MA.912.D: Discrete Mathematics

MA.912.D.2: Understand how graphs of vertices joined by edges can model relationships and be used to solve various problems with relation to directed graphs, weighted graphs, networks, tournaments, transportation flows, matching, and coverage.

MA.912.D.2.4: Use spanning trees, rooted trees, binary trees, and decision trees to solve problems.

 Binomial Probabilities
 Permutations and Combinations

MA.912.D.3: Analyze election data to evaluate different election methods and use weighted voting techniques to decide voting power within a group. Understand and use fair division techniques to solve apportionment problems.

MA.912.D.3.1: Use election theory techniques to analyze election data.

 Polling: City

MA.912.D.6: Develop an understanding of the fundamentals of propositional logic, arguments, and methods of proof.

MA.912.D.6.2: Find the converse, inverse, and contrapositive of a statement.

 Biconditional Statements
 Conditional Statements

MA.912.D.6.3: Determine whether two propositions are logically equivalent.

 Biconditional Statements
 Conditional Statements

MA.912.D.6.4: Use methods of direct and indirect proof and determine whether a short proof is logically valid.

 Biconditional Statements
 Conditional Statements

MA.912.D.6.6: Construct logical arguments using laws of detachment (modus ponens), syllogism, tautology, and contradiction; judge the validity of arguments, and give counterexamples to disprove statements.

 Biconditional Statements
 Conditional Statements

MA.912.D.6.7: Use applications of the universal and existential quantifiers to propositional statements.

 Biconditional Statements

MA.912.D.7: Operate with sets and use set theory to solve problems.

MA.912.D.7.1: Perform set operations such as union and intersection, complement, and cross product.

 Compound Inequalities

MA.912.D.8: Understand how matrices can be used to store and organize data and to solve systems of equations. They also use matrices to solve Markov chain problems that link present events to future events using probabilities.

MA.912.D.8.1: Use matrices to organize and store data. Perform matrix operations (addition, subtraction, scalar multiplication, multiplication).

 Translations

MA.912.D.8.2: Use matrix operations to solve problems.

 Translations

MA.912.D.8.5: Use determinants of 2 x 2 and 3 x 3 matrices as well as higher order matrices with and without the use of technology.

 Solving Linear Systems (Matrices and Special Solutions)

MA.912.D.9: Recognize vectors in both two- and three-dimensions. Recognize that vectors are represented geometrically and algebraically. Perform basic operations on vectors, including addition, scalar multiplication, dot product, and cross product. Solve problems using vectors.

MA.912.D.9.1: Demonstrate an understanding of the geometric interpretation of vectors and vector operations including addition, scalar multiplication, dot product and cross product in the plane and in three-dimensional space.

 Adding Vectors
 Vectors

MA.912.D.9.2: Demonstrate an understanding of the algebraic interpretation of vectors and vector operations including addition, scalar multiplication, dot product and cross product in the plane and in three-dimensional space.

 Adding Vectors
 Vectors

MA.912.D.11: Define and use arithmetic and geometric sequences and series.

MA.912.D.11.3: Find specified terms of arithmetic and geometric sequences.

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Geometric Sequences

MA.912.D.11.5: Explore and use other sequences found in nature such as the Fibonacci sequence and the golden ratio.

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Geometric Sequences

Correlation last revised: 4/4/2018

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.