scope Source
Simplex Method Application Master IN: Academic Standards, 2000, Discrete Math, DM.6.2
  
    Linear Programming: Apply
The learner will be able to apply linear programming methods.
Strand Bloom's Scope Source
Linear Programming Application Master IN: Academic Standards, 2000, Discrete Math, Standard 6
  
    Matrices: Row-Reduction/Problem Solving
The learner will be able to solve problems by applying techniques of row-reduction.
Strand Bloom's Scope Source
Matrices Application Master IN: Academic Standards, 2000, Discrete Math, DM.2.3
  
    Matrices: Operations/Problem Solve
The learner will be able to perform operations with matrices in order to obtain solutions to problems.
Strand Bloom's Scope Source
Matrices Application Master IN: Academic Standards, 2000, Discrete Math, DM.2.2
  
    Matrices: Markov Chains/Problem Solving
The learner will be able to obtain problems solutions using Markov chains.
Strand Bloom's Scope Source
Matrices Application Master IN: Academic Standards, 2000, Discrete Math, DM.2.5
  
    Matrices: Use
The learner will be able to use matrices.
Strand Bloom's Scope Source
Matrices Application Master IN: Academic Standards, 2000, Discrete Math, Standard 2
  
    Matrices: Inverse/Problem Solving
The learner will be able to obtain problems solutions using the inverse of a matrix.
Strand Bloom's Scope Source
Matrices Application Master IN: Academic Standards, 2000, Discrete Math, DM.2.4
  
    Graph Theory: Vertices/Edges
The learner will be able to apply graph theory by representing a problem as edges and vertices in order to solve it.
Strand Bloom's Scope Source
Graph Theory/Networks Application Master IN: Academic Standards, 2000, Discrete Math, DM.4.1
  
    Networks: Critical Path/Problem Solving
The learner will be able to solve scheduling problems by applying critical path analysis.
Strand Bloom's Scope Source
Graph Theory/Networks Application Master IN: Academic Standards, 2000, Discrete Math, DM.4.2
  
    Graph Theory: Coloring/Problem Solving
The learner will be able to solve problems by applying strategies of graph coloring.
Strand Bloom's Scope Source
Graph Theory/Networks Application Master IN: Academic Standards, 2000, Discrete Math, DM.4.3
  
    Graph Theory: Apply
The learner will be able to apply graph theory strategies.
Strand Bloom's Scope Source
Graph Theory/Networks Application Master IN: Academic Standards, 2000, Discrete Math, Standard 4
  
    Networks: Minimal Spanning Trees
The learner will be able to solve problems by applying minimal spanning trees.
Strand Bloom's Scope Source
Graph Theory/Networks Application Master IN: Academic Standards, 2000, Discrete Math, DM.4.4
  
    Networks: Bin-Packing Techniques
The learner will be able to solve problems by applying bin-packing techniques.
Strand Bloom's Scope Source
Graph Theory/Networks Application Master IN: Academic Standards, 2000, Discrete Math, DM.4.5
  

Discrete Mathematics
The Discrete Mathematics Unit includes Competencies/Objectives which focus on the concepts of discrete mathematics, matrices, and recursion.

    Recursion: Apply/Problem Solve
The learner will be able to apply recursive thinking to obtain problem solutions.
Strand Bloom's Scope Source
Recursion Application Master IN: Academic Standards, 2000, Discrete Math, DM.3.1
  
    Recursion: Apply
The learner will be able to apply recursive techniques.
Strand Bloom's Scope Source
Recursion Application Master IN: Academic Standards, 2000, Discrete Math, Standard 3
  
    Discrete Mathematics: Finite Differences
The learner will be able to use finite differences to obtain solutions to problems.
Strand Bloom's Scope Source
Discrete Mathematics Application Master IN: Academic Standards, 2000, Discrete Math, DM.3.2
  
    Matrices: Organize
The learner will be able to organize data collections into matrices.
Strand Bloom's Scope Source
Matrices Application Master IN: Academic Standards, 2000, Discrete Math, DM.2.1
  

Functions
The Functions Unit includes Competencies/Objectives which focus on exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions.

    Functions: Comprehension
The learner will be able to develop a comprehension of basic functions, their graphs, and their real world applications.
Strand Bloom's Scope Source
Functions Master IN: Statewide Testing for Educational Progress (ISTEP+), 1999-2000, Grade 10, 10.5 week tested: 4.
  

Geometry
The Geometry Unit includes Competencies/Objectives which focus on exploring geometric concepts from multiple perspectives. Students study properties and construction of figures, proofs and theorems, history of geometry, transformations, logic, and problem solving.

    Figures: Comprehend/2D-3D/Problems
The learner will be able to comprehend how two- and three-dimensional figures may be used in real world problem situations.
Strand Bloom's Scope Source
Figures: Two-/Three-Dimensional Master IN: Statewide Testing for Educational Progress (ISTEP+), 1999-2000, Grade 10, 10.6 week tested: 4.
  
    Geometric Concepts: Optimization
The learner will be able to solve optimization problems using geometric methods.
Strand Bloom's Scope Source
Geometric Concepts Application Master IN: Academic Standards, 2000, Discrete Math, DM.6.1
  
    Inductive/Deductive: Apply
The learner will be able to apply inductive and deductive reasoning to solve problems.
Strand Bloom's Scope Source
Reasoning Synthesis Master IN: Statewide Testing for Educational Progress (ISTEP+), 1999-2000, Grade 10, 10.3 week tested: 4.
  

Mathematics Processes
The Mathematics Processes Unit includes Competencies/Objectives which focus on mathematical connections. Students communicate and model concepts and procedures.

    Mathematics as Communication: Real World
The learner will be able to express their thoughts (in written and verbal form) concerning mathematical concepts, their power and many applications, and their uses in real world scenarios.
Strand Bloom's Scope Source
Communication Master IN: Statewide Testing for Educational Progress (ISTEP+), 1999-2000, Grade 10, 10.2 week tested: 4.
  

Numeration
The Numeration Unit includes Competencies/Objectives which focus on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships.

    Counting: Apply Strategies
The learner will be able to use counting strategies.
Strand Bloom's Scope Source
Counting Application Master IN: Academic Standards, 2000, Discrete Math, Standard 1
  

Perspective/Role in Society
The Perspective/Role in Society Unit includes Competencies/Objectives which focus on real world mathematics. Students study the mathematics of society and the role of mathematics in personal finance and careers.

    Mathematics of Social Choice
The learner will be able to apply mathematics of social choice.
Strand Bloom's Scope Source
Mathematics of Social Choice Master IN: Academic Standards, 2000, Discrete Math, Standard 5
  
    Social Choice: Fair Division Methods
The learner will be able to divide continuous objects using fair division methods.
Strand Bloom's Scope Source
Mathematics of Social Choice Application Master IN: Academic Standards, 2000, Discrete Math, DM.5.3
  
    Social Choice: Fair Division/Apportion
The learner will be able to solve problems which involve apportionment by applying methods of fair division.
Strand Bloom's Scope Source
Mathematics of Social Choice Application Master IN: Academic Standards, 2000, Discrete Math, DM.5.4
  
    Social Choice: Weighted Voting Methods
The learner will be able to find the voting power within a group by applying weighted voting methods.
Strand Bloom's Scope Source
Mathematics of Social Choice Application Master IN: Academic Standards, 2000, Discrete Math, DM.5.2
  
    Social Choice: Election Theory
The learner will be able to apply election theory methods to study election data.
Strand Bloom's Scope Source
Mathematics of Social Choice Analysis Master IN: Academic Standards, 2000, Discrete Math, DM.5.1
  

Probability/Statistics
The Probability/Statistics Unit includes Competencies/Objectives which focus on data analysis and probability concepts. Students collect, analyze, and make sense of real world data (including overlapping data, inconclusive data, etc.).

    Outcomes: Determine
The learner will be able to determine the number of outcomes in problem scenarios using networks, traceable paths, tree diagrams, Venn diagrams and other various pictorial illustrations.
Strand Bloom's Scope Source
Outcomes Master IN: Academic Standards, 2000, Discrete Math, DM.1.1
  
    Probability: Comprehend/Concept
The learner will be able to comprehend the basic concept of probability.
Strand Bloom's Scope Source
Probability Comprehension Master IN: Statewide Testing for Educational Progress (ISTEP+), 1999-2000, Grade 10, 10.8 week tested: 4.
  
    Probability: Problem Solving/Simulations
The learner will be able to solve probability problems by applying simulation techniques.
Strand Bloom's Scope Source
Probability Application Master IN: Academic Standards, 2000, Discrete Math, DM.1.5
  
    Statistics: Comprehend/Descriptive
The learner will be able to develop a comprehension of descriptive statistics.
Strand Bloom's Scope Source
Statistics Comprehension Master IN: Statewide Testing for Educational Progress (ISTEP+), 1999-2000, Grade 10, 10.7 week tested: 4.
  
    Fundamental Counting Principle: Apply
The learner will be able to find the number of outcomes for a problem situation by applying the fundamental counting principle.
Strand Bloom's Scope Source
Counting Methods Application Master IN: Academic Standards, 2000, Discrete Math, DM.1.2
  
    Combinatorics: Use/Reasoning
The learner will be able to use reasoning with combinatorics in order to problem solve.
Strand Bloom's Scope Source
Combinations Application Master IN: Academic Standards, 2000, Discrete Math, DM.1.3
  
    Simulations: Apply
The learner will be able to apply simulations in order to obtain solutions to counting problems.
Strand Bloom's Scope Source
Event Simulation Application Master IN: Academic Standards, 2000, Discrete Math, DM.1.5
  
    Game Theory: Nonstrictly Determined Game
The learner will be able to find solutions to non-strictly determined games by applying methods of game theory.
Strand Bloom's Scope Source
Game Theory Application Master IN: Academic Standards, 2000, Discrete Math, DM.7.2
  
    Game Theory: Strictly Determined Game
The learner will be able to find solutions to strictly determined games by applying methods of game theory.
Strand Bloom's Scope Source
Game Theory Application Master IN: Academic Standards, 2000, Discrete Math, DM.7.1
  
    Game Theory: Problem Solving
The learner will be able to use game theory in problem solving.
Strand Bloom's Scope Source
Game Theory Application Master IN: Academic Standards, 2000, Discrete Math, Standard 7
  
    Problem Solving: Solve/Probability
The learner will be able to apply counting methods to obtain solutions to probability problems.
Strand Bloom's Scope Source
Problem Solving Application Master IN: Academic Standards, 2000, Discrete Math, DM.1.4
  

Problem Solving
The Problem Solving Unit includes Competencies/Objectives which focus on analyzing problems, evaluating solutions, exploring problems, and developing strategies for solving problems.

    Word Problems: Solve/Elementary
The learner will be able to apply computational abilities, appropriate technology, and/or paper-and-pencil methods in obtaining solutions to elementary word problems.
Strand Bloom's Scope Source
Word Problems Master IN: Statewide Testing for Educational Progress (ISTEP+), 1999-2000, Grade 10, 10.9 week tested: 4.
  
    Strategies: Choose/Real World
The learner will be able to choose problem solving strategies for real world situations.
Strand Bloom's Scope Source
Strategies Application Master IN: Statewide Testing for Educational Progress (ISTEP+), 1999-2000, Grade 10, 10.1 week tested: 4.
  
    Strategies: Apply/Real World
The learner will be able to apply problem solving strategies in real world situations.
Strand Bloom's Scope Source
Strategies Application Master IN: Statewide Testing for Educational Progress (ISTEP+), 1999-2000, Grade 10, 10.1 week tested: 4.
  

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